DETAILED ACTION
This action is in response to communications filed 11/10/2025. Claims 1-5, 11-20 have been amended, claim 6 has been cancelled, no new claims have been added. Claims 1-5 and 7-20 are currently pending.
Notice of Pre-AIA or AIA Status
The present application, filed on or after March 16, 2013, is being examined under the first inventor to file provisions of the AIA .
Response to Amendment
Claims 1-5, 11-20 have been amended. The applicant provided citations to the specification indicating where support for the amendments is found.
The amended claims have been evaluated against the originally filed disclosure. The originally filed disclosure contains adequate support for the claimed amendments such that it is apparent to the examiner that the applicant had possession of the claimed invention at the time of filing. No new matter has been added by way of amendment.
Examiner note:
Applicant is reminded of the proper manner of making amendments in applications. The amended claims received 11/10/2025 contain additions that were not appropriately marked, as required. Three instances of changing previously claimed term “corresponding” to “correspondingly” were noted in the amended claims (See claims 3, 16, and 20) without appropriate underlining to indicate the changes. This appears to be an oversight by the applicant that does not significantly affect the interpretation of the claims. In future amendments, please note the correct manner of making amendments in applications, per MPEP 1.121, with excerpts provided below:
(c) Claims. Amendments to a claim must be made by rewriting the entire claim with all changes (e.g., additions and deletions) as indicated in this subsection, except when the claim is being canceled. Each amendment document that includes a change to an existing claim, cancellation of an existing claim or addition of a new claim, must include a complete listing of all claims ever presented, including the text of all pending and withdrawn claims, in the application. The claim listing, including the text of the claims, in the amendment document will serve to replace all prior versions of the claims, in the application. In the claim listing, the status of every claim must be indicated after its claim number by using one of the following identifiers in a parenthetical expression: (Original), (Currently amended), (Canceled), (Withdrawn), (Previously presented), (New), and (Not entered).
(2) When claim text with markings is required. All claims being currently amended in an amendment paper shall be presented in the claim listing, indicate a status of "currently amended," and be submitted with markings to indicate the changes that have been made relative to the immediate prior version of the claims. The text of any added subject matter must be shown by underlining the added text. The text of any deleted matter must be shown by strike-through except that double brackets placed before and after the deleted characters may be used to show deletion of five or fewer consecutive characters. The text of any deleted subject matter must be shown by being placed within double brackets if strike-through cannot be easily perceived. Only claims having the status of "currently amended," or "withdrawn" if also being amended, shall include markings. If a withdrawn claim is currently amended, its status in the claim listing may be identified as "withdrawn— currently amended."
Response to Arguments
Rejections under 35 U.S.C. § 112
Applicant has amended claims 2-3, 15-17, and 19-20 in response to the rejections under 35 U.S.C. § 112(b).
The amendments to claims sufficiently overcome the previously set forth rejections under 35 U.S.C. § 112(b). Accordingly, the rejections have been withdrawn.
Rejections under 35 U.S.C. § 101
Applicant argues that the claims are directed to a method that optimized material layout for the structure of a target object within a given design space under a given set of loads, boundary conditions; and constraints with the goal of maximizing the performance of the structure and associated computer system and non-transitory computer-readable storage medium. Applicant further argues that the method requires a sequence of steps that can only be performed by a high-performance computer in order to product any technically meaningful result which cannot be obtained by the human mind or using pen and paper as assistive physical aids.
Applicant’s arguments have been considered but are not persuasive. The claims do not set forth any limitation which would prohibit the actions contained within the claims from being performed by the human mind using physical assistive aids such as pen and paper. For example, with respect to the independent claims, a human being can partition a design space for the structure into a plurality of cells by drawing a discretized structure for analysis on a piece of a paper. A human being can further make a numeric approximation for the finite elements of the structure with consideration to the constraints- this would be an evaluation or judgment. A human being can further evaluate the cells with consideration to the approximated solution, wherein the analysis of the sensitivity may indicate an observable phenomenon which can be visualized using pen and paper as assistive physical aids such as pen and paper- that is a human being can impart rules on the analysis wherein certain solutions to the analysis would indicate to a human being the behavior (deformation) of the model. Lastly a model can be modified according to judgements acquired from the sensitivity analysis- that is, a human being can re-draw the model using pen and paper according to the judgements of the sensitivity analysis. There are no limitations recited by the claim which prohibit such steps being performed in the human mind or using assistive physical aids. Even so, per MPEP2106.04(a)(2)(III), the courts do not distinguish between mental processes that are performed entirely in the human mind and claims that recite mental processes performed on a computer.
Applicant further argues that even if the claims were directed to an abstract idea, the amended claims integrate such judicial exception into a practical application of topology optimization process for optimizing a structural design of a target object.
Applicant’s arguments have been considered but are not persuasive. In order for a judicial exception to be integrated into a practical applicant, the claims must recite additional elements that impose meaningful limits on the judicial exception such that the claims are more than a drafting effort designed to monopolize the judicial exception. The additional elements identified in the claims have been classified as Mere Instructions to Apply an Exception (MPEP 2106.05(f)), Insignificant Extra Solution Activity (MPEP 2106.05(g)), and Field of Use and Technological Environment (MPEP 2106.05(h)). These additional elements have been identified by the courts as additional elements which to not integrate the judicial exceptions into a practical application. The additional elements have been evaluated independently and within the claim as a whole, and no additional element has been found to meaningfully limit the judicial exceptions such that they would be integrated into a practical application. Furthermore, the applicant’s argument that the claims “recite[s] detailed operations of a topology optimization process for optimizing a structural design of a target object” is admissions that any purported improvement provided by the claims is the improvement to the mental process itself- that is to say that topology optimization and structural design optimization are processes that can be construed as mental processes.
Accordingly, for the reasons stated in this response, in conjunction with the updated rejections of this office action, the claims remain rejected under 35 U.S.C. § 101.
Rejections under 35 U.S.C. § 102
The independent claims have been amended in response to the rejections set forth under 35 U.S.C. § 102. The applicant argues that the “constraint for a maximal amount of material for constructing the target object” refers to a cap on the amount of material consumed for constructing the target object. The applicant notes that the previous claim mapping to vf as the predefined material volume fraction limit is referring to a maximum volume change of an object under deformation. The applicant further argues that the same amount of material may have different volumes depending on the layout of the structure and the volume of the same object made out of the same material may have different amount of deformations depending on the external load applied to the structure. The applicant alleges that the vf value in the reference Xiao is concerned with the deformation of the object and has nothing to do with the maximal amount of material used for constructing the target object as required by the claims.
Applicant’s arguments have been considered but the examiner respectfully submits that the arguments are not persuasive. Volume fraction is a term well-known in the art that refers to the volume of material with respect to the total volume of a given design space. Contrary to what the applicant states, the material volume fraction limit is exactly a limit of the material used for constructing the target object in a topology optimization process and rather has nothing to do with deformation of the object. Evidentiary support by the examiner’s understanding of the term within the art is given by the following excerpts of other patent document publications that explicitly define the volume fraction in terms of material quantity, as examples:
Couret et al. (US 20210182456 A1)
[0096] The free variables of the objective function may further include the distribution (i.e. layout) of quantity (e.g. volume fraction) of material over the 3D FEM. The optimization may in such cases vary the material quantity (e.g. volume fraction) in each finite element of the mesh to optimize the objective function.
[0114] A constraint function in the general orientation optimization workflow may include the global volume fraction of the structure. Such GVC defines the maximum material volume allowed to be used and therefore, the maximum mass of material constituting the designs.
Eom et al. (US 20220067240 A1)
[0060] The different types of constraints that can be used in topology optimization include: volume fraction constraint (sets a limit on the amount of material that can be removed from the model; as the volume fraction is reached, the optimizer would rearrange the material in the model so that the objective can be reached); stress constraint (limits the amount of stress the model can undergo; the optimizer would add/remove/rearrange the material in the model in order to satisfy this constraint); thickness constraint (limits the thickness of the members/sections in the model; the sections in the model are not allowed to go below the specified thickness); displacement constraint (limits the maximum amount of deformation the model can undergo); and manufacturing constraints (specific to manufacturing methods that are used in the fabrication of the parts/models, such as 3D printing, milling and die-casting).
Won (KR 20140064216 A)
[0045] And the constraint of the topology optimization is the volume fraction, which is the desired volume fraction to leave in the design domain. For example, if you want to perform a topology optimization within a design area that leaves only 50% of the initial volume, the target volume fraction can be defined as 0.5. That is, to minimize the compliance within the range of leaving the desired amount of material in the design area, that is, to derive the design phase that maximizes the rigidity.
Dupont De Dinechin (US 20210004719 A1)
[0235] A constraint function in the general topology optimization workflow may be the global volume fraction of the structure. Such GVC defines the maximum material volume allowed to be used and therefore, the maximum mass of material constituting the designs. Consequently, the optimizer has to find the optimal distribution of this mass in the design space, maximizing the stiffness.
Accordingly, the reference Xiao does in fact teach the challenged limitation.
The remaining limitations that have been added via amendment to the independent claims do not rely on Xiao’s disclosure. In particular, the applicant challenges that Xiao does not disclose that the sensitivity analysis indicates that a first subset of the plurality of cells deform more than other of the plurality of cells. This argument is moot, considering that the reference Stavropoulou is relied on in combination with Xiao to disclose the limitation.
Because the amendments required further search and consideration, which yielded the incorporation of multiple references to disclose the claimed limitations, the rejections under 35 U.S.C. § 102 have been withdrawn. However, a new grounds of rejection has been set forth under 35 U.S.C. § 103. For the reasons stated in this response, in conjunction with the updated rejection of this action, the claims remain rejected over the prior art.
Rejections under 35 U.S.C. § 103
The applicant argues that claims 2-4, 7-10, 12-13, 15-17 and 19-20 are dependent from claims 1, 14 and 18, respectively and should be patentable over the prior art of record.
Applicant’s arguments have been considered but are not persuasive, for the reasons stated above in the response to the rejections under 35 U.S.C. § 102.
Claim Rejections - 35 USC § 101
35 U.S.C. 101 reads as follows:
Whoever invents or discovers any new and useful process, machine, manufacture, or composition of matter, or any new and useful improvement thereof, may obtain a patent therefor, subject to the conditions and requirements of this title.
Claims 1-5 and 7-20 are rejected under 35 U.S.C. 101 because the claimed invention is directed to an abstract idea without significantly more. The following section follows the 2019 Patent Eligibility Guidance (PEG) for analyzing subject matter eligibility:
Step 1 - Statutory Category:
Step 1 of the PEG analysis entails considering whether the claimed subject matter falls within the four statutory categories of patentable subject matter identified by 35 U.S.C. 101 (process, machine, manufacture, or composition of matter).
Step 2A Prong 1 - Judicial exception:
In Step 2A Prong 1, examiners evaluate whether the claim recites a judicial exception (an abstract idea, law of nature, or a natural phenomenon).
Step 2a Prong 2 - Integration into a practical application:
If claims recite a judicial exception, the claim requires further analysis in Step 2A Prong 2. In Step 2A Prong 2, examiners evaluate whether the claim as a whole integrates the exception into a practical application.
Step 2B - Significantly More:
If the additional elements identified in Step 2A Prong 2 do not integrate the exception into a practical application, then the claim is directed to the recited judicial exception and requires further analysis under Step 2B- Significantly More.
As noted in the MPEP 2106.05(II): The identification of the additional element(s) in the claim from Step 2A Prong 2, as well as the conclusions from Step 2A Prong 2 on the considerations discussed in MPEP 2106.05(a) -(c), (e), (f), and (h) are to be carried over. Claim limitations identified as Insignificant Extra-Solution Activities are further evaluated to determine if the elements are beyond what is well -understood, routine, and conventional (WURC) activity, as dictated by MPEP 2106.05(II).
Independent Claims:
Claim 1:
Step 1: Claim 1 and its dependent claims 2-5 and 7-13 are directed to a method which falls within one of the four statutory categories of a process.
Step 2A Prong 1: Claim 1 recites a judicial exception, noted in bold:
partitioning a design space for the structure into a plurality of cells; and The claim limitation can be reasonably read to entail discretizing a design space into a plurality of cells. This task can be performed within the human mind or using a pen and paper as an assistive physical aid. For example, a piece of paper can be a design space for a structure and a human could mentally evaluate how to discretize the space and subsequently draw cells to represent the discretization. Therefore, this claim includes the recitation of the judicial exception of abstract ideas of a mental process.
obtaining a first approximate finite element analysis (FEA) solution for the plurality of cells based on the set of constraints; The claim limitation can be reasonably read to entail observing the constraints and evaluating a finite element analysis solution with regard for the constraints. This task can be performed within the human mind or using a pen and paper as an assistive physical aid. Therefore, this claim includes the recitation of the judicial exception of abstract ideas of a mental process. Furthermore, FEA entails solving numeric equations to derive the solution and therefore this limitation also includes the recitation of the abstract idea of mathematical concepts as mathematical calculations.
performing a sensitivity analysis on the plurality of cells based on the approximate FEA solution, wherein the sensitivity analysis indicates that a first subset of a plurality of cells deform more than others of the plurality of cells; and The claim limitation can be reasonably read to entail performing a sensitivity analysis (which is understood to be numerically analyzing and quantifying how inputs to a physical model affect outputs of the model) using the approximate FEA solution. This task can be performed within the human mind or using a pen and paper as an assistive physical aid. For example, a human being can analyze the approximate FEA solution and further analyze the sensitivity on the plurality of cells to draw conclusions on the sensitivity of the model. Furthermore, sensitivity analysis entails performing mathematical calculations to derive numeric outcomes that quantify the model and therefore this limitation also includes the recitation of the abstract idea of mathematical concepts.
updating the structural model for the structure of the target object based on the sensitivity analysis of the plurality of cells. The claim limitation can be reasonably read to entail evaluating the sensitivity analysis of the plurality of cells to make a judgement on how to update the structural model in response to the evaluation. This task can be performed within the human mind or using a pen and paper as an assistive physical aid. Therefore, this claim includes the recitation of the judicial exception of abstract ideas of a mental process.
