Boundary integral based graded element for elastic analysis of 2D functionally graded plates

A two-dimensional (2D) elastic analysis of functionally graded materials (FGMs) is conducted using the proposed boundary integral based graded element formulation. The graded element model is based on independent internal and frame field approximations. The elemental stiffness contains element boundary integrals only and is calculated using the exact expression of the graded material property. In the construction of the element model, the fundamental solutions of functionally graded plate with quadratic variation of elastic properties are employed to construct the internal approximation and then the graded element is constructed, in which the material definition entails naturally graded variation. Three numerical examples are considered: verification of fundamental solutions, a functionally graded cantilever beam, and a functionally graded link bar, to assess the performance of the hybrid graded model and to show the advantages of FGMs over homogeneous materials.