Gaussian Basis Shape Optimization for CAE Meshing
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Solution Overview
Problem
Existing topology optimization methods in computer-aided engineering (CAE) face challenges with efficient performance due to large numbers of bits required for finer meshes, leading to degraded convergence and potential checkerboard problems in shape optimization.
Innovation Solution
The use of Gaussian functions as basis functions for shape optimization, where the presence or absence of material is determined by a normalized Gaussian network, allowing for efficient optimization by reducing the number of bits needed and avoiding discrete material distribution issues.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If topology optimization uses annealing with bits assigned to CAE meshes to determine material disposition, then the shape optimization can be performed, but the number of bits becomes enormous when meshes are made finer, leading to degraded convergence and reduced efficient performance
Solution Approach 1:
The design region is divided into a plurality of regions, and Gaussian functions are assigned to each region instead of individual meshes. This segmentation approach reduces the total number of binary variables from the mesh count to the region count, enabling finer meshing within each region without proportionally increasing the bit requirement.
Solution Approach 2:
The patent introduces a hierarchical dimension by defining regions that contain multiple meshes. The optimization operates at the region level using Gaussian functions, while the underlying mesh structure remains fine-grained. This dimensional hierarchy allows fine meshes to be represented compactly through regional Gaussian function combinations.
2Measurement precision
If topology optimization uses annealing with a large number of bits for finer meshes, then measurement precision improves, but convergence degrades and efficient performance is reduced
Solution Approach 1:
By segmenting the design region into manageable sub-regions and applying Gaussian functions at this coarser level, the patent reduces the computational complexity of the annealing process. The optimization converges faster because it operates on fewer binary variables (region-level Gaussians) while still achieving fine shape determination through the combination of these regional functions.
Solution Approach 2:
The hierarchical structure creates a computational advantage where the optimization proceeds efficiently at the region level while the fine mesh detail is recovered through the Gaussian function combinations, achieving both fast convergence and high precision.
3Shape
If topology optimization uses traditional mesh-based approaches, then shape optimization can be performed, but checkerboard problems may occur due to discrete material distribution
Solution Approach 1:
The patent employs Gaussian functions, which are inherently smooth and continuous mathematical functions with curved profiles. These functions replace the discrete, step-like material distribution of traditional mesh approaches, producing smooth transitions and eliminating the checkerboard artifact by enforcing continuity through the Gaussian function forms.
4Manufacturing precision
If the number of CAE meshes is increased to improve optimization accuracy, then manufacturing precision improves, but the number of bits required for annealing increases enormously
Solution Approach 1:
The patent segments the fine mesh structure into coarser regions for optimization purposes. Each region is represented by a Gaussian function with binary coefficients, allowing the system to achieve fine mesh-level accuracy through the mathematical combination of regional Gaussians while requiring bits only for the regional representation, not for each individual mesh.
Solution Approach 2:
The patent introduces a hierarchical dimension where region-level Gaussian coefficients serve as control variables for fine mesh material distribution. This dimensional separation allows fine optimization accuracy to be achieved through the mathematical properties of Gaussian combinations rather than through proportional increases in binary variable count.
Data Source
AI summary
A non-transitory computer-readable storage medium storing an optimization program that causes at least one computer to execute a process, the process includes setting, for a region of a design target, a plurality of Gaussian functions as basis functions of a shape function that corresponds to a shape of a design target item in the region; and identifying the shape of the design target item indicated by the shape function obtained by combining the plurality of Gaussian functions identified to be disposed by identifying whether to dispose the plurality of Gaussian functions.