A Three-Dimensional Comparative Study of the Isoparametric Graded Boundary and Finite Element Methods for Nonhomogeneous FGM Plates with Eccentric Cutouts

Abstract

In the present paper, a comparative study is presented between three-dimensional (3D) graded finite element and boundary integral equation methods capable of modeling quasi-static behaviors of heterogeneous plates with circular holes made of functionally graded materials (FGMs). The formulations are derived based on the 3D theory of elasticity. The volume fractions of the constituent materials of the FGM plates are assumed to vary through the thickness direction according to an exponential law. The graded finite element formulations are developed based on the Rayleigh–Ritz energy method. Somigliana stress identity is implemented numerically for 3D elasticity analysis of the heterogeneous isotropic plates, employing graded elements. Based on the resulting governing equations and the weighted residual technique, an effective boundary element formulation is implemented for the elastic FGM plates. To verify numerical results of the present work, several examples are provided. The comparison made for a homogenous plate shows an excellent concordance between the results.