Mesh deformation based on fully stressed design: the method and 2‐D examples
Su‐Yuen Hsu, Chau‐Lyan Chang · International Journal for Numerical Methods in Engineering · 2007
Abstract Mesh deformation in response to redefined boundary geometry is a frequently encountered task in shape optimization and analysis of fluid–structure interaction. We propose a simple and concise method for deforming meshes defined with three‐node triangular or four‐node tetrahedral elements. The mesh deformation method is suitable for large boundary movement. The approach requires two consecutive linear elastic finite element analyses of an isotropic continuum using a prescribed displacement at the mesh boundaries. The first analysis is performed with homogeneous elastic property and the second with inhomogeneous elastic property. The fully stressed design is employed with a vanishing Poisson ratio and a proposed form of equivalent strain (modified Tresca equivalent strain) to calculate, from the strain result of the first analysis, an element‐specific Young's modulus for the second analysis. The theoretical aspect of the proposed method, its convenient numerical implementation using a typical linear elastic finite element code in conjunction with very minor extra coding for data processing, and results for examples of large deformation of 2‐D meshes are presented in this paper. Copyright © 2007 John Wiley & Sons, Ltd.