Three-dimensional thermo-elastoplastic analysis of thick functionally graded plates using the meshless local Petrov–Galerkin method

A numerical method based on the meshless local Petrov–Galerkin (MLPG) method is presented for three-dimensional (3D) thermo-elastoplastic analysis of thick functionally graded (FG) plates subjected to combined thermal and mechanical loads. The FG plate is assumed to be made of two constituents, whose volume fractions vary continuously in the thickness direction according to a power law. All material properties are considered to be temperature dependent. The von-Mises yield criterion and isotropic strain hardening rule are employed to describe the elastoplastic behaviors of the FG plates. The weak form is derived using the 3D equilibrium equations, and then it is transformed into local integral equations on brick-shaped local sub-domains by using a Heaviside step function as the test function. The proposed approach makes it possible to distribute more nodes in the direction of the material variation to construct the shape and test functions. Consequently, more accurate solutions can be obtained easily and effectively. Several numerical examples for temperature, displacement and stress analysis of thick FG plates are presented for different material gradients and boundary conditions. The obtained results have been compared with accurate finite element results and an excellent agreement has been observed.