Bending and free vibration analysis of orthotropic in-plane functionally graded plates using a Chebyshev spectral approach

This paper presents a Chebyshev spectral approach for the bending and free vibration analysis of orthotropic in-plane functionally graded (IPFG) plates with general boundary conditions. Material properties and distributed loadings are assumed to be varying in the plane of the plates arbitrarily. Both of them are approximated by high-order Chebyshev expansions combining with Gauss-Lobatto sampling. Then, based on the Mindline-Reissner first-order shear deformation theory, the governing equations for the bending and free vibration are derived for orthotropic IPFG plates respectively by employing the principle of minimum total potential energy and the Lagrange's equation, which are consistent for any kind of material and loading distribution. Several numerical examples, involving various boundary conditions, types of loadings, and thickness length ratios, are presented to demonstrate the accuracy and efficiency of the proposed method. The results are compared with those reported in the literature and those obtained by commercial finite element software ABAQUS. Excellent agreements are observed, demonstrating the effectiveness of the Chebyshev spectral method for the static and dynamic analysis of orthotropic IPFG plates.