Analytical solutions for elastic deformation of functionally graded thick plates with in-plane stiffness variation using higher order shear deformation theory

Abstract

Abstract This paper presents the deformation solution of functionally graded (FG) plates with variation of material stiffness through their length using higher order shear deformation theory (HSDT) including stretching effects. The present theory accounts for both the shear deformation and thickness stretching effect by a sinusoidal variation of the displacement field across the thickness. Equations of motion are derived from Hamilton's principle, and the relevant governing equations of elasticity are solved with a power law distribution of material property (material stiffness) to derive the analytical solution of the deflection of the FG plate. The problem is then modelled using the finite element method (FEM). The resultant analytical solutions are verified against the finite element (FE) solutions. The FE solutions are obtained using linear hexahedral solid elements with spatially graded property distribution (at different Gauss points), which is implemented by a user material subroutine (UMAT) in the ABAQUS FE software. It can be concluded that the present exact formulation is not only accurate, but also simple in predicting the bending of FG plates. Also, this study can be applied to find the optimum material distribution to produce controlled-stiffness distribution in FG plates corresponding to prescribed characteristics. Moreover, the good agreement found between the exact solution and the numerical simulation demonstrates the effectiveness of graded solid elements in the modelling of FG plate deflection under bending.