Meshless local Petrov-Galerkin analysis for 2D functionally graded elastic solids under mechanical and thermal loads

Numerical solutions obtained by the meshless local Petrov-Galerkin (MLPG) method are presented for 2D functionally graded solids, which is subjected to either mechanical or thermal loads. The MLPG method is a truly meshless approach, as it does not need any background mesh for integration in the weak form. In this MLPG analysis, the penalty method is used to efficiently enforce the essential boundary conditions, and the test function is chosen to equal the weight function of the moving least squares approximation. Two types of material gradations are considered; one is based on the continuum model in which material properties are assumed to be analytical functions (e.g. exponential or power law variation of material properties) and the other is based on the micromechanics model in which the effective material properties are determined by either the Mori-Tanaka or self-consistent scheme. Examples are given for different types of 2D structural components made of the functionally graded materials, namely, the link bar, circular cylinder and simply supported beam. Results obtained from the MLPG method are validated by available analytical and numerical solutions. Different profiles of non-homogeneity of material constituents are also investigated to assess the response of 2D functionally graded solids.