3D free vibration analysis of multi-directional FGM parallelepipeds using the quadrature element method

Abstract

• A novel element for analyzing 3D vibration of multidirectional FGM solid is established. • Stiffness matrix is explicitly given when integration points do not coincide with nodes to achieve higher accuracy. • Comparisons show the accuracy of the proposed multidirectional FGM parallelepiped element. In this paper, the existing quadrature element method (QEM) is extended to analyze the three-dimensional (3D) free vibration of multi-directional functionally graded material (FGM) parallelepipeds under general boundary conditions. The material properties vary continuously in multiple directions according to a power-law form. Formulations of the multi-directional FGM parallelepiped element are given. Since the element nodes do not coincide with the integration points, a different way is used to compute the strains at integration points to derive explicit element stiffness matrix. A number of case studies on multi-directional FGM square and rhombic thick plates with general boundary conditions and different power-law exponents have been conducted. The effect of power-law exponents and boundary conditions on the free vibration behavior of FGM plates is investigated. The natural frequencies are in excellent agreement with either existing results or data obtained by ABAQUS using fine meshes. It is demonstrated that the extended QEM is simple in formulations and capable of capturing the 3D vibration behavior of the multi-directional FGM plates with high precision. New results are presented and may be used as benchmark solutions for future researches.