Therefore, the claim recites a judicial exception.
Step 2A Prong 2: Additional elements were identified and are noted in italics.
obtaining a set of constraints for a structure of a target object,- This limitation has been identified as Insignificant Extra Solution Activity (MPEP 2106.05(g)) of mere data gathering because the limitation amounts to merely collecting data for use in the mental process/mathematical calculations.
the set of constraints including an external force constraint, a constraint for a maximal amount of material for constructing the target object and one or more constraints for fixed point locations of the structure that are fixed to other objects and cannot move under the external force constraint; This limitation has been identified as Field of Use and Technological Environment (MPEP 2106.05(h)) for generally linking the use of the judicial exception to a particular technological environment or field of use
wherein the plurality of cells define a structural model of the structure of the target object; and - This limitation has been identified as Field of Use and Technological Environment (MPEP 2106.05(h)) for generally linking the use of the judicial exception to a particular technological environment or field of use
in accordance with the external force constraint being applied to the structure:- This limitation has been identified as Field of Use and Technological Environment (MPEP 2106.05(h)) because the limitation amounts to limiting the use of the judicial exception to a particular technological environment.
The courts have found that adding insignificant extra- solution activity to the judicial exception (Insignificant Extra Solution Activity (MPEP 2106.05(g))); and generally linking the use of a judicial exception to a particular technological environment or field of use (Field of Use and Technological Environment (MPEP 2106.05(h))) does not integrate the judicial exception into a practical application.
When viewed independently and within the claim as a whole, the additional elements do not appear to integrate the judicial exception into a practical application.
Step 2B: As discussed in Step 2A Prong 2, additional elements were identified as Insignificant Extra Solution Activity (MPEP 2106.05(g)) which must be further evaluated to determine if they are beyond WURC activities. Additional elements identified otherwise and conclusions from Step 2A Prong 2 are carried over for evaluating if the claim, as a whole, amounts to an inventive concept that is significantly more than the judicial exception:
obtaining a set of constraints for a structure of a target object,– This limitation has been identified as the insignificant extra solution activity of mere data gathering, as stated previously. Under broadest reasonable interpretation and when read in light of the specification ([0042]), the claim limitation includes receiving or transmitting data over a network, which has been recognized by the courts as a computer function that is well-understood, routine, and conventional activity when claimed in a merely generic manner or as insignificant extra-solution activity. (See MPEP 2106.05(d)(II)(i)).
The courts have found that simply appending insignificant extra solution activities that are well-understood, routine, and conventional activities to the judicial exception does not qualify the limitations as “significantly more” than the recited judicial exception. The remaining additional element was identified as Field of Use and Technological Environment (MPEP 2106.05(h)), as stated previously. The courts have found that merely using a computer as a tool to perform a mental process (as in the preamble) and generally linking the use of a judicial exception to a particular technological environment does not qualify the limitations as “significantly more” than the recited judicial exception.
With the additional elements viewed independently and as part of the ordered combination, the claim as a whole does not appear to amount to significantly more than the recited judicial exception because the claim is using generic computing components recited at a high level of generality and functioning in their normal capacity in conjunction with well-understood, routine, and conventional activity to enable the performance of a task that can practically be performed within the human mind or using pen and paper as an assistive physical aid. Therefore, the claim does not include additional elements, alone or in combination that are sufficient to amount to significantly more than the recited judicial exception.
Conclusion: Based on this rationale, the claim has been deemed to be ineligible subject matter under 35 U.S.C. 101.
Claim 14:
Step 1: Claim 14 and its dependent claims 15-17 are directed to a system which falls within one of the four statutory categories of a machine.
Step 2A Prong 1: Claim 14 recites a judicial exception, noted in bold:
partitioning a design space for the structure into a plurality of cells, The claim limitation can be reasonably read to entail discretizing a design space into a plurality of cells. This task can be performed within the human mind or using a pen and paper as an assistive physical aid. For example, a piece of paper can be a design space for a structure and a human could mentally evaluate how to discretize the space and subsequently draw cells to represent the discretization. Therefore, this claim includes the recitation of the judicial exception of abstract ideas of a mental process.
obtaining a first approximate finite element analysis (FEA) solution for the plurality of cells based on the set of constraints; The claim limitation can be reasonably read to entail observing the constraints and evaluating a finite element analysis solution with regard for the constraints. This task can be performed within the human mind or using a pen and paper as an assistive physical aid. Therefore, this claim includes the recitation of the judicial exception of abstract ideas of a mental process. Furthermore, FEA entails solving numeric equations to derive the solution and therefore this limitation also includes the recitation of the abstract idea of mathematical concepts as mathematical calculations.
performing a sensitivity analysis on the plurality of cells based on the approximate FEA solution, wherein the sensitivity analysis indicates that a first subset of the plurality of cells deform more than others of the plurality of cells; and The claim limitation can be reasonably read to entail performing a sensitivity analysis (which is understood to be numerically analyzing and quantifying how inputs to a physical model affect outputs of the model) using the approximate FEA solution. This task can be performed within the human mind or using a pen and paper as an assistive physical aid. For example, a human being can analyze the approximate FEA solution and further analyze the sensitivity on the plurality of cells to draw conclusions on the sensitivity of the model. Furthermore, sensitivity analysis entails performing mathematical calculations to derive numeric outcomes that quantify the model and therefore this limitation also includes the recitation of the abstract idea of mathematical concepts.
updating the structural model for the structure of the target object based on the sensitivity analysis of the plurality of cells. The claim limitation can be reasonably read to entail evaluating the sensitivity analysis of the plurality of cells to make a judgement on how to update the structural model in response to the evaluation. This task can be performed within the human mind or using a pen and paper as an assistive physical aid. Therefore, this claim includes the recitation of the judicial exception of abstract ideas of a mental process.
Therefore, the claim recites a judicial exception.
Step 2A Prong 2: Additional elements were identified and are noted in italics.
one or more processors; memory; and one or more programs stored in the memory and configured for execution by the one or more processors, the one or more programs comprising instructions for:- These limitations have been identified as Mere Instructions to Apply an Exception (MPEP 2106.05(f)) because the limitations amount to mere instructions to implement the abstract idea or other exception on a computer. The claim invokes computers merely as a tool to perform an existing process.
obtaining a set of constraints for a structure of a target object;- This limitation has been identified as Insignificant Extra Solution Activity (MPEP 2106.05(g)) of mere data gathering because the limitation amounts to merely collecting data for use in the mental process/mathematical calculations.
the set of constraints including an external force constraint, a constraint for a maximal amount of material for constructing the target object and one or more constraints for fixed point locations of the structure that are fixed to other objects and cannot move under the external force constraint; - This limitation has been identified as Field of Use and Technological Environment (MPEP 2106.05(h)) for generally linking the judicial exception to a particular technological environment or field of use.
Wherein the plurality of cells define a structural model of the structure of the target object; and - This limitation has been identified as Field of Use and Technological Environment (MPEP 2106.05(h)) for generally linking the judicial exception to a particular technological environment or field of use.
in accordance with the external force constraint being applied to the structure:- This limitation has been identified as Field of Use and Technological Environment (MPEP 2106.05(h)) because the limitation amounts to limiting the use of the judicial exception to a particular technological environment.
The courts have found that merely including instructions to implement an abstract idea on a computer or merely using a computer as a tool to perform an abstract idea (Mere Instructions to Apply an Exception (MPEP 2106.05(f))); adding insignificant extra- solution activity to the judicial exception (Insignificant Extra Solution Activity (MPEP 2106.05(g))); and generally linking the use of a judicial exception to a particular technological environment or field of use (Field of Use and Technological Environment (MPEP 2106.05(h))) does not integrate the judicial exception into a practical application.
When viewed independently and within the claim as a whole, the additional element does not appear to integrate the judicial exception into a practical application.
Step 2B: As discussed in Step 2A Prong 2, additional elements were identified as Insignificant Extra Solution Activity (MPEP 2106.05(g)) which must be further evaluated to determine if they are beyond WURC activities. Additional elements identified otherwise and conclusions from Step 2A Prong 2 are carried over for evaluating if the claim, as a whole, amounts to an inventive concept that is significantly more than the judicial exception:
obtaining a set of constraints for a structure of a target object;– This limitation has been identified as the insignificant extra solution activity of mere data gathering, as stated previously. Under broadest reasonable interpretation and when read in light of the specification ([0042]), the claim limitation includes receiving or transmitting data over a network, which has been recognized by the courts as a computer function that is well-understood, routine, and conventional activity when claimed in a merely generic manner or as insignificant extra-solution activity. (See MPEP 2106.05(d)(II)(i)).
The courts have found that simply appending insignificant extra solution activities that are well-understood, routine, and conventional activities to the judicial exception does not qualify the limitations as “significantly more” than the recited judicial exception. The remaining additional elements were identified as Field of Use and Technological Environment (MPEP 2106.05(h)) and Mere Instructions to Apply an Exception (MPEP 2106.05(f)) , as stated previously. The courts have found that merely using a computer as a tool to perform a mental process and generally linking the use of a judicial exception to a particular technological environment does not qualify the limitations as “significantly more” than the recited judicial exception.
With the additional elements viewed independently and as part of the ordered combination, the claim as a whole does not appear to amount to significantly more than the recited judicial exception because the claim is using generic computing components recited at a high level of generality and functioning in their normal capacity in conjunction with well-understood, routine, and conventional activity to enable the performance of a task that can practically be performed within the human mind or using pen and paper as an assistive physical aid. Therefore, the claim does not include additional elements, alone or in combination that are sufficient to amount to significantly more than the recited judicial exception.
Conclusion: Based on this rationale, the claim has been deemed to be ineligible subject matter under 35 U.S.C. 101.
Claim 18:
Step 1: Claim 18 and its dependent claims 19-20 are directed to a non-transitory computer-readable storage medium which falls within one of the four statutory categories of a manufacture.
Step 2A Prong 1: Claim 18 recites a judicial exception, noted in bold:
partitioning a design space for the structure into a plurality of cells, The claim limitation can be reasonably read to entail discretizing a design space into a plurality of cells. This task can be performed within the human mind or using a pen and paper as an assistive physical aid. For example, a piece of paper can be a design space for a structure and a human could mentally evaluate how to discretize the space and subsequently draw cells to represent the discretization. Therefore, this claim includes the recitation of the judicial exception of abstract ideas of a mental process.
obtaining an approximate finite element analysis (FEA) solution for the plurality of cells based on the set of constraints; The claim limitation can be reasonably read to entail observing the constraints and evaluating a finite element analysis solution with regard for the constraints. This task can be performed within the human mind or using a pen and paper as an assistive physical aid. Therefore, this claim includes the recitation of the judicial exception of abstract ideas of a mental process. Furthermore, FEA entails solving numeric equations to derive the solution and therefore this limitation also includes the recitation of the abstract idea of mathematical concepts as mathematical calculations.
performing a sensitivity analysis on the plurality of cells based on the approximate FEA solution, wherein the sensitivity analysis indicates that a first subset of the plurality of cells deform more than others of the plurality of cells; and The claim limitation can be reasonably read to entail performing a sensitivity analysis (which is understood to be numerically analyzing and quantifying how inputs to a physical model affect outputs of the model) using the approximate FEA solution. This task can be performed within the human mind or using a pen and paper as an assistive physical aid. For example, a human being can analyze the approximate FEA solution and further analyze the sensitivity on the plurality of cells to draw conclusions on the sensitivity of the model. Furthermore, sensitivity analysis entails performing mathematical calculations to derive numeric outcomes that quantify the model and therefore this limitation also includes the recitation of the abstract idea of mathematical concepts.
updating the structural model for the structure of the target object based on the sensitivity analysis of the plurality of cells. The claim limitation can be reasonably read to entail evaluating the sensitivity analysis of the plurality of cells to make a judgement on how to update the structural model in response to the evaluation. This task can be performed within the human mind or using a pen and paper as an assistive physical aid. Therefore, this claim includes the recitation of the judicial exception of abstract ideas of a mental process.
Therefore, the claim recites a judicial exception.
Step 2A Prong 2: Additional elements were identified and are noted in italics.
obtaining a set of constraints for a structure of a target object;- This limitation has been identified as Insignificant Extra Solution Activity (MPEP 2106.05(g)) of mere data gathering because the limitation amounts to merely collecting data for use in the mental process/mathematical calculations.
the set of constraints including an external force constraint, a constraint for a maximal amount of material for constructing the target object and one or more constraints for fixed point locations of the structure that are fixed to other objects and cannot move under the external force constraint; - This limitation has been identified as Field of Use and Technological Environment (MPEP 2106.05(h)) because the limitation amounts to limiting the use of the judicial exception to a particular technological environment.
wherein the plurality of cells define a structural model of the structure of the target object; and - This limitation has been identified as Field of Use and Technological Environment (MPEP 2106.05(h)) because the limitation amounts to limiting the use of the judicial exception to a particular technological environment.
in accordance with the external force constraint being applied to the structure:- This limitation has been identified as Field of Use and Technological Environment (MPEP 2106.05(h)) because the limitation amounts to limiting the use of the judicial exception to a particular technological environment.
