Plane Orthotropic Layer by Transfer Matrix‐Spline Boundary Element

Abstract

Stress analysis of anisotropic layers under various loading conditions is of interest in the mechanics of composites or geomechanics. In an attempt to develop an efficient numerical approach for such an analysis, a solution method is developed herein. Based on the state space approach and the Fourier transform, the fundamental solution for an orthotropic elastic layer under the action of arbitrary surface loads and volume forces is obtained in the form of infinite integrals, which are then evaluated numerically. In order to remedy the slow convergence of the numerical integrals associated with the fundamental solution, a procrustean technique is introduced. The fundamental solution is then implemented in the spline‐boundary‐element method and a computational strategy for the numerical implementation is discussed. As an illustrative example, a problem of anisotropic layer containing an elliptic cavity is considered for two different boundary conditions and numerical results are compared to the finite‐element solutions.