Static and dynamic analysis of FG plates using a locking free 3D plate bending element

Abstract

The main contribution of this study is the development of an efficient element in modeling thin to thick functionally graded (FG) square plates. To accomplish this goal, a 3D plate bending element is developed by taking advantages of the mixed interpolation of tensorial components approach (MITC). The recommended element has four nodes with six degrees of freedom at each node. Both higher-order shear deformation and the thickness stretching are considered. A fully 3D constitutive relation is adopted. Utilizing an assumed strain field for transverse normal strain causes the element to perform well, even when the thickness becomes thin. Based on the rule of mixture and Mori–Tanaka scheme, a Voigt model is also employed in this study to represent through the thickness distribution of FG material property. Static, free and force vibration analyses of the square FG plates, with different boundary conditions, are investigated in this paper. Several benchmark problems are studied to demonstrate the ability of the element in the static and dynamic analysis of thin/thick plates. Moreover, the effects of different power index and boundary conditions on the response of plate are also investigated.