The courts have found that adding insignificant extra- solution activity to the judicial exception (Insignificant Extra Solution Activity (MPEP 2106.05(g))); and generally linking the use of a judicial exception to a particular technological environment or field of use (Field of Use and Technological Environment (MPEP 2106.05(h))) does not integrate the judicial exception into a practical application.
When viewed independently and within the claim as a whole, the additional elements do not appear to integrate the judicial exception into a practical application.
Step 2B: As discussed in Step 2A Prong 2, additional elements were identified as Insignificant Extra Solution Activity (MPEP 2106.05(g)) which must be further evaluated to determine if they are beyond WURC activities. Additional elements identified otherwise and conclusions from Step 2A Prong 2 are carried over for evaluating if the claim, as a whole, amounts to an inventive concept that is significantly more than the judicial exception:
obtaining a set of constraints for a structure of a target object;– This limitation has been identified as the insignificant extra solution activity of mere data gathering, as stated previously. Under broadest reasonable interpretation and when read in light of the specification ([0042]), the claim limitation includes receiving or transmitting data over a network, which has been recognized by the courts as a computer function that is well-understood, routine, and conventional activity when claimed in a merely generic manner or as insignificant extra-solution activity. (See MPEP 2106.05(d)(II)(i)).
The courts have found that simply appending insignificant extra solution activities that are well-understood, routine, and conventional activities to the judicial exception does not qualify the limitations as “significantly more” than the recited judicial exception. The remaining additional element was identified as Field of Use and Technological Environment (MPEP 2106.05(h)), as stated previously. The courts have found that merely using a computer as a tool to perform a mental process and generally linking the use of a judicial exception to a particular technological environment does not qualify the limitations as “significantly more” than the recited judicial exception.
With the additional elements viewed independently and as part of the ordered combination, the claim as a whole does not appear to amount to significantly more than the recited judicial exception because the claim is using generic computing components recited at a high level of generality and functioning in their normal capacity in conjunction with well-understood, routine, and conventional activity to enable the performance of a task that can practically be performed within the human mind or using pen and paper as an assistive physical aid. Therefore, the claim does not include additional elements, alone or in combination that are sufficient to amount to significantly more than the recited judicial exception.
Conclusion: Based on this rationale, the claim has been deemed to be ineligible subject matter under 35 U.S.C. 101.
Dependent Claims:
Examiner notes limitations identified as judicial exceptions are indicated in italicized bold and limitations identified as additional elements are indicated using italics.
Claim 2
Step 1: Regarding dependent claim 2, the judicial exception of independent claim 1 is further incorporated. The claim falls within the corresponding statutory category as stated previously.
Step 2A Prong 1: Claim 2 additionally recites the limitation generating a second approximate FEA solution based on the updated structural model, which can reasonably be read to entail using the updated structural model to inform the evaluation of FEA approximation. This task can be performed within the human mind or using a pen and paper as an assistive physical aid. Therefore, this claim includes the recitation of the judicial exception of abstract ideas of a mental process. Furthermore, this claim includes the recitation of mathematical calculations for approximating an FEA solution and additionally includes the recitation of abstract ideas of mathematical concepts. Claim 2 further recites performing a second sensitivity analysis based on the second approximate FEA solution; which can reasonably be read to entail performing a sensitivity analysis (which is understood to be numerically analyzing and quantifying how inputs to a physical model affect outputs of the model) using the approximate FEA solution. This task can be performed within the human mind or using a pen and paper as an assistive physical aid. For example, a human being can analyze the approximate FEA solution and further analyze the sensitivity on the plurality of cells to draw conclusions on the sensitivity of the model. Furthermore, sensitivity analysis entails performing mathematical calculations to derive numeric outcomes that quantify the model and therefore this limitation also includes the recitation of the abstract idea of mathematical concepts. Lastly, claim 2 recites updating the structural model again based on the second sensitivity analysis; and which can be reasonably read to entail evaluating the sensitivity analysis of the plurality of cells to make a judgement on how to update the structural model in response to the evaluation. This task can be performed within the human mind or using a pen and paper as an assistive physical aid. Therefore, this claim includes the recitation of the judicial exception of abstract ideas of a mental process.
Step 2a Prong 2: Claim 2 additionally recites the limitation after updating the structural model again, displaying the structural model to a user. This limitation has been identified as insignificant extra solution activity of mere data outputting. The courts have ruled appending insignificant extra solution activity to a recited judicial exception does not integrate the judicial exception into a practical application. With the additional element viewed in conjunction with the other limitations, the claim as a whole does not appear to integrate the judicial exception into a practical application.
Step 2B: Because limitations were identified in Step 2a Prong 2 as insignificant extra solution activity, the limitation must be evaluated to determine if the element is beyond well-understood, routine, and conventional activity. The limitation after updating the structural model again, displaying the structural model to a user amounts to outputting data representative of a structural model to a screen. This activity is well-understood, routine, and conventional activity within the art, and this assertion is supported by evidence. Autodesk (Autodesk, “About Structural Display”, Accessed August 2025, Autodesk AutoCAD Plant 3D 2022 Documentation, https://help.autodesk.com/view/PLNT3D/2022/ENU/?guid=GUID-BEF08988-FB2F-4495-8E06-899981E20D65), a commercially available software for modeling structures, comes equipped with displaying structural data to a user as a standard functionality. This is demonstrated in the user documentation, depicting different ways a structure can be displayed to a user.
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Because this functionality comes standard to a widely-used product within the art, displaying structural models to a user in a generic and non-specific way is understood to be well-understood, routine and conventional activity. The courts have found that adding well understood, routine, and conventional activity previously known to the industry and specified at a high level of generality to a judicial exception are not enough to qualify the claim as significantly more than the abstract idea. Therefore, the claim does not include additional elements, alone or in the ordered combination that are sufficient to amount to significantly more than the recited judicial exception.
This claim is not eligible subject matter under 35 U.S.C. 101.
Claim 3
Step 1: Regarding dependent claim 3, the judicial exception of independent claim 1 and dependent claim 2 is further incorporated. The claim falls within the corresponding statutory category as stated previously.
Step 2A Prong 1: Claim 3 additionally recites the limitation further comprising repeating the generating the second approximate FEA solutions and correspondingly the second sensitivity analyses iteratively until a convergent structural model is obtained., which can reasonably be read to entail performing mathematical calculations to approximate FEA solutions and evaluating the solutions to determine if convergence has occurred. This task can be performed within the human mind or using a pen and paper as an assistive physical aid. Therefore, this claim includes the recitation of the judicial exception of abstract ideas of a mental process. Furthermore, because the limitation recites performing FEA approximations and sensitivity analyses and these are understood to be mathematical calculations, the claim further recites the judicial exception of mathematical concepts.
Step 2a Prong 2 & Step 2B: Claim 3 does not recite any additional elements that would integrate the judicial exception(s) into a practical application, nor amount to significantly more.
This claim is not eligible subject matter under 35 U.S.C. 101.
Claim 4
Step 1: Regarding dependent claim 4, the judicial exception of independent claim 1 is further incorporated. The claim falls within the corresponding statutory category as stated previously.
Step 2A Prong 1: Claim 4 does not recite any additional judicial exceptions.
Step 2a Prong 2: Claim 4 additionally recites the limitation wherein the first approximate FEA solution describes an object deformation for the structure in accordance with the external force constraint. This limitation has been identified as Field of Use and Technological Environment (MPEP 2106.05(h)) because the limitation particularly describes the technological environment in which the judicial exceptions are executed. The courts have ruled generally linking the use of a judicial exception to a particular field of use or technological environment does not integrate the judicial exception into a practical application. With the additional element viewed in conjunction with the other limitations, the claim as a whole does not appear to integrate the judicial exception into a practical application.
Step 2B: The courts have found that limitations that amount to generally linking the use of the judicial exception to a particular field of use or technological environment are not enough to qualify the claim as significantly more than the abstract idea. Therefore, the claim does not include additional elements, alone or in the ordered combination that are sufficient to amount to significantly more than the recited judicial exception.
This claim is not eligible subject matter under 35 U.S.C. 101.
Claim 5
Step 1: Regarding dependent claim 5, the judicial exception of independent claim 1 is further incorporated. The claim falls within the corresponding statutory category as stated previously.
Step 2A Prong 1: Claim 5 additionally recites the limitation wherein the first approximate FEA solution comprises a partial solution to a set of linear equations representing the structure, which can reasonably be read to include using linear equations to derive a partial FEA approximation solution. Therefore, this claim includes the recitation of the judicial exception of abstract ideas as a mathematical concept.
Step 2a Prong 2 & Step 2B: Claim 5 does not recite any additional elements that would integrate the judicial exception(s) into a practical application, nor amount to significantly more.
This claim is not eligible subject matter under 35 U.S.C. 101.
Claim 7
Step 1: Regarding dependent claim 7, the judicial exception of independent claim 1 is further incorporated. The claim falls within the corresponding statutory category as stated previously.
Step 2A Prong 1: Claim 7 additionally recites the limitation obtaining an update direction from the sensitivity analysis; which can reasonably be read to entail evaluating the sensitivity analysis to make a judgement as to an appropriate update direction. This task can be performed within the human mind or using a pen and paper as an assistive physical aid. Therefore, this claim includes the recitation of the judicial exception of abstract ideas of a mental process. Claim 7 additionally recites the limitation computing a decreasing step size for the update direction; and which can be reasonably read to entail evaluating the current step size to subsequently computer a step size that is decreased with regard to the current step size. This task can be performed within the human mind or using a pen and paper as an assistive physical aid. Therefore, this claim includes the recitation of the judicial exception of abstract ideas of a mental process. Furthermore, the computation of a decreased step size includes the recitation of mathematical concepts of mathematical calculations and relationships and therefore this limitation also falls within the mathematical concepts grouping of abstract ideas. Lastly, Claim 7 recites the limitation wherein the structural model for the structure is updated based on the update direction and the step size which can be reasonably read to entail evaluating the update direction and the step size to inform a judgment on how to update the structural model. This task can be performed within the human mind or using a pen and paper as an assistive physical aid. Therefore, this claim includes the recitation of the judicial exception of abstract ideas of a mental process.
Step 2a Prong 2 & Step 2B: Claim 7 does not recite any additional elements that would integrate the judicial exception(s) into a practical application, nor amount to significantly more.
This claim is not eligible subject matter under 35 U.S.C. 101.
Claim 8
Step 1: Regarding dependent claim 8, the judicial exception of independent claim 1 and dependent claim 7 is further incorporated. The claim falls within the corresponding statutory category as stated previously.
Step 2A Prong 1: Claim 8 additionally recites the limitation the method further comprises generating a refined model update from the preliminary model in accordance with one or more material requirement constraints for the structure, which can reasonably be read to entail observing the material requirement constraints and using the observations to inform an evaluation of how the model should be updated. This task can be performed within the human mind or using a pen and paper as an assistive physical aid. Therefore, this claim includes the recitation of the judicial exception of abstract ideas of a mental process.
Step 2a Prong 2: Claim 8 additionally recites the limitation wherein the structural model updated based on the update direction and the step size is a preliminary model; and. This limitation has been identified as Field of Use and Technological Environment (MPEP 2106.05(h)) because the limitation merely describes the technological environment that the judicial exception is used in to reflect the nature of the model and how it is referred to. The courts have ruled generally linking the use of a judicial exception to a particular technological environment does not integrate the judicial exception into a practical application. With the additional element viewed in conjunction with the other limitations, the claim as a whole does not appear to integrate the judicial exception into a practical application.
Step 2B: The courts have found that limitations that amount to generally linking the use of the judicial exception to a particular technological environment or field of use are not enough to qualify the claim as significantly more than the abstract idea. Therefore, the claim does not include additional elements, alone or in the ordered combination that are sufficient to amount to significantly more than the recited judicial exception.
This claim is not eligible subject matter under 35 U.S.C. 101.
Claim 9
Step 1: Regarding dependent claim 9, the judicial exception of independent claim 1 and dependent claims 7 and 8 is further incorporated. The claim falls within the corresponding statutory category as stated previously.
Step 2A Prong 1: Claim 9 additionally recites the limitation wherein generating the refined model update comprises, for a point in the preliminary model determined to be outside of the one or more material requirement constraints for the structure, selecting a replacement point having a minimum Euclidean distance from the point., which can reasonably be read to entail observing the placement of a point with regard for the material requirement constraints and subsequently making a judgement as to the placement of a replacement point with respect to a minimum Euclidean distance. This task can be performed within the human mind or using a pen and paper as an assistive physical aid. Therefore, this claim includes the recitation of the judicial exception of abstract ideas of a mental process.
Step 2a Prong 2 & Step 2B: Claim 9 does not recite any additional elements that would integrate the judicial exception(s) into a practical application, nor amount to significantly more.
This claim is not eligible subject matter under 35 U.S.C. 101.
Claim 10
Step 1: Regarding dependent claim 10, the judicial exception of independent claim 1 and dependent claims 7 and 8 is further incorporated. The claim falls within the corresponding statutory category as stated previously.
