Inverse Pre-Deformation Finite Element Mesh for Metal Forming
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Solution Overview
Problem
Conventional finite element analysis methods for large deformation, such as Lagrangian analysis, result in distorted elements that lead to inaccurate results, slow convergence, and premature analysis termination, particularly in metal-forming processes like forging and extrusion, due to the limitations of adaptive remeshing and Arbitrary Lagrangian-Eulerian (ALE) techniques.
Innovation Solution
The method employs inverse pre-deformation to generate a deformed input mesh by performing a pre-analysis, mapping node locations from the deformed mesh to the undeformed boundary, and using techniques like bubble analysis and barycentric interpolation to improve mesh quality, reducing the occurrence of inverted and ill-shaped elements.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Stability of the object's composition
If pure Lagrangian method is used for large deformation analysis, then the mesh follows material deformation throughout the analysis, but severe mesh distortion occurs leading to inaccurate results and premature termination
Solution Approach 1:
The patent performs a preliminary analysis to predict the deformed configuration of the mesh before the actual analysis. Based on this prediction, a pre-deformed mesh is generated that anticipates the distortion that would occur during analysis. This preliminary action prevents severe mesh distortion during the actual analysis by starting with a mesh that is already adapted to the expected deformed state.
Solution Approach 2:
Instead of deforming a uniform mesh forward to its final configuration, the patent inverts the approach by generating a mesh that is pre-deformed in the opposite direction of the expected distortion. The pre-deformed mesh is created by applying an inverse transformation to the predicted deformed configuration, so that when the actual deformation occurs, the elements maintain better shape quality.
2Shape
If adaptive remeshing is used to replace distorted mesh, then mesh quality is improved, but computational cost increases significantly due to complete remeshing and variable mapping
Solution Approach 1:
The patent performs mesh generation and pre-deformation as preliminary actions before the main analysis. By predicting the deformed configuration in advance and generating an appropriately pre-deformed mesh, the need for adaptive remeshing during the analysis is reduced or eliminated, thereby avoiding the high computational cost of repeated remeshing and variable mapping operations.
Solution Approach 2:
The patent skips the adaptive remeshing step entirely by using a pre-deformed mesh that is designed to maintain element quality throughout the analysis. This allows the analysis to rush through the deformation process without needing to pause for remeshing operations, significantly reducing computational cost while maintaining mesh quality.
3Duration of action of stationary object
If ALE method is used to reduce remeshing, then mesh topology is maintained, but computational cost is much higher than pure Lagrangian analysis due to mesh velocity calculations
Solution Approach 1:
The patent extracts the essential benefit of ALE (maintaining mesh topology and avoiding remeshing) while removing the computationally expensive components (mesh velocity calculations and arbitrary mesh motion). By using a pre-deformed mesh with fixed topology that naturally accommodates deformation, the method achieves ALE-like continuity without the overhead of ALE formulation.
Solution Approach 2:
The patent uses a simple pre-deformed mesh configuration that is computationally inexpensive to generate and maintain. Rather than implementing the complex, expensive ALE framework, the patent employs a simpler approach that achieves the same practical effect (maintained mesh quality without remeshing) at a fraction of the computational cost.
4Ease of manufacture
If uniform input mesh is used for Lagrangian analysis, then mesh generation is simple, but inverted and ill-shaped elements occur at later stages of analysis
Solution Approach 1:
The patent performs a preliminary analysis to predict how a uniform mesh would deform during the actual analysis. Based on this prediction, a pre-deformed mesh is generated that compensates for the expected distortion. This preliminary action transforms the simple uniform mesh into a more complex pre-deformed mesh that will maintain element quality throughout the analysis, thereby improving reliability while starting from an easy-to-generate base mesh.
Data Source
AI summary
Finite element analysis methods and computer systems for analyzing deformation to an object are disclosed. According to various embodiments, the method includes the steps of: (1) performing a partial analysis on the object to generate a deformed boundary for the object from an undeformed boundary for the object; (2) generating a first deformed input mesh for the object based on the deformed boundary; (3) mapping node locations from the first deformed input mesh to the undeformed boundary for the object; and (4) performing an analysis on the undeformed boundary of the object using the first deformed input mesh.