Meshless approach for thermo-mechanical analysis of functionally graded materials

On the basis of analog equation theory, the method of fundamental solutions coupling with radial basis functions (MFS–RBF), a meshless algorithm is developed to simulate the static thermal stress distribution in two-dimensional (2D) functionally graded materials (FGMs). The analog equation method (AEM) is used to obtain the equivalent homogeneous system to the original nonhomogeneous equation, after which RBF and MFS are used to construct the related approximated particular part and complementary part, respectively. Finally, all unknowns are determined by satisfying the governing equations in terms of displacement components and boundary conditions. Numerical experiments are performed for different 2D structures made of FGMs, and the proposed meshless method is validated by comparing available analytical and numerical results.