2D Stress Analysis of an Infinite Plate with Orthotropic Inclusions by Embedding Continuous Force Doublet

Abstract

The body force method is an elastic stress analysis method based on the principle of superposition, where the concentrated force is distributed to satisfy the boundary conditions to obtain a highly accurate elastic solution. In the problem of orthotropic inclusions, the strain difference caused by orthotropic inclusions is expressed as a pair of concentrated forces called a force doublet. For this purpose, the interior of the orthotropic inclusion is discretized by triangular elements, and the fundamental solution of the force doublet is calculated by surface integrating inside the elements. The singularity of concentrated force doublet can be easily eliminated by Green’s theorem when distributing force doublet of uniform magnitude inside a triangular element. However, since the stress distribution inside the orthotropic inclusion is represented by a discontinuous function and the magnitude of the force doublet, the stress inside the inclusion cannot be analyzed accurately. By approximating the magnitude of the force doublet in a triangular element with a linear function, it is possible to obtain the internal stress distribution continuously. The method used to analyze the crack problem is applied to deal with the singularity of the concentrated force doublet. The above method was validated by solving the problem of orthotropic inclusions in the vicinity of the stress concentration.