Step 2A Prong 1: Claim 10 additionally recites the limitation generating the refined model update comprises solving a piecewise linear equation to clamp points of the preliminary model update in accordance with the one or more material requirement constraints for the structure which can reasonably be read to entail solving piecewise linear equations to account for material requirement constraints. This task can be performed within the human mind or using a pen and paper as an assistive physical aid. Therefore, this claim includes the recitation of the judicial exception of abstract ideas of a mental process. Furthermore, solving linear equations is the explicit recitation of mathematical calculations and therefore the claim additionally recites the judicial exception of abstract ideas of mathematical concepts.
Step 2a Prong 2 & Step 2B: Claim 10 does not recite any additional elements that would integrate the judicial exception(s) into a practical application, nor amount to significantly more.
This claim is not eligible subject matter under 35 U.S.C. 101.
Claim 11
Step 1: Regarding dependent claim 11, the judicial exception of independent claim 1 is further incorporated. The claim falls within the corresponding statutory category as stated previously.
Step 2A Prong 1: Claim 11 additionally recites the limitation wherein obtaining the first approximate FEA solution comprises applying a pre-conditioning matrix to a set of linear equations representing the structure. which can reasonably be read to entail applying a preconditioning matrix to a set of linear equations. This task can be performed within the human mind or using a pen and paper as an assistive physical aid. Therefore, this claim includes the recitation of the judicial exception of abstract ideas of a mental process. This claim also include the recitation of mathematical calculations and therefore the claim additionally falls under the mathematical concepts grouping of abstract ideas.
Step 2a Prong 2 & Step 2B: Claim 11 does not recite any additional elements that would integrate the judicial exception(s) into a practical application, nor amount to significantly more.
This claim is not eligible subject matter under 35 U.S.C. 101.
Claim 12
Step 1: Regarding dependent claim 12, the judicial exception of independent claim 1 is further incorporated. The claim falls within the corresponding statutory category as stated previously.
Step 2A Prong 1: Claim 12 additionally recites the limitation wherein obtaining the first approximate FEA solution comprises performing one or more iterations of the Jacobi method which can reasonably be read to entail performing the Jacobi method, which is understood to be an iterative technique for solving systems of linear equations. This task can be performed within the human mind or using a pen and paper as an assistive physical aid. Therefore, this claim includes the recitation of the judicial exception of abstract ideas of a mental process. Furthermore, the Jacobi method entails mathematical calculations and therefore the claim additionally falls within to the abstract idea grouping of mathematical concepts.
Step 2a Prong 2 & Step 2B: Claim 12 does not recite any additional elements that would integrate the judicial exception(s) into a practical application, nor amount to significantly more.
This claim is not eligible subject matter under 35 U.S.C. 101.
Claim 13
Step 1: Regarding dependent claim 13, the judicial exception of independent claim 1 is further incorporated. The claim falls within the corresponding statutory category as stated previously.
Step 2A Prong 1: Claim 13 additionally recites the judicial exception obtaining the first approximate FEA solution requires a solution of a set of linear equations having a linear computation complexity This claim limitation describes the mathematical calculation of solving a set of linear equations. Therefore, this claim limitation includes the recitation of the judicial exception of abstract ideas as a mathematical concept.
Step 2a Prong 2 & Step 2B: Claim 13 does not recite any additional judicial exceptions that would integrate the judicial exceptions into a practical application nor amount to significantly more than the recited judicial exceptions.
This claim is not eligible subject matter under 35 U.S.C. 101.
Claim 15
Step 1: Regarding dependent claim 15, the judicial exception of independent claim 14 is further incorporated. The claim falls within the corresponding statutory category as stated previously.
Step 2A Prong 1: Claim 15 additionally recites the limitation generating a second approximate FEA solution based on the updated structural model, which can reasonably be read to entail using the updated structural model to inform the evaluation of FEA approximation. This task can be performed within the human mind or using a pen and paper as an assistive physical aid. Therefore, this claim includes the recitation of the judicial exception of abstract ideas of a mental process. Furthermore, this claim includes the recitation of mathematical calculations for approximating an FEA solution and additionally includes the recitation of abstract ideas of mathematical concepts. Claim 15 further recites performing a second sensitivity analysis based on the second approximate FEA solution; which can reasonably be read to entail performing a sensitivity analysis (which is understood to be numerically analyzing and quantifying how inputs to a physical model affect outputs of the model) using the approximate FEA solution. This task can be performed within the human mind or using a pen and paper as an assistive physical aid. For example, a human being can analyze the approximate FEA solution and further analyze the sensitivity on the plurality of cells to draw conclusions on the sensitivity of the model. Furthermore, sensitivity analysis entails performing mathematical calculations to derive numeric outcomes that quantify the model and therefore this limitation also includes the recitation of the abstract idea of mathematical concepts. Lastly, claim 15 recites the limitation updating the structural model again based on the second sensitivity analysis; and which can be reasonably read to entail evaluating the sensitivity analysis of the plurality of cells to make a judgement on how to update the structural model in response to the evaluation. This task can be performed within the human mind or using a pen and paper as an assistive physical aid. Therefore, this claim includes the recitation of the judicial exception of abstract ideas of a mental process.
Step 2a Prong 2: Claim 15 additionally recites the limitation after updating the structural model again, displaying the structural model to a user. This limitation has been identified as insignificant extra solution activity of mere data outputting. The courts have ruled appending insignificant extra solution activity to a recited judicial exception does not integrate the judicial exception into a practical application. With the additional element viewed in conjunction with the other limitations, the claim as a whole does not appear to integrate the judicial exception into a practical application.
Step 2B: Because limitations were identified in Step 2a Prong 2 as insignificant extra solution activity, the limitation must be evaluated to determine if the element is beyond well-understood, routine, and conventional activity. The limitation after updating the structural model again, displaying the structural model to a user amounts to outputting data representative of a structural model to a screen. This activity is well-understood, routine, and conventional activity within the art, and this assertion is supported by evidence. Autodesk, a commercially available software for modeling structures, comes equipped with displaying structural data to a user as a standard functionality. This is demonstrated in the user documentation, depicting different ways a structure can be displayed to a user, as shown previously in the rejection of claim 2. Because this functionality comes standard to a widely-used product within the art, displaying structural models to a user in a generic and non-specific way is understood to be well-understood, routine and conventional activity. The courts have found that adding well understood, routine, and conventional activity previously known to the industry and specified at a high level of generality to a judicial exception are not enough to qualify the claim as significantly more than the abstract idea. Therefore, the claim does not include additional elements, alone or in the ordered combination that are sufficient to amount to significantly more than the recited judicial exception.
This claim is not eligible subject matter under 35 U.S.C. 101.
Claim 16
Step 1: Regarding dependent claim 16, the judicial exception of independent claim 14 and dependent claim 15 is further incorporated. The claim falls within the corresponding statutory category as stated previously.
Step 2A Prong 1: Claim 16 additionally recites the limitation wherein the one or more programs further comprise instructions for repeating the generating the second approximate FEA solutions and correspondingly the second sensitivity analyses iteratively until a convergent structural model is obtained which can reasonably be read to entail performing mathematical calculations to approximate FEA solutions and evaluating the solutions to determine if convergence has occurred. This task can be performed within the human mind or using a pen and paper as an assistive physical aid. Therefore, this claim includes the recitation of the judicial exception of abstract ideas of a mental process. Furthermore, because the limitation recites performing FEA approximations and sensitivity analyses and these are understood to be mathematical calculations, the claim further recites the judicial exception of mathematical concepts.
Step 2a Prong 2 & Step 2B: Claim 16 does not recite any additional elements that would integrate the judicial exception(s) into a practical application, nor amount to significantly more.
This claim is not eligible subject matter under 35 U.S.C. 101.
Claim 17
Step 1: Regarding dependent claim 17, the judicial exception of independent claim 14 and dependent claim 15 is further incorporated. The claim falls within the corresponding statutory category as stated previously.
Step 2A Prong 1: Claim 17 additionally recites the limitation wherein obtaining the first approximate FEA solution comprises applying a pre-conditioning matrix to a set of linear equations representing the structure which can reasonably be read to entail applying a preconditioning matrix to a set of linear equations. This task can be performed within the human mind or using a pen and paper as an assistive physical aid. Therefore, this claim includes the recitation of the judicial exception of abstract ideas of a mental process. This claim also include the recitation of mathematical calculations and therefore the claim additionally falls under the mathematical concepts grouping of abstract ideas
Step 2a Prong 2 & Step 2B: Claim 17 does not recite any additional elements that would integrate the judicial exception(s) into a practical application, nor amount to significantly more.
This claim is not eligible subject matter under 35 U.S.C. 101.
Claim 19
Step 1: Regarding dependent claim 19, the judicial exception of independent claim 18 is further incorporated. The claim falls within the corresponding statutory category as stated previously.
Step 2A Prong 1: Claim 19 additionally recites the limitation generating a second approximate FEA solution based on the updated structural model, which can reasonably be read to entail using the updated structural model to inform the evaluation of FEA approximation. This task can be performed within the human mind or using a pen and paper as an assistive physical aid. Therefore, this claim includes the recitation of the judicial exception of abstract ideas of a mental process. Furthermore, this claim includes the recitation of mathematical calculations for approximating an FEA solution and additionally includes the recitation of abstract ideas of mathematical concepts. Claim 19 further recites performing a second sensitivity analysis based on the second approximate FEA solution; which can reasonably be read to entail performing a sensitivity analysis (which is understood to be numerically analyzing and quantifying how inputs to a physical model affect outputs of the model) using the approximate FEA solution. This task can be performed within the human mind or using a pen and paper as an assistive physical aid. For example, a human being can analyze the approximate FEA solution and further analyze the sensitivity on the plurality of cells to draw conclusions on the sensitivity of the model. Furthermore, sensitivity analysis entails performing mathematical calculations to derive numeric outcomes that quantify the model and therefore this limitation also includes the recitation of the abstract idea of mathematical concepts. Lastly, claim 19 recites updating the structural model again based on the second sensitivity analysis; and which can be reasonably read to entail evaluating the sensitivity analysis of the plurality of cells to make a judgement on how to update the structural model in response to the evaluation. This task can be performed within the human mind or using a pen and paper as an assistive physical aid. Therefore, this claim includes the recitation of the judicial exception of abstract ideas of a mental process.
Step 2a Prong 2: Claim 19 additionally recites the limitation after updating the structural model again, displaying the structural model to a user. This limitation has been identified as insignificant extra solution activity of mere data outputting. The courts have ruled appending insignificant extra solution activity to a recited judicial exception does not integrate the judicial exception into a practical application. With the additional element viewed in conjunction with the other limitations, the claim as a whole does not appear to integrate the judicial exception into a practical application.
Step 2B: Because limitations were identified in Step 2a Prong 2 as insignificant extra solution activity, the limitation must be evaluated to determine if the element is beyond well-understood, routine, and conventional activity. The limitation after updating the structural model again, displaying the structural model to a user amounts to outputting data representative of a structural model to a screen. This activity is well-understood, routine, and conventional activity within the art, and this assertion is supported by evidence. Autodesk, a commercially available software for modeling structures, comes equipped with displaying structural data to a user as a standard functionality. This is demonstrated in the user documentation, depicting different ways a structure can be displayed to a user, as shown previously in the rejection of claim 2. Because this functionality comes standard to a widely-used product within the art, displaying structural models to a user in a generic and non-specific way is understood to be well-understood, routine and conventional activity. The courts have found that adding well understood, routine, and conventional activity previously known to the industry and specified at a high level of generality to a judicial exception are not enough to qualify the claim as significantly more than the abstract idea. Therefore, the claim does not include additional elements, alone or in the ordered combination that are sufficient to amount to significantly more than the recited judicial exception.
This claim is not eligible subject matter under 35 U.S.C. 101.
Claim 20
Step 1: Regarding dependent claim 20, the judicial exception of independent claim 18 and dependent claim 19 is further incorporated. The claim falls within the corresponding statutory category as stated previously.
Step 2A Prong 1: Claim 20 additionally recites the limitation wherein the one or more programs further comprise instructions for repeating the generating the second approximate FEA solutions and correspondingly the second sensitivity analyses iteratively until a convergent structural model is obtained, which can reasonably be read to entail performing mathematical calculations to approximate FEA solutions and evaluating the solutions to determine if convergence has occurred. This task can be performed within the human mind or using a pen and paper as an assistive physical aid. Therefore, this claim includes the recitation of the judicial exception of abstract ideas of a mental process. Furthermore, because the limitation recites performing FEA approximations and sensitivity analyses and these are understood to be mathematical calculations, the claim further recites the judicial exception of mathematical concepts.
Step 2a Prong 2 & Step 2B: Claim 20 does not recite any additional elements that would integrate the judicial exception(s) into a practical application, nor amount to significantly more.
This claim is not eligible subject matter under 35 U.S.C. 101.
Claim Rejections - 35 USC § 103
In the event the determination of the status of the application as subject to AIA 35 U.S.C. 102 and 103 (or as subject to pre-AIA 35 U.S.C. 102 and 103) is incorrect, any correction of the statutory basis (i.e., changing from AIA to pre-AIA ) for the rejection will not be considered a new ground of rejection if the prior art relied upon, and the rationale supporting the rejection, would be the same under either status.
The following is a quotation of 35 U.S.C. 103 which forms the basis for all obviousness rejections set forth in this Office action:
A patent for a claimed invention may not be obtained, notwithstanding that the claimed invention is not identically disclosed as set forth in section 102, if the differences between the claimed invention and the prior art are such that the claimed invention as a whole would have been obvious before the effective filing date of the claimed invention to a person having ordinary skill in the art to which the claimed invention pertains. Patentability shall not be negated by the manner in which the invention was made.
