Bending and free vibration analysis of FG circular plates using a five unknown high order shear deformation theory

Abstract

In this study, the bending and free vibrations of functionally graded material (FGM) circular plates are investigated using a new quadrilateral finite element based on a five-unknown high-order shear deformation theory. The proposed model accounts for a quadratic distribution of the transverse shear stress through the plate thickness and zero transverse shear stress at the top and bottom surfaces of the plate. The properties of the plate are changed through its thickness according to a power law in which the index varies from 0 value for a fully ceramic plate to infinity for a fully metallic plate. The concept of the physical neutral plane is introduced to avoid membrane-bending coupling. The total potential energy principle and the kinetic energy are used to derive the elementary rigidity and mass matrices. The performance and the convergence of the developed element are demonstrated through examples from the literature. Furthermore, the effect of various parameters, such as the power law index and the radius-to-thickness ratio, on the plate behavior is also considered.