A meshless BEM for 2-D stress analysis in linear elastic FGMs

Abstract

A meshless boundary element method (BEM) for stress analysis in two-dimensional (2-D), isotropic, continuously non-homogeneous, and linear elastic functionally graded materials (FGMs) is presented in this paper. It is assumed that Young's modulus has an exponential variation, while Poisson's ratio is taken to be constant. Since no fundamental solutions are yet available for general FGMs, fundamental solutions for isotropic, homogeneous, and linear elastic solids are applied, which results in a boundary-domain integral formulation. Normalized displacements are introduced in the formulation, which avoids displacement gradients in the domain-integrals. The radial integration method (RIM) is used to transform the domain-integrals into boundary integrals along the global boundary. The normalized displacements appearing in the domain-integrals are approximated by a series of prescribed basis functions, which are taken as a combination of radial basis functions and polynomials in terms of global coordinates. Numerical examples are presented to verify the accuracy and the efficiency of the present meshless BEM.