The factual inquiries for establishing a background for determining obviousness under 35 U.S.C. 103 are summarized as follows:
1. Determining the scope and contents of the prior art.
2. Ascertaining the differences between the prior art and the claims at issue.
3. Resolving the level of ordinary skill in the pertinent art.
4. Considering objective evidence present in the application indicating obviousness or nonobviousness.
This application currently names joint inventors. In considering patentability of the claims the examiner presumes that the subject matter of the various claims was commonly owned as of the effective filing date of the claimed invention(s) absent any evidence to the contrary. Applicant is advised of the obligation under 37 CFR 1.56 to point out the inventor and effective filing dates of each claim that was not commonly owned as of the effective filing date of the later invention in order for the examiner to consider the applicability of 35 U.S.C. 102(b)(2)(C) for any potential 35 U.S.C. 102(a)(2) prior art against the later invention.
Claims 1, 5, 11, 14, and 18 are rejected under 35 U.S.C. 103 as being unpatentable over Xiao et al (CN 113987887 A), hereinafter referred to as Xiao, in view of Pigso Learning (Pigso Learning, “Types of Supports and Reactions”, August 31, 2021, pigsolearning.com), hereinafter referred to as Pigso, further in view of Stavropoulou (Stavropoulou, E., “Sensitivity analysis and regularization for shape optimization of coupled problems”, 2015, Doctoral Dissertation, Technische Universitat Munchen), hereinafter referred to as Stavropoulou.
Regarding claim 1, Xiao teaches (except the limitations surrounded by brackets ([[..]])) A method of optimizing a structural design performed at a computing system having memory and one or more processors, the method comprising: A method for topology optimization is disclosed. The methodology can be implemented by a device (computing system) that has memory and a processor ((Xiao, ¶6) "In a first aspect, an embodiment of the present application provides a multi-fidelity dynamic reduction topology optimization method, the method comprising…"); ((Xiao, ¶22-24) "In a third aspect, an embodiment of the present application provides a multi-fidelity dynamic reduction topology optimization device, the topology optimization device comprising a memory and a processor; The memory is used to store computer executable instructions; The processor is used to execute the computer executable instructions, and can implement the topology optimization method described in the first aspect and any one of various possible implementation methods of the first aspect.").
obtaining a set of constraints for a structure of a target object, the set of constraints including an external force constraint, a constraint for a maximal amount of material for constructing the target object and one or more constraints for fixed point locations of the structure [[that are fixed to other objects and cannot move under the external force constraint;]] The constraint conditions for a structural model are constructed and include a stress constraint, wherein a stress is understood to be an external force. A constraint is given for the predefined material volume fraction limit (as the amount of material) and a constraint is given for displacements (where displacement array is understood to be a collection of displacements at each node in the finite element model, and wherein the location of each node is defined by the properties of the node) ((Xiao, ¶57-61) "Step S101: construct the objective function and constraint conditions, and set the convergence accuracy and the maximum number of iterations, wherein the constraint conditions include volume constraint and stress constraint. Specifically, the optimization formula formed by constructing the objective function and the constraints can be expressed as follows: [[equations in paras 59 and 60]] Among them, is the normalized equivalent stress corresponding to unit e, and the stress evaluation point is located at the geometric center of the unit; is the maximum normalized equivalent stress in the structural model; is the upper limit of stress applied to the structural model; c is the optimization target, that is, flexibility; ρ represents the array composed of unit density; u and f represent the displacement and external load arrays respectively; K represents the overall stiffness matrix; ve represents the unit volume; vf represents the predefined material volume fraction limit."); The structural model includes a fixed support surface, wherein one having ordinary skill in the art would understand that a surface is represented through a collection of interconnected nodes (points) and so the fixed surface is defined by its corresponding fixed points ((Xiao, ¶133) "The upper surface is a fixed support surface."). Therefore, if the model includes a fixed surface and displacement as a constraint, the set of constraints includes constraints for fixed point locations of the structure.
partitioning a design space for the structure into a plurality of cells, wherein the plurality of cells define a structural model of the structure of the target object; and ((Xiao, ¶62) "Step S102: Discretize the structural model into a finite element mesh and apply loads."); ((Xiao, ¶132-133) "The following is a calculation example to illustrate the topology optimization method provided by this embodiment in detail. As shown in FIG6 , the structural model is an L-shaped beam. The length, height and width of the L-shaped beam design domain are 60×60×8. The design domain is discretized using a standard eight-vertex hexahedron unit with a unit volume.")
in accordance with the external force constraint being applied to the structure: A load is applied to the structure ((Xiao, ¶62) "Step S102: Discretize the structural model into a finite element mesh and apply loads."); ((Xiao, ¶133) "The line load f is distributed on the corresponding nodes along the z-axis, with a vertical downward direction and a magnitude of 1. In order to avoid excessive stress at the load application point, the load f is evenly distributed from the upper right corner along the negative direction of the y-axis to the 6 adjacent nodes.")
obtaining a first approximate finite element analysis (FEA) solution for the plurality of cells based on the set of constraints; An approximate solution is obtained through solving the core equation (FEA analysis solution) ((Xiao, ¶170) "The core equation is solved globally, including: using a multi-grid iterative algorithm to solve the core equation, and using the obtained approximate solution as the global solution."). Figure 1 depicts a flowchart of the methodology, wherein the iterative calculation step S103 includes generating an FEA solution, and is subsequent to the step of constructing the constraint conditions in step S101 and discretizing the structural model (into a plurality of cells) in step S102. Therefore, it is understood that the FEA solution is based on the set of constraints and the plurality of cells (Xiao, Figure 1)
performing a sensitivity analysis on the plurality of cells based on the approximate FEA solution, [[wherein the sensitivity analysis indicates that a first subset of the plurality of cells deform more than others of the plurality of cells; and]] A sensitivity analysis is performed in step S203 ((Xiao, ¶156) "Step S203: Calculate the objective function and its sensitivity, as well as the constraint conditions and their sensitivity."). Step S203 is executed after step S202 in which the dynamic order reduction calculation is performed on the core equation to derive the approximated solution (as stated previously), thereby indicating that the sensitivity analysis is based on the approximate FEA solution ((Xiao, ¶155) "Step S202: Perform dynamic order reduction calculation on the core equation, wherein the core equation includes the equilibrium equation and the adjoint equation.")
updating the structural model for the structure of the target object based on the sensitivity analysis of the plurality of cells. Design variables are updated which are understood as the variables that define the design of the structural model in step S204 ((Xiao, ¶157) "Step S204: Optimize and solve and update design variables."). Step S204 is executed after step S203 which is the sensitivity analysis (as stated previously), thereby indicating that the model updated is based on the sensitivity analysis ((Xiao, ¶156) "Step S203: Calculate the objective function and its sensitivity, as well as the constraint conditions and their sensitivity.").
Xiao does not explicitly describe the fixed support surface in terms of the explicit definition; however, Pigso Learning discloses that a fixed support is a type of connection that are fixed to other objects and cannot move under the external force constraint; ((Pigso, ¶1) "Supports connect the member to the ground or to some other parts of the structure. "); ((Pigso, ¶5) "Fixed Support reactions are rigid supports. fixed support reactions are restrained against both rotation and translation so they can resist any type of force or moment. to provides good stability to the structure, at least one rigid support should be provided. ")
Pigso is analogous to the claimed invention because it is reasonably pertinent to the problem faced by the inventor. Pigso is a learning resource for FEA terminology that would be relevant for topology optimization using FEA. It would have been obvious to one of ordinary skill to which said subject matter pertains at the time the invention was filed to have incorporated the teachings of Pigso into the disclosure of Xiao because combining prior art element according to known methods would yield predictable results. Xiao discloses the utilization of a fixed support surface but does not explicitly define what a fixed support surface entails. Pigso explicitly describes a fixed support as an FEA mechanism by which to connect the modeled member to the ground or some other part of the structure and further describes a fixed support in terms of its reactions against force and moments. By combining the prior art references, one having skill in the art would obtain a more comprehensive and explicit definition of the terminology and accordingly the combination would have been obvious.
The proposed combination discloses a sensitivity analysis being performed as part of the topology optimization but does not particularly describe the sensitivity analysis in terms of the explicit behavior analyzed as part of the analysis. However, Stavropoulou discloses wherein the sensitivity analysis indicates that a first subset of the plurality of cells deform more than others of the plurality of cells; and A sensitivity analysis is done for an initial and a final design, wherein the sensitivity analysis shows a gradient wherein higher values in the gradient indicate larger deformation. ((Stavropoulou, Page 78, ¶3) "The improvement of the design can be also seen through the sensitivity map on the bend of the duct. Figure 4.8 displays the surface sensitivity at the initial design as well as at the improved design using in-plane regularization. The high sensitivity region undergoes the largest deformation. This area is where the mesh fails when no in-plane regularization is applied. In the final design the high sensitivities are removed while some sensitivity still remains close to the boundary of the design domain since it should be kept unchanged during optimization in order to have a smooth transition from the design to the non-design surface. "). The images of the sensitivity analysis in Figure 4.8 comprise cell elements as the representations of the design
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Stavropoulou is analogous to the claimed invention because it is related to the same field of endeavor or using finite element analysis for design optimization. It would have been obvious to one of ordinary skill to which said subject matter pertains at the time the invention was filed to have implemented the sensitivity analysis indicating larger areas of deformation as disclosed by Stavropoulou into the proposed combination because some teaching, suggestion, or motivation in the prior art would have led one having skill in the art to do so in order to arrive at the claimed invention. Xiao discloses performing a sensitivity analysis in a topology optimization process but does not provide particular details as to how the sensitivity analysis is performed. Stavropoulou explicitly describes the sensitivity analysis of a design optimization that analyzes finite element representations in terms of the insights that can be obtained from the sensitivity analysis, including insights pertaining to areas of high deformation. Because Xiao suggests that a sensitivity analysis is performed and Stavropoulou explicitly provides a mechanism by which to do the sensitivity analysis, the combination would have accordingly been obvious.
Regarding claim 5, the proposed combination teaches The method of claim 1, as stated previously. The proposed combination in further view of Xiao teaches wherein the first approximate FEA solution comprises a partial solution to a set of linear equations representing the structure. The core equations are solved (as the FEA solution) to obtain an approximate solution using a multi-grid iterative algorithm ((Xiao, ¶93) "The core equations are solved in a multi-fidelity global manner, including: solving the core equations using a multi-grid iterative algorithm, and using the obtained approximate solution as the global solution"). The multigrid iterative algorithm solves linear equations ((Xiao, ¶94) "The multigrid iterative algorithm is a fast iterative algorithm for solving linear equations derived from boundary value problems of partial differential equations."). Therefore, because the solution is approximated and inexact (where an exact solution would be understood as a full solution), the FEA solutions solved by the multigrid iterative algorithm are understood to be partially solved.
Regarding claim 11, the proposed combination teaches The method of claim 1, as stated previously. The proposed combination in further view of Xiao teaches wherein obtaining the first approximate FEA solution comprises applying a pre-conditioning matrix to a set of linear equations representing the structure. During the multigrid iterative calculations wherein the approximate FEA solution is solved (as stated previously in the rejection of claim 1), a smoothing operator is employed using the pre-conditioned conjugate gradient method, wherein one having ordinary skill in the art would understand that the “pre-conditioned” nature of the conjugate gradient method implies applying a pre-conditioning matrix and the conjugate gradient method is an iterative algorithm used to solve systems of linear equations ((Xiao, ¶97) "Since the equilibrium equations in large-scale topology optimization finite element analysis are highly sparse, symmetrical and positively definite, this embodiment uses the pre-conditioned conjugate gradient method as the smoothing operator for relaxation on the fine grid."). The smoothing operations (by the pre-conditioned conjugate gradient method) are performed to obtain the displacement vector of the structure, thereby indicating that the pre-conditioning matrix is applied to a set of equations representing the structure ((Xiao, ¶110) "If the number of iterations is equal to the number of grid levels, the displacement vector u(i) ＝(K(i) )-1 f(i) . Otherwise, the following steps are performed: Perform pre-smoothing to obtain the displacement vector approximate solution u(i) ; Calculate the residual of the equilibrium equation: d(i) ＝f(i) -K(i) u(i) ; Project the residual onto the coarse grid by the restriction operator: Let the error calculation vi+1 ＝MG(K(i+1) ,u(i+1) ,d(i+1) ,i+1); Transfer the error vi+1 to the fine grid by the extension operator: Coarse grid correction: Perform post-smoothing to obtain the displacement vector approximate solution u(i).")
Regarding claim 14, Xiao teaches A computing system, comprising: one or more processors; memory; and ((Xiao, ¶22) " In a third aspect, an embodiment of the present application provides a multi-fidelity dynamic reduction topology optimization device, the topology optimization device comprising a memory and a processor;")
one or more programs stored in the memory and configured for execution by the one or more processors, the one or more programs comprising instructions for: ((Xiao, ¶23-24) " The memory is used to store computer executable instructions; The processor is used to execute the computer executable instructions, and can implement the topology optimization method described in the first aspect and any one of various possible implementation methods of the first aspect.")
