Voxelized Mesh Boundary Conditions for Accurate Generative Design
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Solution Overview
Problem
Existing CAD software struggles with accurate application of boundary conditions on voxelized meshes during generative design, leading to inaccurate simulation results and poor design outcomes.
Innovation Solution
Applying boundary conditions on voxelized meshes using local coordinate systems and interpolation constraints to ensure precise distribution of loading values and displacement constraints, leveraging Saint-Venant's principle to enhance accuracy and allow for more complex conditions.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If boundary conditions are applied using traditional methods on voxelized meshes, then the generative design process can be performed, but the simulation results become inaccurate
Solution Approach 1:
The patent introduces an intermediary transformation process that converts boundary conditions from the B-Rep domain to the Voxel domain through a systematic mapping approach. This intermediary layer resolves the incompatibility between exact surface representations and discrete voxel grids, enabling accurate boundary condition application without requiring direct manipulation of complex geometric representations.
Solution Approach 2:
The patent applies parameter transformation by converting boundary condition parameters (forces, moments, displacements) from continuous B-Rep space into discrete voxel-node equivalents. This involves calculating equivalent nodal forces and moments by integrating over the surface geometry and distributing them according to the voxel mesh topology, thereby preserving physical accuracy in the discrete domain.
2Productivity
If B-Rep models are converted to voxelized meshes for generative design, then computational efficiency improves, but boundary condition application accuracy deteriorates
Solution Approach 1:
The patent segments the boundary condition application process into distinct stages: (1) identifying surface voxels that correspond to B-Rep surfaces, (2) calculating equivalent nodal loads by integrating boundary conditions over the surface geometry, and (3) distributing these loads to voxel nodes through a systematic mapping. This segmentation allows the system to maintain B-Rep accuracy where needed while using efficient voxelized representations for computational domains.
Solution Approach 2:
The patent replaces direct mechanical application of boundary conditions on voxel surfaces with a computational substitution approach. Instead of physically applying forces to voxel faces (which would be inaccurate), the system computes equivalent nodal forces through integration and transformation, substituting the mechanical application process with a mathematical equivalence that preserves accuracy.
3Reliability
If complex boundary conditions are applied to ensure accuracy, then simulation reliability improves, but computational resource requirements increase
Solution Approach 1:
The patent applies local quality by concentrating computational effort only where boundary conditions are applied, rather than processing the entire voxelized model uniformly. The surface identification and equivalent nodal load calculation are performed only on voxels corresponding to boundary surfaces, while the rest of the domain uses standard efficient voxelized FEM procedures, thereby reducing overall computational cost.
Data Source
AI summary
Methods, systems, and apparatus, including medium-encoded computer program products, for computer aided design of physical structures include: obtaining a design space, design criteria, and boundary conditions for numerical simulation; defining an application of the boundary conditions to a voxelized mesh, including specifying a distribution of a load to nodes of voxels in the voxelized mesh that correspond to a surface of preserve geometry; and iteratively modifying a generatively designed three dimensional shape in the design space in accordance with the design criteria and a physical response of the modeled object determined by the numerical simulation performed using the application of the boundary conditions to the voxelized mesh, wherein the distribution of the total loading value during determination of the physical response ensures an equivalence between the total loading value and a sum of loading values distributed to the respective nodes of the voxels that correspond to the surface.