# US 2021/0173979 A1 · Geometrical Dimensionality Control in Optimization > Agents: this data is available as JSON from the patentgrep API and MCP server — see https://patentgrep.com/llms.txt - Number: US 2021/0173979 A1 - Document ID: US20210173979A1 - Status: Published application - Kind: A1 - Application number: 17/114,577 - Filed: 2020-12-08 - Published: 2021-06-10 - Earliest claimed: 2019-12-10 - Assignees: Dassault Systemes Simulia Corp. - Applicants: Dassault Systemes Simulia Corp. - Inventors: Nikolai Gerzen; Claus Bech Wittendorf Pedersen; Thorsten Horst Henryk Michalski - Web page: https://patentgrep.com/patent/US20210173979A1 ## CPC - G06F 30/23: using finite element methods [FEM] or finite difference methods [FDM] - G06F 30/10: Geometric CAD - G06T 17/20: Finite element generation, e.g. wire-frame surface description, {tesselation} - G06F 2111/04: Constraint-based CAD - G06F: ELECTRIC DIGITAL DATA PROCESSING (computer systems based on specific computational models G06N) - G06T: IMAGE DATA PROCESSING OR GENERATION, IN GENERAL ## Abstract A computer-implemented method of automatically determining an optimized design for manufacturing a real-world object includes: defining, in memory of a computer-based processor, a finite element model representing a real-world object, the finite element comprising a plurality of elements; evaluating, with the computer-based processor, a distribution of a design variable throughout a vicinity of the finite element model, using singular value decomposition (SVD), to produce a singular value for the design variable in each respective element in the vicinity of the finite element model; defining optimization constraints for the vicinity of the finite element model based on the singular values produced from the SVD; and optimizing the finite element model with respect to the design variable by locally enforcing a geometry of the real-world object in the vicinity based on the defined optimization constraints. ## Claims ### Claim 1 A computer-implemented method of automatically determining an optimized design for manufacturing a real-world object, the method comprising: defining, in memory of a computer-based processor, a finite element model representing a real-world object, the finite element comprising a plurality of elements; evaluating, with the computer-based processor, a distribution of a design variable throughout a vicinity of the finite element model, using singular value decomposition (SVD), to produce a singular value for the design variable in each respective element in the vicinity of the finite element model; defining optimization constraints for the vicinity of the finite element model based on the singular values produced from the SVD; and optimizing the finite element model with respect to the design variable by locally enforcing a geometry of the real-world object in the vicinity based on the defined optimization constraints. ### Claim 2 (depends on 1) The computer-implemented method of claim 1, further comprising: updating a property of a given one of the elements in the finite element model to reflect the optimized design variable, thereby creating an optimized model of the real-world object for manufacturing. ### Claim 3 (depends on 2) The computer-implemented method of claim 2, further comprising: determining, with the computer-based processor, whether optimization has converged; and depending on an outcome of the computer-based processor's determination: starting a new optimization cycle; or creating a final optimized design, wherein the computer-based processor determines that the optimization has converged if constraints for associated design responses have been fulfilled and if an associated objective function has been optimized. ### Claim 4 (depends on 2) The computer-implemented method of claim 2, further comprising: causing the real-world object to be manufactured according to the final optimized design. ### Claim 5 (depends on 1) The computer-implemented method of claim 1, wherein the design variable represents relative density, and wherein design responses represent compliance, stiffness, stress, strain, force, modal eigenfrequency, and/or other typical structural design responses. ### Claim 6 (depends on 1) The computer-implemented method of claim 1, wherein defining the optimization constraints comprises: applying, with the computer-based processor, a smoothing approximation function to each of the singular values produced from the SVD to produce smoothed approximations; identifying, with the computer-based processor, additional values by performing an SVD where all elemental design variable values are set to a predetermined value; and calculating the optimization constraints utilizing the smoothed approximations and the additional values. ### Claim 7 (depends on 1) The computer-implemented method of claim 1, wherein evaluating the distribution of the design variable throughout the vicinity of the finite element model, using singular value decomposition (SVD), comprises, using the computer-based processor to: read data, from the memory of the computer-based processor, representing a geometrical description of the finite element model from memory; solve equilibriums of the finite element model based on the data; model design responses and equilibrium design responses and associated sensitivities with respect to the design variable based on the data; and determine design responses and sensitivities of calculated singular values for geometrical dimensionality control with respect to design variables. ### Claim 8 (depends on 7) The computer-implemented method of claim 7, wherein defining the optimization constraints comprises: applying, with the computer-based processor, the design responses to define an optimization problem consisting of constraints to be fulfilled and an objective function to optimized. ### Claim 9 (depends on 8) The computer-implemented method of claim 8, wherein defining the optimization constraints further comprises: solving the optimization problem with the computer-based processor using an optimization computation based upon user-defined values of design targets, design responses, and sensitivities of the design responses. ### Claim 10 A computer-based system for automatically determining an optimized design for