Boundary Integral Equation Analysis of an Inhomogeneous Medium Made of Functionally Graded Materials

Abstract

The present work develops direct graded boundary integral equation formulation for behavior investigation of the inhomogeneous media made of functionally graded materials. The isoparametric boundary elements, the elastostatic governing equations and a weighted residual technique are implemented with the material characteristics that vary continuously along a given dimension. The resulting algorithm is capable of solving the quasistatic problems for elastic functionally graded media with a variety of the boundary conditions and loadings. The inhomogeneous media is made of a ceramic–metal mixture, in which the material properties vary continuously according to a power law graded distribution in a given direction. Avoiding the use of internal elements in the graded boundary element formulation is one of the main objectives of this paper, which results only in numerical discretization of the boundaries of the considered media. Some examples with continuously inhomogeneous isotropic materials were provided under different boundary conditions to evaluate the proposed numerical formulation for the FGMs.