Stress distributions of anisotropic three-dimensional semi-infinite bodies by a refined finite difference formulation

Abstract

This paper deals with normal and shear stress distributions of anisotropic three-dimensional (3D) semi-infinite bodies using improved finite difference method (FDM). In the numerical analysis of various mechanical problems involving complex partial differential equations, the FDM has an advantage over the finite element method in its ability to avoid mesh generation and numerical integration. In this study, one of the important points in the finite difference formulation for 3D anisotropic problems is the generalized approach for various boundary conditions. A large number of studies in FDM have been made on clamped or simple boundary conditions by merely an energy approach. These approaches cannot be satisfied, however, with pivotal points along the free boundary. This study addresses the 3D problem of anisotropic semi-infinite bodies by adopting a refined 3D finite difference modeling elimination of pivotal difference points in the case of a free boundary condition. Moreover, the numerical examples present stress distribution characteristics through the depth direction of more complicated anisotropic semi-infinite bodies. The study also demonstrates the differences between the displacement and stress characteristics of isotropic, orthotropic and anisotropic cases.