Isogeometric Analysis Mesh Refinement via Pre-Refinement Geometric Map
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Solution Overview
Problem
Current finite element analysis methods require approximated geometry, leading to inaccuracies in mechanical property testing of computer-designed parts, especially with curved surfaces, and struggle with optimal convergence in isogeometric analysis, particularly for Cr elements during h-refinement.
Innovation Solution
A system and method for creating meshes from CAD models using a pre-refinement geometric map that maintains consistency during refinement, allowing for controlled mesh creation and convergence towards refinement criteria, ensuring Cr smoothness and stability in isogeometric analysis.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Ease of manufacture
If conventional FEA uses approximated geometry to break parts into elements, then mesh generation becomes easier, but geometric accuracy and measurement precision deteriorate
Solution Approach 1:
The patent applies preliminary action by constructing a pre-refinement geometric map before mesh refinement. This geometric map preserves the exact CAD geometry and is used to guide the refinement process, ensuring that the exact geometry is maintained throughout mesh generation rather than being lost in approximation steps
Solution Approach 2:
The patent introduces a geometric map as an intermediary between the CAD model and the finite element mesh. This geometric map serves as a mediator that preserves exact geometry information while enabling mesh generation, allowing the system to maintain both geometric accuracy and mesh generation capability
2Adaptability or versatility
If T-splines are used for local mesh refinement, then flexibility in representing complex shapes improves, but treatment of extraordinary points and analysis-suitable refinement becomes more difficult
Solution Approach 1:
The geometric map acts as an intermediary that handles the complexity of extraordinary points and T-spline refinement. By using the geometric map to preserve geometry information, the patent simplifies the treatment of extraordinary points while maintaining the flexibility of T-splines for representing complex shapes
3Measurement precision
If Cr elements are used in isogeometric analysis, then numerical accuracy improves, but optimal convergence during h-refinement becomes difficult to achieve
Solution Approach 1:
The patent applies preliminary action by constructing the geometric map before refinement. This pre-established geometric map ensures that Cr continuity is maintained during h-refinement, enabling optimal convergence rates to be achieved while preserving the high numerical accuracy of Cr elements
4Measurement precision
If NURBS basis functions are used for both geometry representation and solution approximation, then geometric approximation error is eliminated, but device complexity increases
Solution Approach 1:
The patent applies universality by using NURBS basis functions for both geometry representation and solution approximation. This multi-functional use of the same basis functions eliminates geometric approximation error while the geometric map helps manage the associated complexity
Data Source
AI summary
A system and method for carrying out an isogeometric analysis process includes accessing the CAD model of the object from the memory. The process also includes analyzing the CAD model to generate a pre-refinement geometric map of the CAD object that has a smoothness projected to maintain a consistency of a geometric map based on the pre-refinement geometric map during a refinement of the mesh. The process further includes refining the mesh based on the pre-refinement geometric map to converge toward a refinement criteria associated with the CAD model.