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

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 multidirectional FGM plates with high precision. New results are presented and may be used as benchmark solutions for future researches. (C) 2018 Elsevier Inc. All rights reserved.