Meshless local Petrov-Galerkin analysis for thermoelastic deformations of functionally graded beams

Numerical solutions obtained by the Meshless Local Petrov-Galerkin (MLPG) method are presented for a functionally graded (FG) beam under either the mechanical or thermal load. 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 method, a 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. The FG beam is made of a two-phase mteal-ceramic composite that have a power law through-the-thickness variation of volume fractions of constituents. The effective material properties are computed by either the Mori-Tanaka or the self-consistent scheme. Results are computed for a simply supported beam to show the accuracy and validity of the MLPG method in analyzing thermo-mechanical deformations of the FG structures. Excellent agreements are obtained between the results of the MLPG method and the analytical solution. Parametric studies are also investigated for varying volume fractions of material constituents.