Meshfree-Enriched Finite Element Method for Structural Simulation
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Solution Overview
Problem
Traditional Finite Element Analysis (FEA) and meshfree methods face challenges in accurately simulating structural behaviors in compressible and near-incompressible regions, such as volumetric locking, due to mesh distortion and computational inefficiencies, which hinder precise predictions of structural responses under various environmental loads.
Innovation Solution
The implementation of a meshfree-enriched finite element method (ME-FEM) that enriches finite elements with additional meshfree nodes, applying a displacement-based first-order convex meshfree approximation and area-weighted integration to ensure divergence-free properties and avoid pressure oscillations, thereby improving the accuracy of structural simulations.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If traditional FEM is used for structural simulation, then computational efficiency is maintained, but accuracy deteriorates due to volumetric locking in compressible and near-incompressible regions
Solution Approach 1:
The patent merges FEM and meshfree methods into a hybrid ME-FEM approach. Meshfree nodes are added to enrich the displacement field within elements, combining the structured efficiency of FEM with the flexibility of meshfree methods to eliminate volumetric locking while maintaining computational tractability
Solution Approach 2:
The methodology creates a composite numerical model combining conventional finite elements with meshfree enrichment. The displacement field is represented as a combination of element-based shape functions and meshfree radial basis functions, creating a composite approximation scheme that leverages the strengths of both approaches
2Reliability
If meshfree method is used to avoid mesh distortion, then accuracy in large deformation is improved, but computational cost increases significantly
Solution Approach 1:
Instead of fully implementing meshfree methods throughout the entire domain, the patent applies meshfree enrichment only partially within selected finite elements. This partial enrichment provides the necessary accuracy for handling large deformations and incompressibility while significantly reducing the overall computational cost compared to full meshfree implementation
Solution Approach 2:
The computational domain is segmented into conventional finite elements, and within each element, meshfree nodes are strategically placed to provide enrichment only where needed. This segmentation allows the model to maintain FEM efficiency in regions requiring less accuracy while applying meshfree capabilities where high accuracy is critical
3Productivity
If conventional FEM elements are used, then computational efficiency is maintained, but pressure oscillations occur in near-incompressible regions
Solution Approach 1:
Meshfree nodes serve as intermediary degrees of freedom within finite elements that mediate between the displacement field and pressure field. These intermediate nodes provide additional flexibility to the displacement approximation, enabling more accurate pressure calculation in near-incompressible regions without sacrificing computational efficiency
Solution Approach 2:
The patent changes the parameters of the displacement approximation by adding meshfree enrichment functions with different radial basis functions (Gaussian, Lagrange, B-spline). This parameter enrichment allows the model to accurately capture pressure distributions in near-incompressible materials while maintaining the computational efficiency of the underlying FEM framework
Data Source
AI summary
System, method and software product for numerically simulating structural behaviors of an engineering product in compressible and near-incomprssible region is disclosed. Meshfree enriched finite element method (ME-FEM) is used for such numerical simulation. ME-FEM requires an engineering product be represented by a FEM model comprising a plurality of finite elements. Finite elements used in the ME-FEM are generally low-order finite elements. Each of the finite elements in the FEM model is enriched by at least one meshfree enriched (ME) node located within the element's domain. Each ME node has additional degrees-of-freedom for the element it belongs independent from those of the corner nodes. A displacement based first-order convex meshfree approximation is applied to the ME node. The convex meshfree approximation has Knonecker-delta property at the element's boundary. The gradient matrix of ME-FEM element satisfies integration constraint. ME-FEM interpolation is an element-wise meshfree interpolation that is discrete divergence-free at the incompressible limit.