Boundary-based finite element method for anisotropic functionally graded materials

This paper presents a boundary-based finite element method (BFEM) for stress analysis of anisotropic functionally graded materials (FGMs). By using the method of piece-wise homogeneous layers, the problem is reduced approximately to the case of an anisotropic elastic plate containing N layers. Each layer is made of different material constants and thus can be solved by the BFEM. In the BFEM, the relation between the nodal force of the finite element and the surface traction of the boundary element is employed, which allows the combination of boundary elements in each layer to form a single finite element and assemble following the rule of the finite element method. BFEM does not require domain meshing, which then reduces the computational and meshing efforts. The BFEM can capture both anisotropy and gradation effects and can be applied to both continuous and discontinuous anisotropic FGMs. With the proposed BFEM, numerical examples are presented to demonstrate the correctness and the versatility of the method. In these numerical examples, the results are compared with the existing analytical solutions. In addition, parametric studies are conducted to investigate the influence of material anisotropy, gradation property, and selection of fundamental solutions on the responses of anisotropic FGMs.