Static response of advanced composite plates by a new non-polynomial higher-order shear deformation theory

The static responses of functionally graded plates are investigated by using an accurate recently developed higher order shear deformation theory (HSDT), which is also compared with other HSDTs available in the literature. A practical generalized numerical code for solving the plate governing equations, which can include the shear strain shape functions of existing HSDTs, is utilized. The plate governing equations and boundary conditions are derived by employing the principle of virtual work. Navier-type analytical solution is obtained for FG plates subjected to transverse bi-sinusoidal and distributed loads for simply supported boundary conditions. For the generality of the present HSDT, a continuous isoparametric Lagrangian finite element with 7 of freedom per node are also presented. Results are provided for thick to thin FG plates and for different volume fraction distributions. The accuracy of the present code is verified by comparing it with various HSDTs available in the literature. Results show good agreement between the HSDTs for normal and transversal displacements, normal stresses and in-plane shear stresses. However, opposite occurs for transverse shear stresses. It is because the shear stress results are sensible to the shear strain shape functions used in the formulation of displacement field of a particular HSDT having five unknowns.