Mesh deformation based on fully stressed design: The method and 2-D examples

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.