The remaining limitations obtaining a set of constraints for a structure of a target object, the set of constraints including an external force constraint, a constraint for a maximal amount of material for constructing the target object and one or more constraints for fixed point locations of the structure that are fixed to other objects and cannot move under the external force constraint;
partitioning a design space for the structure into a plurality of cells, wherein the plurality of cells define a structural model of the structure of the target object; and
in accordance with the external force constraint being applied to the structure:
obtaining a first approximate finite element analysis (FEA) solution for the plurality of cells based on the set of constraints;
performing a sensitivity analysis on the plurality of cells based on the approximate FEA solution, wherein the sensitivity analysis indicates that a first subset of the plurality of cells deform more than other of the plurality of cells; and
updating the structural model for the structure of the target object based on the sensitivity analysis of the plurality of cells are substantially similar to that recited in claim 1 and are therefore rejected under the same rationale.
Regarding claim 18, Xiao teaches A non-transitory computer-readable storage medium storing one or more programs configured for execution by a computing device having one or more processors, memory, and a display, the one or more programs comprising instructions for: ((Xiao, ¶25) " In a fourth aspect, an embodiment of the present application provides a computer-readable storage medium, wherein the computer-readable storage medium stores executable instructions, and a computer executes the executable instructions to implement the topology optimization method described in the first aspect and any one of the various possible implementation methods of the first aspect."). Computing devices such as personal computers, handheld devices, and tablet devices are disclosed as being possible computing devices by which to execute the claimed functionality of the topology optimization, wherein these devices are understood to have display capabilities ((Xiao, ¶186) "All or part of this application can be used in many general or special computer system environments or configurations. For example: personal computers, server computers, handheld devices or portable devices, tablet devices, mobile communication terminals, multi-processor systems, microprocessor-based systems, programmable electronic devices, distributed computing environments including any of the above systems or devices, etc. ")
The remaining limitations obtaining a set of constraints for a structure of a target object, the set of constraints including an external force constraint, a constraint for a maximal amount of material for constructing the target object and one or more constraints for fixed point locations of the structure that are fixed to other objects and cannot move under the external force constraint;
partitioning a design space for the structure into a plurality of cells, wherein the plurality of cells define a structural model of the structure of the target object; and
in accordance with the external force constraint being applied to the structure:
obtaining an approximate finite element analysis (FEA) solution for the plurality of cells based on the set of constraints;
performing a sensitivity analysis on the plurality of cells based on the approximate FEA solution, wherein the sensitivity analysis indicates that a first subset of the plurality of cells deform more than others of the plurality of cells; and
updating the structural model for the structure of the target object based on the sensitivity analysis of the plurality of cells are substantially similar to that recited in claim 1 and are therefore rejected under the same rationale.
Claims 2, 3, 4, 15, 16, 17, 19, and 20 are rejected under 35 U.S.C. 103 as being unpatentable over Xiao in view of Heap et al (Heap, R., Hepworth, A., and Jensen, C., “Real-Time Visualization of Finite Element Models Using Surrogate Modeling Methods”, March 1, 2015, Journal of Computing and Information Science Engineering, 15(1), https://doi.org/10.1115/1.4029217), hereinafter referred to as Heap.
Regarding claim 2, the proposed combination teaches The method of claim 1, as stated previously.
The proposed combination in further view of Xiao teaches (except the limitations surrounded by brackets) further comprising, after updating the structural model: Examiner interprets this limitation to mean after “obtaining the updated structural model of claim 1”. An iterative calculation module is employed to perform iterative calculations such as that described in claim 1 (steps S201-S204), thereby indicating that the steps can be repeated after an updated model with updated design variables has been obtained. ((Xiao, ¶153) "The iterative calculation module 403 is used to perform iterative calculation until the iterative result reaches the convergence accuracy or the number of iterative steps reaches the maximum number of iterative steps. It includes steps S201 to S204.")
generating a second approximate FEA solution based on the updated structural model; A dynamic order reduction calculation, which includes obtaining an approximate solution, as stated previously in the rejection of claim 1, is part of an iterative process and thereby is understood to include obtaining a second approximated solution ((Xiao, ¶155) "Step S202: Perform dynamic order reduction calculation on the core equation, wherein the core equation includes the equilibrium equation and the adjoint equation."); ((Xiao, ¶153) "The iterative calculation module 403 is used to perform iterative calculation until the iterative result reaches the convergence accuracy or the number of iterative steps reaches the maximum number of iterative steps. It includes steps S201 to S204.")
performing a second sensitivity analysis based on the second approximate FEA solution; A sensitivity calculation is performed based on the approximate FEA solution, as stated previously in the rejection of claim 1 and is also part of the iterative process, thereby indicating that a second sensitivity analysis can be performed during the second iteration ((Xiao, ¶156) "Step S203: Calculate the objective function and its sensitivity, as well as the constraint conditions and their sensitivity."); ((Xiao, ¶153) "The iterative calculation module 403 is used to perform iterative calculation until the iterative result reaches the convergence accuracy or the number of iterative steps reaches the maximum number of iterative steps. It includes steps S201 to S204.")
updating the structural model again based on the second sensitivity analysis; and The design variables of the structural model are updated, as stated previously in the rejection of claim 1 as part of an iterative process, thereby indicating that the structural model can be updated again ((Xiao, ¶157) " Step S204: Optimize and solve and update design variables."); ((Xiao, ¶153) "The iterative calculation module 403 is used to perform iterative calculation until the iterative result reaches the convergence accuracy or the number of iterative steps reaches the maximum number of iterative steps. It includes steps S201 to S204.")
[[after updating the structural model again, displaying the structural model to a user.]]
Xiao does not explicitly teach after updating the structural model again, displaying a structural model to a user. Xiao implicitly suggests that the optimal topology derived as part of the iterative calculations can be displayed (as depicted in Figures 9a-9c) and one having ordinary skill in the art would recognize that because the methodology can be implemented on a device having display capabilities such as a computer, the display of the structure (such as that shown in Figs 9a-9c) could be to a user observing the execution of the methodology on said computer ((Xiao, ¶186) "The various embodiments in this specification are described in a progressive manner, and the same or similar parts between the various embodiments can be referred to each other, and each embodiment focuses on the differences from other embodiments. All or part of this application can be used in many general or special computer system environments or configurations. For example: personal computers, server computers, handheld devices or portable devices, tablet devices, mobile communication terminals, multi-processor systems, microprocessor-based systems, programmable electronic devices, distributed computing environments including any of the above systems or devices, etc."). For the sake of completeness and clarity, as well as in the interest of compact prosecution, an additional reference is placed on the record to explicitly teach the limitation.
Heap explicitly teaches after updating the structural model again, displaying a structural model to a user. A graphical user interface is utilized to display structural models to a user in real-time ((Heap, Page 2, Col 1, ¶2) “With the methods proposed herein, the solution set of multiple FEA runs will be approximated to produce a simplified, continuous postprocessing function. This will allow the postprocessing results to be viewed as a geometric model in real-time for quick design space exploration."); (See also Heap, Figure 10); ((Heap, Page 9, Col 1, ¶3) "Once the surrogate models are created, the automated loop ends with the visualization GUI where the surrogate models are evaluated for real-time model updates.")
Heap and Xiao are analogous arts because they are both related to the same field of endeavor of finite element analysis for geometric/structural models. It would have been obvious to one of ordinary skill to which said subject matter pertains at the time the invention was filed to have modified Xiao to incorporate the display aspect of Heap because some teaching, suggestion, or motivation in the prior art would have led one of ordinary skill to combine the prior art references to arrive at the claimed invention. Xiao teaches a topology optimization methodology that includes finite element analysis and the iterative updates of design variables for a structural model. Heap teaches the real-time visualization of surrogate models as design parameters are changed for a model. Heap notes that it is desirable for a designer to be able to visualize how changes in design parameters affect the FEA solution of interest before fully executing the model through the optimization loop ((Heap, ¶Abstract) "Parametric finite element analysis (FEA) models are commonly used in iterative design processes to obtain an optimum model given a set of loads, constraints, objectives, and design parameters to vary. In some instances, it is desirable for a designer to obtain some intuition about how changes in design parameters can affect the FEA solution of interest, before simply sending the model through the optimization loop. For example, designers who wish to explore the design space and understand how each variable changes the output in a visual way, looking at the whole model and not just numbers or a response surface of a single FEA node."). Therefore, one having ordinary skill in the art would be motivated to combine the teachings of Xiao and Heap to arrive at the claimed invention.
Regarding claim 3, the proposed combination teaches The method of claim 2, as stated previously. Xiao further teaches further comprising repeating the generating the second approximate FEA solutions and correspondingly the second sensitivity analyses iteratively until a convergent structural model is obtained. Iterative calculations are performed as part of step S103 until convergence is reached. ((Xiao, ¶63) "Step S103: perform iterative calculation until the iterative result reaches convergence accuracy or the number of iterative steps reaches the maximum number of iterative steps."); Step S103 comprises steps S201-S204, wherein S202 is the step in which an approximate FEA solution is determined, as stated previously and S203 is the step in which a sensitivity analysis is performed, as stated previously ((Xiao, ¶64-68) "Specifically, the iterative calculation of step S103 includes steps S201 to S204 , as shown in FIG. 2 . Step S201: Calculate the overall stiffness of the structural model. Step S202: Perform dynamic order reduction calculation on the core equation, wherein the core equation includes the equilibrium equation and the adjoint equation. Step S203: Calculate the objective function and its sensitivity, as well as the constraints and their sensitivity. Step S204: Optimize and solve and update design variables.")
Regarding claim 4, the proposed combination teaches The method of claim 1, as stated previously. Xiao further teaches (except the limitations surrounded by brackets ([[..]])) wherein the first approximate FEA solution describes [[an object deformation]] for the structure in accordance with the external force constraint. The iterative calculation (that obtains the approximate FEA solution, as stated previously), includes using a power function interpolation which is described to explicitly include variables such as stress vector, constitutive matrix, strain-displacement matrix, and node displacement vector ((Xiao, ¶119-121) " In order to solve the problem of singular solutions, the iterative calculation provided in this embodiment also includes: using a power function interpolation form to penalize the intermediate density value to avoid generating singular solutions. The specific format is as follows: [[equation]] Among them, σe represents the penalized stress vector; represents the stress vector actually calculated at unit e; q represents the stress penalty factor, which is usually less than 1 based on experience; D0 represents the constitutive matrix of the solid material; B represents the strain-displacement matrix; ue represents the node displacement vector generated by unit e. "). The elements of the FEA solution describe the structure in accordance with the external force constraint.
The proposed combination in further view of Xiao does not explicitly teach; however, Heap teaches an object deformation. An approximate FEA solution is derived for visualization purposes ((Heap, Page 1, Col 1, ¶1) "These approximated FEA solutions can be viewed in real-time by evaluating the surrogate models allowing for instant examination of a parametric FEA model family member."). An object can be visualized under load, wherein the approximate FEA solution enables visualization of bending and torsion (object deformation) ((Heap, Page 10, Col 1, ¶1) "The C-beam has a point load on the tip of the “c” shape acting in the negative z-axis direction to induce bending and torsion. The I-beam has a distributed load across each node on the farthest edge to produce bending, and another distributed load on the top and bottom cap acting perpendicular to the face of the web in opposite directions in order to produce torsion."). See also Figures 12-17 which shows the structural model under load and also shows the deformation of the object as a result of approximated FEA solutions dictated by inputs to the GUI (Heap, Figs 12-17).
Heap and Xiao are analogous arts because they are both related to the same field of endeavor of finite element analysis for geometric/structural models. It would have been obvious to one of ordinary skill to which said subject matter pertains at the time the invention was filed to have incorporated the object deformation taught by Heap being included in the FEA approximation analysis taught by Xiao because some teaching, suggestion, or motivation in the prior art would have led one of ordinary skill to combine the prior art reference teachings to arrive at the claimed invention. Xiao teaches obtaining an approximate FEA solution for a structure under load and explicitly notes matrices and values that could be used to mathematically derive object deformation values. Heap teaches using an approximated FEA solution to visualize deformation of a structure under load. Heap notes that the visualization of the surrogate model during real-time enables designers to gain intuition and understand the behavior of the model ((Heap, ¶Abstract) "When engineers build parametric models, one typical objective is to explore the design space to see where the optimum model or Pareto front of optimum models fall. In some instances, it is desirable for a designer to obtain some intuition about how changes in design parameters can affect the FEA solution of interest, before simply sending the model through the optimization loop. Typically, the postprocessing of FEA allows the user to view the results in relation to the model geometry. Intuition about the model can be obtained by running the FEA on the parametric model for a set of model family members, but this can be very time consuming and only gives snapshots of the real behavior of the model. Approximation techniques have been developed that can take values at many different design points within an n-dimensional design space and interpolate those values. The result of such an approximation is a continuous function that provides a best guess approach when examining other design points."). As such, one having ordinary skill in the art looking to optimize the topology of a structure, as in Xiao, would be compelled to visualize the object deformation during the process to ensure the approximated solution behaves in a realistic and predictable manner so as to derive a high-fidelity end solution. Therefore, it would have been obvious to one of ordinary skill to further modify Xiao in view of Heap.
Regarding claim 15, the limitations The computing system of claim 14, wherein the one or more programs further comprise instructions for, after updating the structural model:
generating a second approximate FEA solution based on the updated structural model;
performing a second sensitivity analysis based on the second approximate FEA
solution;
updating the structural model again based on the second sensitivity analysis; and
after updating the structural model again, displaying the structural model to a user are substantially similar to that recited in claim 2 but with respect to claim 14 and is therefore rejected under the same rationale of the proposed combination.
