Generalized shear deformation theory for functionally graded isotropic and sandwich plates based on isogeometric approach

Abstract

A generalized shear deformation theory for static, dynamic and buckling analysis of functionally graded material (FGM) made of isotropic and sandwich plates is presented in this paper. Two new distribution functions are proposed in the present formulation. These functions determine the distribution of the transverse shear strains and stresses across the thickness of the plates. The present theory is derived from the classical plate theory (CPT), and hence the shear locking phenomenon can be ignored. It has same number of degrees of freedom as the first order shear deformation theory (FSDT), but it does not require shear correction factors because the shear stress free surface conditions are naturally satisfied. As demonstrated in the following sections, the proposed theory yields very accurate prediction for displacement, stresses, natural frequencies and critical buckling load compared to three-dimensional (3D) elasticity solution. Galerkin weak form of static, free vibration and buckling models for FGM isotropic and sandwich plates are used to create the discrete system of equations. This weak form requires C1-continuity for generalized displacements. It can be solved by a number of methods such as analytical methods, finite element methods based on the Hermite interpolation functions, meshfree method and recently developed NURBS based isogeometric analysis (IGA). The NURBS basis functions used in IGA are Cp−1 continuous and therefore can easily satisfy the C1-continuity condition. Numerical examples are presented to illustrate the effectiveness of the proposed method compared to other methods reported in the literature.