Finite Element Approach of Bending and Buckling Analysis of FG Beams Based on Refined Zigzag Theory

Abstract

This is the first attempt to utilize the refined zigzag theory (RZT) to study the bending and buckling behavior of a functional graded (metal/ceramic) thick beam. RZT, which has been exploited for the analysis of multilayered composite and sandwich beams does not employ shear correction factor. Furthermore, the number of kinematics variables of the RZT is not dependent to the number of layers in comparison with the layerwise theory. With regarding to the numerical solution, RZT, also requires C0 continuity interpolation, which leads to the development of this theory in finite element method. It is assumed that the mechanical properties of the beam varies through the thickness. According to the volume fraction of metal and ceramic, it is discretized across the thickness; consequently, the functionally graded beam (FGB) is modeled as a multi-layered one. The beam subjected to uniformly transverse and axial loadings. The equilibrium equations are established using the principle of virtual work. Using the shape functions of the first and second order forms, the non-isoparametric finite element consisting of three nodes and nine degrees of freedom are extracted. To confirm the excellent accuracy of the present approach, some numerical examples are provided and compared with those available in the literature that reveals that RZT is a trusty and validated theory to analyze the FG thick beams.