Abstract
Based on the relationship between finite element (FE) solution and mesh size, a new approach based on mesh depending on the material properties is proposed to make the finite element analysis results more efficient and more close to the optimal solution. This optimal solution is often evaluated either by experiment or by finite element method (FEM). At the opposite of the accuracy obtained by sensitivities analysis of the FEM which requires time-consuming, our approach allows getting the optimal meshing based on the material properties.
Highlights
The solving process in finite element method (FEM)includes four main steps: first step, is to discrete the physical model
Meshing is a critical step in FEM [1,2,3]
The choice of mesh size in FEM is the eternal question for numerical simulation [4,5]
Summary
Includes four main steps: first step, is to discrete the physical model. Second step, is to determine the governing equations and their boundary conditions. Meshing is a critical step in FEM [1,2,3] It affects directly the accuracy of analysis results. For FEM under certain conditions, the accuracy of the mesh is more precise when it’s size is quite small. Such as small size lead to high computation cost. When we select the mesh size for FE simulation, there must be some error in the FE solution and in the solution of the differential equation. For the FEM using the displacement method, the stiffness of the finite element model increases with the increase of the mesh size under certain conditions [10,11,12,13]. We propose a new approach to identify the mesh dependency on material properties to solve this problem
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