manufacturing a real-world object, the computer-based system comprising: a computer-based processor; and computer-based memory coupled to the computer-based processor, wherein computer-based memory stores data that defines a finite element model representing a real-world object, the finite element comprising a plurality of elements, and wherein the computer-based memory stores computer-readable instructions that, when executed by the computer-based processor, cause the computer-based processor to: evaluate a distribution of a design variable throughout a vicinity of the finite element model, using singular value decomposition (SVD), to produce a singular value for the design variable in each respective element in the vicinity of the finite element model; define optimization constraints for the vicinity of the finite element model based on the singular values produced from the SVD; and optimize the finite element model with respect to the design variable by locally enforcing a geometry of the real-world object in the vicinity based on the defined optimization constraints. ### Claim 11 (depends on 10) The computer-based system of claim 10, wherein the computer-based memory stores further computer-readable instructions that, when executed by the computer-based processor, cause the computer-based processor to: update a property of a given one of the elements in the finite element model to reflect the optimized design variable, thereby creating an optimized model of the real-world object for manufacturing. ### Claim 12 (depends on 11) The computer-based system of claim 11, wherein the computer-based memory stores further computer-readable instructions that, when executed by the computer-based processor, cause the computer-based processor to: determine whether optimization has converged; and depending on an outcome of the determination: start a new optimization cycle; or create a final optimized design, wherein the computer-based processor determines that the optimization has converged if constraints for associated design responses have been fulfilled and if an associated objective function has been optimized. ### Claim 13 (depends on 12) The computer-based system of claim 12, wherein the computer-based memory stores further computer-readable instructions that, when executed by the computer-based processor, cause the computer-based processor to: cause the real-world object to be manufactured according to the final optimized design. ### Claim 14 (depends on 10) The computer-based system of claim 10, wherein the design variable represents relative density and wherein a design response represents compliance, stiffness, stress, strain, force, modal eigenfrequency, and/or other typical structural design responses. ### Claim 15 (depends on 10) The computer-based system of claim 10, wherein the instructions that cause the computer-based processor to define the optimization constraints, further comprise instructions that cause the computer-based processor to: apply a smoothing approximation function to each of the singular values produced from the SVD to produce smoothed approximations; identify, with the computer-based processor, additional values by performing an SVD where all elemental design variable values are set to a predetermined value; and calculate the optimization constraints utilizing the smoothed approximations and the additional values. ### Claim 16 (depends on 10) The computer-based system of claim 10, wherein the instructions that cause the computer-based processor to evaluate the distribution of the design variable throughout the vicinity of the finite element model, using singular value decomposition (SVD), further comprise instructions that cause the computer-based processor to: read data, from the memory of the computer-based processor, representing a geometrical description of the finite element model from memory; solve equilibriums of the finite element model based on the data; model design responses and equilibrium design responses and associated sensitivities with respect to the design variable based on the data; and determine design responses and sensitivities of calculated singular values for geometrical dimensionality control with respect to design variables. ### Claim 17 (depends on 16) The computer-based system of claim 16, wherein the instructions that cause the computer-based processor to define the optimization constraints further comprise instructions that cause the computer-based processor to: apply the design responses to define an optimization problem consisting of constraints to be fulfilled and an objective function to optimized. ### Claim 18 (depends on 17) The computer-based system of claim 17, wherein the instructions that cause the computer-based processor to define the optimization constraints further comprise instructions that cause the computer-based processor to: solve the optimization problem with the computer-based processor using an optimization computation based upon user-defined values of design targets, design responses, and sensitivities of the design responses. ### Claim 19 A non-transitory computer readable medium having stored thereon computer-readable instructions that, when executed by a computer-based processor, causes the computer-based processor to: evaluate a distribution of a design variable throughout a vicinity of the finite element model, using singular value decomposition (SVD), to produce a singular value for the design variable in each respective element in the vicinity of the finite element model; define optimization constraints for the vicinity of the finite element model based on the singular values produced from the SVD; and optimize the finite element model with respect to the design variable by locally enforcing a geometry of the real-world object in the vicinity based on the defined optimization constraints. ### Claim 20 (depends on 19) The non-transitory computer program product of claim 19, wherein the computer readable medium further comprises computer-readable instructions that, when executed by the computer-based processor, causes the processor to: updating a property of a given one of the elements in the finite element model to reflect the optimized design variable, thereby creating an optimized model of the real-world object for manufacturing.