A new semi-analytical solution of bending, buckling and free vibration of functionally graded plates using scaled boundary finite element method

This paper is devoted to study the bending response, free vibration and mechanical buckling of functionally graded material (FGM) plates based on the scaled boundary finite element method (SBFEM) for the first time. On the basis of the three-dimensional (3D) theory of elasticity, the SBFEM governing equations of the FGM plate are derived from the principle of virtual work and solved analytically in the thickness direction to obtain the displacements, stresses, natural frequencies and critical buckling loads. A high order spectral element only with three degrees of freedom per node that is able to satisfy the high order continuity of the displacement fields while facilitating the numerical computation is applied. In the present method, only the bottom surface of plate structures needs to be discretized while numerical approximations in the thickness direction are no longer required, which leads to an accurate solution of the displacement in the thickness direction and a considerable reduction of the computational cost. Furthermore, the model strictly follows 3D theory of elasticity without employing any kinematic assumptions of plate theory, so that it is able to eliminate the shear locking problem for numerical simulations of FGM plates when the thickness becomes thinner. Accuracy and superior computational efficiency of the present formulations have been verified by comparing with the available analytical and numerical solutions achieved by other researchers.