Regarding claim 16 the limitations The computing system of claim 15, wherein the one or more programs further comprise instructions for repeating the generating the second approximate FEA solutions and correspondingly the second sensitivity analyses iteratively until a convergent structural model is obtained are substantially similar to that recited in claim 3 but with respect to independent claim 14 and dependent claim 15 and is therefore rejected under the same rationale.
Regarding claim 17, the proposed combination teaches The computing system of claim 15, as stated previously. The proposed combination in further view of Xiao teaches wherein obtaining the first approximate FEA solution comprises applying a pre-conditioning matrix to a set of linear equations representing the structure. During the multigrid iterative calculations wherein the approximate FEA solution is solved (as stated previously in the rejection of claim 14), a smoothing operator is employed using the pre-conditioned conjugate gradient method, wherein one having ordinary skill in the art would understand that the “pre-conditioned” nature of the conjugate gradient method implies applying a pre-conditioning matrix and the conjugate gradient method is an iterative algorithm used to solve systems of linear equations ((Xiao, ¶97) "Since the equilibrium equations in large-scale topology optimization finite element analysis are highly sparse, symmetrical and positively definite, this embodiment uses the pre-conditioned conjugate gradient method as the smoothing operator for relaxation on the fine grid."). The smoothing operations (by the pre-conditioned conjugate gradient method) are performed to obtain the displacement vector of the structure, thereby indicating that the pre-conditioning matrix is applied to a set of equations representing the structure ((Xiao, ¶110) "If the number of iterations is equal to the number of grid levels, the displacement vector u(i) ＝(K(i) )-1 f(i) . Otherwise, the following steps are performed: Perform pre-smoothing to obtain the displacement vector approximate solution u(i) ; Calculate the residual of the equilibrium equation: d(i) ＝f(i) -K(i) u(i) ; Project the residual onto the coarse grid by the restriction operator: Let the error calculation vi+1 ＝MG(K(i+1) ,u(i+1) ,d(i+1) ,i+1); Transfer the error vi+1 to the fine grid by the extension operator: Coarse grid correction: Perform post-smoothing to obtain the displacement vector approximate solution u(i).")
Regarding claim 19, the proposed combination discloses The non-transitory computer-readable storage medium of claim 18, as stated previously.
The limitations wherein the one or more programs further comprise instructions for, after updating the structural model:
generating a second approximate FEA solution based on the updated structural model;
performing a second sensitivity analysis based on the second approximate FEA solution;
updating the structural model again based on the second sensitivity analysis; and
after updating the structural model again, displaying the structural model to a user are substantially similar to that recited in claim 2 and are therefore rejected under the same rationale of the proposed combination.
Regarding claim 20, the proposed combination discloses The non-transitory computer-readable storage medium of claim 19, as stated previously. The limitations wherein the one or more programs further comprise instructions for repeating the generating the second approximate FEA solutions and correspondingly the second sensitivity analyses iteratively until a convergent structural model is obtained are substantially similar to that recited in claim 3 and are therefore rejected under the same rationale.
Claims 7 and 8 are rejected under 35 U.S.C. 103 as being unpatentable over Xiao as applied to claim 1 above, and further in view of Amir et al (Amir, O., Stolpe, M., Sigmund, O., “Efficient use of iterative solvers in nested topology optimization”, December 19, 2009, Structural and Multidisciplinary Optimization, Volume 43, Pages 55-72), hereinafter referred to as Amir2009.
Regarding claim 7, the proposed combination teaches The method of claim 1, as stated previously. The proposed combination in further view of Xiao teaches (except the limitations surrounded by brackets) [[further comprising: obtaining an update direction from the sensitivity analysis;]]
[[computing a decreasing step size for the update direction; and]]
wherein the structural model for the structure is updated [[based on the update direction and the step size.]] The design parameters are described as being updated after the sensitivity analysis is performed ((Xiao, ¶156-157) "Step S203: Calculate the objective function and its sensitivity, as well as the constraint conditions and their sensitivity. Step S204: Optimize and solve and update design variables.")
Xiao does not explicitly teach; however, Amir2009 teaches further comprising: obtaining an update direction from the sensitivity analysis; The adjoint method is applied for sensitivity analysis ((Amir2009, Page 57, Col 2, ¶1) "Therefore, when applying the adjoint method for sensitivity analysis, the complete iterative procedure performed in order to obtain the approximation is taken into account"). The direction vector (update direction) is computed as part of the adjoint method ((Amir2009, Page 57, Col 2, ¶2) "Compute the initial residual r1 and direction vector p1: r1 = f − Ku1, z1 = M−1r1, p1 = z1.")
computing a decreasing step size for the update direction; and Alpha (as the step size) is computed with regard for the update direction vector p_i using equation 19, wherein it can be seen that the step size can decrease based on the values of the equation. ((Amir2009, Page 71, Col 2, Lines 13-28 ) "In summary, the adjoint PCG procedure aimed at finding ri (i = 1, ...,m), zi (i = 1, ...,m − 1) andα i (i = 1, ..., m − 1) which are required for computing the design sensitivities is performed as follows 1. First cycle: (a) Set u (17, 18). (b) Compute α m−1 (19). (c) Compute p m−1 (20). 2. For i = (m-2):-1:1 do (a) Computeβi (22). (b) Compute z i+1 (23, 24). (c) Compute r i+1 (14, 15). (d) Compute α i (19). (e) Compute pi (21). 3. Compute z1 (25). 4. Compute r1 (16)."); ((Amir2009, Page 71, Col 1, Lines 6-7) "
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based on the update direction and the step size. The update direction and step size are determined as part of the adjoint method, which is used for sensitivity analysis ((Amir2009, Page 71, Col 2, Lines 13-28 ) "In summary, the adjoint PCG procedure aimed at finding ri (i = 1, ...,m), zi (i = 1, ...,m − 1) andα i (i = 1, ..., m − 1) which are required for computing the design sensitivities is performed as follows 1. First cycle: (a) Set u (17, 18). (b) Compute α m−1 (19). (c) Compute p m−1 (20). 2. For i = (m-2):-1:1 do (a) Computeβi (22). (b) Compute z i+1 (23, 24). (c) Compute r i+1 (14, 15). (d) Compute α i (19). (e) Compute pi (21). 3. Compute z1 (25). 4. Compute r1 (16).");
Xiao and Amir2009 are analogous arts because they are both related to the same field of endeavor as topology optimization methodologies. It would have been obvious to one of ordinary skill to which said subject matter pertains at the time the invention was filed to have modified Xiao’s methodology to incorporate the teachings of Amir2009 because some teaching, suggestion, or motivation would have led one of ordinary skill in the art to do so to arrive at the claimed invention. Xiao discloses performing a sensitivity analysis based on the adjoint method but does not particularly disclose elements of the adjoint equation ((Xiao, ¶51) "In addition, in each optimization cycle, when the adjoint method is used to derive the sensitivity expression of the stress constraint, it is necessary to solve an ultra-large-scale evolutionary linear system (adjoint equation), which requires huge computational effort. "). Amir2009 explicitly describes the mathematical calculations of the adjoint method to include computations of update direction and step size, which may be decreasing, as stated previously. Because Xiao suggests the computations disclosed by Amir2009 but does not indicate specific details and Amir2009 provides explicit details, it would have been obvious to one of ordinary skill in the art to explicitly describe the details of the sensitivity analysis of Xiao to the same level of detail as Amir2009.
Regarding claim 8, the proposed combination discloses The method of claim 7, wherein the structural model updated based on the update direction and the step size as stated previously.
The proposed combination further teaches in view of Xiao is a preliminary model; and. Iterative calculations are performed indicating that an updated structural model can be preliminary to a subsequent round of iterative calculations that include updating the model again ((Xiao, ¶64-68) "Specifically, the iterative calculation of step S103 includes steps S201 to S204 , as shown in FIG. 2 . Step S201: Calculate the overall stiffness of the structural model. Step S202: Perform dynamic order reduction calculation on the core equation, wherein the core equation includes the equilibrium equation and the adjoint equation. Step S203: Calculate the objective function and its sensitivity, as well as the constraints and their sensitivity. Step S204: Optimize and solve and update design variables."). The design variables are understood to be those variables which define the structural model.
the method further comprises generating a refined model update from the preliminary model in accordance with one or more material requirement constraints for the structure. The iterative nature of the calculations encompasses using the previously updated model for the next iteration ((Xiao, ¶64-68) "Specifically, the iterative calculation of step S103 includes steps S201 to S204 , as shown in FIG. 2 . Step S201: Calculate the overall stiffness of the structural model. Step S202: Perform dynamic order reduction calculation on the core equation, wherein the core equation includes the equilibrium equation and the adjoint equation. Step S203: Calculate the objective function and its sensitivity, as well as the constraints and their sensitivity. Step S204: Optimize and solve and update design variables."). Each model in the iterative calculations is optimized, indicating refinement of the model, as in step S204 and convergence is eventually obtained, further indicating model refinement ((Xiao, ¶153) "The iterative calculation module 403 is used to perform iterative calculation until the iterative result reaches the convergence accuracy or the number of iterative steps reaches the maximum number of iterative steps. It includes steps S201 to S204."). The iterative calculations are performed with consideration to the constraints in step S203. The constraints include that of a volume fraction limit, which is understood to be a material requirement constraint ((Xiao, ¶58-61) "Specifically, the optimization formula formed by constructing the objective function and the constraints can be expressed as follows: [[equations]] Among them, is the normalized equivalent stress corresponding to unit e, and the stress evaluation point is located at the geometric center of the unit; is the maximum normalized equivalent stress in the structural model; is the upper limit of stress applied to the structural model; c is the optimization target, that is, flexibility; ρ represents the array composed of unit density; u and f represent the displacement and external load arrays respectively; K represents the overall stiffness matrix; ve represents the unit volume; vf represents the predefined material volume fraction limit.").
Claims 9 and 10 are rejected under 35 U.S.C. 103 as being unpatentable over Xiao and Amir2009 as applied to claim 8 above, and further in view of Liao et al (Liao, H., Vaitheeswaran, P., Song, T., Subbarayan, G., “Algebraic Point Projection for Immersed Boundary Analysis on Low Degree NURBS Curves and surfaces”, March 31, 2020, Algorithms 2020, 13(4), 82, https://doi.org/10.3390/a13040082), hereinafter referred to as Liao.
Regarding claim 9, the proposed combination teaches The method of claim 8 wherein generating the refined model update, comprises, as stated previously.
The proposed combination in further view of Xiao teaches (except the limitations surrounded by brackets) [[for a point in the]] preliminary [[model determined to be outside of]] the one or more material requirement constraints for the structure, [[selecting a replacement point having a minimum Euclidean distance from the point.]] Iterative calculations are performed indicating that an updated structural model can be preliminary to a subsequent round of iterative calculations that include updating the model again ((Xiao, ¶64-68) "Specifically, the iterative calculation of step S103 includes steps S201 to S204 , as shown in FIG. 2 . Step S201: Calculate the overall stiffness of the structural model. Step S202: Perform dynamic order reduction calculation on the core equation, wherein the core equation includes the equilibrium equation and the adjoint equation. Step S203: Calculate the objective function and its sensitivity, as well as the constraints and their sensitivity. Step S204: Optimize and solve and update design variables."). The design variables are understood to be those variables which define the structural model. The constraints include that of a volume fraction limit, which is understood to be a material requirement constraint ((Xiao, ¶58-61) "Specifically, the optimization formula formed by constructing the objective function and the constraints can be expressed as follows: [[equations]] Among them, is the normalized equivalent stress corresponding to unit e, and the stress evaluation point is located at the geometric center of the unit; is the maximum normalized equivalent stress in the structural model; is the upper limit of stress applied to the structural model; c is the optimization target, that is, flexibility; ρ represents the array composed of unit density; u and f represent the displacement and external load arrays respectively; K represents the overall stiffness matrix; ve represents the unit volume; vf represents the predefined material volume fraction limit.").
Xiao does not explicitly teach; however, Xiao in view of Liao teaches for a point in the … model determined to be outside of … selecting a replacement point having a minimum Euclidean distance from the point. A boundary is given by phi ((Liao, Page 6, ¶1) " This form yields a smooth distance function across the boundary φ = 0. "). Points are evaluated if they are inside or outside of the boundary (Liao, Figures 4 and 5). Points identified away from the boundary are projected onto the boundary ((Liao, Page 4, ¶2) "In this paper, a robust and efficient point projection technique for low degree two-dimensional (2D) NURBS curves and three-dimensional (3D) NURBS surfaces is developed. The proposed technique preserves and operates directly on the parametric description of the NURBS curve or surface. Therefore, the technique gives a projected point directly on the curve or surface when query points lie on the parametric curve or surface."). Point projection is described as projecting the point of interest onto the closest point of a curve or surface, wherein the distance function is a Euclidean distance function ((Liao, Page 1, ¶1-2) "Given a test point and a parametric entity (curve or surface), the generalized point projection problem is to find the closest point (footpoint) on the entity as well as the corresponding parameter value. Since the footpoint is the closest point on the curve or surface, the line connecting the test point to the footpoint is normal to the curve or the surface [1]: 𝑔(𝑢)=𝐂′(𝑢)·(𝐂(𝑢)−𝐏)=0g(u)=C′(u)·(C(u)−P)=0 (1) Given a parametric curve or surface entity 𝐂(𝑢)∈ℝ𝑛C(u)∈Rn (u is treated as a vector when the entity is a surface), the Euclidean distance function 𝑑𝐸(𝐱)dE(x) is defined as the shortest distance from physical test point 𝐱x to 𝐂(𝑢)C(u) given by: 𝑑𝐸(𝐱)=inf𝑢∥𝐱−𝐂(𝑢)∥dE(x)=infu∥x−C(u)∥ (2) where 𝐂(𝑢)C(u) is a physical point on the curve or surface of interest.")
