Non-Linear Bending Analysis of Moderately Thick Functionally Graded Plates Using Generalized Differential Quadrature Method

Linear and non-linear bending analysis of moderately thick functionally graded (FG) rectangular plates with different boundary conditions are presented using generalized differential quadrature (GDQ) method. The modulus of elasticity of plates is assumed to vary according to a power law distribution in terms of the volume fractions of the constituents. Based on the first-order shear deformation theory and Von Karman type non-linearity, the governing system of equations include a system of thirteen partial differential equations (PDEs) in terms of unknown displacements, forces and moments. To derive linear system of equations, non-linear terms are omitted in former equations. Presence of all plate variables in the governing equations provides a simple procedure to satisfy different boundary conditions. Successive application of the GDQ technique to the governing equations resulted in a system of non-linear algebraic equations. The Newton–Raphson iterative scheme is then employed to solve the resulting system of non-linear equations. Illustrative examples are presented to demonstrate accuracy and rapid convergence of the presented GDQ technique. Accuracy of the results for both displacement and stress components are verified with comparing the present results with those of analytical and finite element methods. It is found that the theory can predict accurately the displacement and stress components even for small number of grid points.