Automated Mechanical Design Analysis Using Parametric Grid Embedding
Find Innovative SolutionsGenerate Solutions
Solution Overview
Problem
Conventional CAD systems face challenges in solving Partial Differential Equations (PDEs) on volumetric NURBS representations, particularly in shape optimization, due to the need for repeated conversion and remeshing, which limits their effectiveness in design optimization.
Innovation Solution
The system performs automated analysis and optimization by parameterizing CAD models using NURBS patches, embedding them in a simulation grid for consistent geometry, and employing modified quadrature rules and XFEM to handle complex subvolumes and shape changes efficiently.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Productivity
If volumetric mesh representation is used to solve PDEs, then computational feasibility is improved, but differentiability and optimization capability deteriorate due to repeated conversion and remeshing requirements
Solution Approach 1:
The patent introduces a volumetric grid as an intermediary structure that mediates between the boundary representation (NURBS) and the PDE solver. The grid serves as a fixed reference framework that does not need to be regenerated during optimization, while still allowing accurate representation of complex geometries through the boundary definition approach.
Solution Approach 2:
The patent changes the fundamental parameter from mesh-based representation to boundary-based parameterization. By using NURBS control points and boundary definitions as the primary parameters, the system achieves both computational efficiency and differentiability, as these parameters can be directly manipulated for optimization without requiring remeshing.
2Manufacturing precision
If NURBS boundary representation is used for CAD, then modeling precision and manufacturability are improved, but PDE solution capability deteriorates due to lack of volumetric representation
Solution Approach 1:
The patent segments the volumetric domain into a structured grid while maintaining the boundary representation for geometric definition. This segmentation allows the PDE solver to operate on a regular grid structure that is computationally efficient, while the NURBS boundary provides the precise geometric information needed for manufacturing.
Solution Approach 2:
The patent transitions from a 2D boundary surface representation to a 3D volumetric grid representation for PDE solving. This dimensional change enables efficient volumetric computation while the boundary NURBS patches maintain geometric precision through their parameterization.
3Adaptability or versatility
If repeated conversion and remeshing is performed for design optimization, then design flexibility is improved, but computational cost and time increase significantly
Solution Approach 1:
The patent performs the grid generation and volumetric representation setup as a preliminary action that is done once and remains fixed during optimization. The boundary NURBS definition is established beforehand, and the corresponding volumetric grid is pre-computed, eliminating the need for repeated generation during design iterations.
Solution Approach 2:
The patent creates a fixed copy of the volumetric grid structure that mirrors the boundary geometry. This grid copy serves as a stable computational framework that does not need to be regenerated when design parameters change, as it faithfully represents the geometry at any given design state.
Data Source
AI summary
An automated mechanical design analysis system includes a computing platform having a hardware processor and a system memory storing a software code. The hardware processor executes the software code to receive an input model of a mechanical object, identify one or more design parameter(s) of the input model for automated analysis, and perform a parametric mapping of the input model based on the design parameter(s) to produce a parameterized model corresponding to the input model. The hardware processor further executes the software code to embed the parameterized model in a grid to produce model-grid intersections defining multiple subvolumes of the parameterized model, and generate a simulation of the input model based on the model-grid intersections and the subvolumes, where the simulation of the input model provides a differentiable mathematical representation of the input model.