Liao is analogous art because it is reasonably pertinent to the problem of meshing and visualizing geometric models as well as computer-aided engineering and particularly of interest with regard to reduction of computational complexity of these tasks. It would have been obvious to one of ordinary skill to which said subject matter pertains at the time the invention was filed to have incorporated the teachings of Liao into the method of the proposed combination because some teaching, suggestion, or motivation in the prior art would have led one having ordinary skill in the art to combine the references to arrive at the claimed invention. Xiao teaches a structural model with material constraints, as stated previously. Liao teaches an explicitly-defined boundary of a domain and utilizing point projection to ensure accurate behavior analysis of the approximations of the domain ((Liao, Page 2, ¶4 ) "In any immersed boundary problem solution, capturing the interaction of the field approximation defined on the immersed (explicitly defined) boundary with the approximations on the enriched domain requires one to determine the nearest point on the boundary from any given point in the underlying domain. This projection from the spatial point to the boundary is necessary to compute the influence of the domain approximation on those approximations defined on the boundary (see Figure 2).").One having ordinary skill in the art would be motivated to combine the prior art references because Liao teaches that point projection is important in computer aided engineering applications (topology optimization) to ensure accurate analyses as boundaries evolve (such as during the model updates of the iterative steps taught by Xiao) ((Liao, Page 2, ¶2) "This problem is of importance in geometric modeling. For instance, while fitting a curve or surface to sampled data, one may need to compute corresponding parameter values and errors at data points since the error is the distance between the data point and the fitting curve or surface [2]. Point projection also plays an important role in computer aided engineering (CAE), especially when boundaries are immersed into the domain and evolved. Such immersed boundary analysis [3] uses a non-conforming mesh to significantly reduce computational cost required for mesh generation as the boundaries evolve. "). Therefore, one having skill in the art could incorporate an additional material constraint as a physical boundary by which the material cannot exceed (such as taught by Liao) into the material constraints (as taught by Xiao) and combine the teachings of the prior art references to arrive at the claimed invention.
Regarding claim 10, the proposed combination teaches The method of claim 8, wherein generating the refined model update as stated previously. The proposed combination further in view of Xiao teaches (except the limitations surrounded by brackets) [[comprises solving a piecewise linear equation to clamp points]] of the preliminary model update in accordance with the one or more material requirement constraints for the structure. Iterative calculations are performed indicating that an updated structural model can be preliminary to a subsequent round of iterative calculations that include updating the model again ((Xiao, ¶64-68) "Specifically, the iterative calculation of step S103 includes steps S201 to S204 , as shown in FIG. 2 . Step S201: Calculate the overall stiffness of the structural model. Step S202: Perform dynamic order reduction calculation on the core equation, wherein the core equation includes the equilibrium equation and the adjoint equation. Step S203: Calculate the objective function and its sensitivity, as well as the constraints and their sensitivity. Step S204: Optimize and solve and update design variables."). The design variables are understood to be those variables which define the structural model. ."). The iterative calculations are performed with consideration to the constraints in step S203. The constraints include that of a volume fraction limit, which is understood to be a material requirement constraint ((Xiao, ¶58-61) "Specifically, the optimization formula formed by constructing the objective function and the constraints can be expressed as follows: [[equations]] Among them, is the normalized equivalent stress corresponding to unit e, and the stress evaluation point is located at the geometric center of the unit; is the maximum normalized equivalent stress in the structural model; is the upper limit of stress applied to the structural model; c is the optimization target, that is, flexibility; ρ represents the array composed of unit density; u and f represent the displacement and external load arrays respectively; K represents the overall stiffness matrix; ve represents the unit volume; vf represents the predefined material volume fraction limit.").
The proposed combination in further view of Xiao does not teach; however, Liao teaches comprises solving a piecewise linear equation to clamp points A linear system is solved to enable point projection for Bezier segments ((Liao, Page 17, ¶4) "Projection in the physical space to the closest Bézier segment involves finding the gradient and Hessian of the Bezout/Dixon matrix, which requires the solution to a linear system (see Equations (21) and (22)). "). Level sets are used on Bezier segments, showing a discontinuous nature of the boundary, indicating the piece-wise nature of the solution ((Liao, Page 15, ¶4) "To compute 𝑢𝑓uf on a NURBS curve, which is piece-wise polynomial, projection onto the appropriate Bézier segment is required. For this purpose, one can identify the closest Bézier segment using individual algebraic level sets, and apply algebraic point projection on the closest Bézier segment."); (See Also Liao Figure 3). Projected points are referred to as control points, wherein control points are understood to clamp the geometry and behavior of a given model ((Liao, Page 3, Figure 2) "Figure 2. Behavioral analysis in the presence of complex free form embedded surface. The spatial point may only influence a local region of the surface with the highlighted control points, which can be identified by point projection."); ((Liao, Page 6, ¶2) "A well known property of Bézier and NURBS geometry is the convex hull property, which assures that the curve/surface is contained within its convex hull constructed using the control points.").
Liao is analogous art because it is reasonably pertinent to the problem of meshing and visualizing geometric models as well as computer-aided engineering and particularly of interest with regard to reduction of computational complexity of these tasks. It would have been obvious to one of ordinary skill to which said subject matter pertains at the time the invention was filed to have incorporated the teachings of Liao into the method of the proposed combination because some teaching, suggestion, or motivation in the prior art would have led one having ordinary skill in the art to combine the references to arrive at the claimed invention. Xiao teaches a structural model with material constraints, as stated previously. Liao teaches an explicitly-defined boundary of a domain and utilizing point projection that involves solving a piecewise linear equation to ensure accurate behavior analysis of the approximations of the domain ((Liao, Page 2, ¶4) "In any immersed boundary problem solution, capturing the interaction of the field approximation defined on the immersed (explicitly defined) boundary with the approximations on the enriched domain requires one to determine the nearest point on the boundary from any given point in the underlying domain. This projection from the spatial point to the boundary is necessary to compute the influence of the domain approximation on those approximations defined on the boundary (see Figure 2).").One having ordinary skill in the art would be motivated to combine the prior art references because Liao teaches that point projection is important in computer aided engineering applications (topology optimization) to ensure accurate analyses as boundaries evolve (such as during the model updates of the iterative steps taught by Xiao) ((Liao, Page 2, ¶2) "This problem is of importance in geometric modeling. For instance, while fitting a curve or surface to sampled data, one may need to compute corresponding parameter values and errors at data points since the error is the distance between the data point and the fitting curve or surface [2]. Point projection also plays an important role in computer aided engineering (CAE), especially when boundaries are immersed into the domain and evolved. Such immersed boundary analysis [3] uses a non-conforming mesh to significantly reduce computational cost required for mesh generation as the boundaries evolve."). Therefore, one having skill in the art could incorporate an additional material constraint as a physical boundary by which the material cannot exceed (such as taught by Liao) into the material constraints (as taught by Xiao) and combine the teachings of the prior art references to arrive at the claimed invention.
Claims 12 and 13 are rejected under 35 U.S.C. 103 as being unpatentable over Xiao as applied to claim 1 above, and further in view of Amir et al (Amir, O., Aage, N., and Lazarov, B., “On multigrid-CG for efficient topology optimization”, November 14, 2013, Structural and Multidisciplinary Optimization, Volume 49, pp 815-829), hereinafter referred to as Amir2013.
Regarding claim 12, the proposed combination teaches The method of claim 1, as stated previously. Xiao further teaches (except the limitations surrounded by brackets) wherein obtaining the first approximate FEA solution [[comprises performing one or more iterations of the Jacobi method.]] An approximate FEA solution is taught as being obtained in the multigrid method, as stated previously ((Xiao, ¶93) "The core equations are solved in a multi-fidelity global manner, including: solving the core equations using a multi-grid iterative algorithm, and using the obtained approximate solution as the global solution.")
Xiao does not teach; however, Amir2013 teaches comprises performing one or more iterations of the Jacobi method. A single damped Jacobi smoothening cycle is applied during a multigrid cycle ((Amir2013, Page 825, Col 1, ¶2) "Within the multigrid V-cycle, we apply a single damped Jacobi smoothening cycle with ω = 0.8.")
Xiao and Amir2013 are analogous arts because they are both related to the same field of endeavor of computationally efficient topology optimization methods. It would have been obvious to one of ordinary skill to which said subject matter pertains at the time the invention was filed to have incorporated the Jacobi method as part of a multigrid cycle taught by Amir2013 into the multigrid iterative solver taught by Xiao because some teaching, suggestion, or motivation in the prior art would have led one of ordinary skill in the art to combine the prior art references to arrive at the claimed invention. Xiao teaches the utilization of a multigrid solver with a smoothing process for deriving FEA solutions but does not give particular details into the particularities of the methodology used for the smoothing process. Similarly, Amir2013 teaches the utilization of a multigrid solver for deriving FEA solutions and further describes the utilization of the Jacobi method within the multigrid solver for smoothing purposes. Amir2013 explicitly discloses that smoothing is typically based on the Gauss-Seidel or Jacobi method ((Amir2013, Page 818, Col 1, ¶2) "Smoothing and coarse-grid correction. The smoothing process reduces the oscillatory error in the solution and is typically based on a stationary iterative method such as Gauss-Seidel or Jacobi"). Because the Jacobi method is described as being typically used for smoothing and Xiao does not explicitly disclose the methodology by which smoothing is done, one having ordinary skill in the art with the teachings of Xiao and Amir2013 before them would be motivated to combine the teachings of the prior art references to arrive at the claimed invention.
Regarding claim 13, the proposed combination teaches (except the limitations surrounded by brackets) The method of claim 1, as stated previously. Xiao further teaches wherein obtaining the first approximate FEA solution requires a solution of a set of linear equations having [[a linear]] computational complexity. The global solution (exact) for FEA is described as having high computational cost and the reduced solution (approximated) for FEA is described as having low computational cost ((Xiao, ¶89) "In the above-mentioned reduction calculation of the core equation, by judging the level of the force residual, the reduced solution with low computational cost is used instead of the global solution with high computational cost in each iteration to solve the core equation, thereby improving the computational efficiency, reducing the computational time, and reducing the total computational cost"). The multigrid solution that is used to approximate finite element solutions is further described as solving linear equations ((Xiao, ¶93) " The multigrid iterative algorithm is a fast iterative algorithm for solving linear equations derived from boundary value problems of partial differential equations."); ((Xiao, ¶110) " By using the above-mentioned multi-grid iterative algorithm to solve the core equations and taking the obtained approximate solution as the global solution, the amount of calculation is further reduced, the calculation efficiency is improved, and the calculation time is shortened.")
Xiao does not teach; however, Amir2013 teaches a linear computational complexity. The iterative solver of the multigrid method is described as having a computational cost of O(n), which is linear ((Amir2013, Page 818, Col 1, ¶2) "Multigrid (MG) is a multilevel iterative method originally developed for solving discretized homogeneous elliptic problems. Nowadays it constitutes a family of methods that can be used to solve also inhomogeneous and non-elliptic partial differential equations. MG is considered numerically scalable as it can provide the solution of a linear system for a computational cost of O(n).")
Xiao and Amir2013 are analogous arts because they are both related to the same field of endeavor of computationally efficient topology optimization methods. It would have been obvious to one of ordinary skill to which said subject matter pertains at the time the invention was filed to have incorporated the teachings of Amir2013 regarding computational complexity of the methodology disclosed by Xiao because some teaching, suggestion, or motivation would have led one of ordinary skill in the art to combine the references to arrive at the claimed invention. Xiao teaches that direct solves have high computational complexity and that iterative solves have reduced computational complexity but does not explicitly quantify the computational complexity of the different solve methods. Amir2013 discloses explicitly the computational complexities for direct solves and iterative solves. Amir2013 particularly discusses the multigrid method, which is leveraged by the methodology disclosed by Xiao and therefore there is an implicit suggestion as to seeking out the explicit computational complexity of the approaches. Therefore, it would have been obvious to combine the teachings of Amir2013 with the teachings of Xiao to arrive at the claimed invention such that the disclosure was more comprehensive in the quantification of the computational complexities of the solutions involved in the methodology.
Conclusion
The prior art made of record and not relied upon is considered pertinent to applicant's disclosure.
JP 5774733 B2 Discloses a topology optimization method using finite element method for structural analysis and notes that existing topology methods rely on sensitivity analyses.
Zheng et al. (Zheng, Z., and Ma, F., “An efficient gradient projection method for structural topology optimization”, November 2020, Advances in Engineering Software, Volume 149) disclose an efficient method for gradient projection for topological optimization problems.
Homayounfar et al. (Homayounfar, S., Tavakoli, R., and Bagheri, R., “Energy management through topology optimization of composites microstructure using projected gradient method”, July 22, 2015, Structural and Multidisciplinary Optimization, Volume 52, pp 1121-1133) discloses the projected gradient method for topology optimization applications, wherein a sensitivity analysis is performed using the adjoint sensitivity.
Applicant's amendment necessitated the new ground(s) of rejection presented in this Office action. Accordingly, THIS ACTION IS MADE FINAL. See MPEP § 706.07(a). Applicant is reminded of the extension of time policy as set forth in 37 CFR 1.136(a).
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/E.G.L./Examiner, Art Unit 2187
/EMERSON C PUENTE/Supervisory Patent Examiner, Art Unit 2187