Stability analysis of FGM plates by using layer wise displacement model

Abstract

In this paper, the stability analysis of simply supported functionally graded material (FGM) plate under mechanical in–plane compressive loads is analyzed. The displacement model based on Generalized Laminate Plate Theory (GLPT) assumes piece–wise linear variation of in–plane displacements, constant transverse displacement, non–linear strain–displacement relations (in von Karman sense) and linear material properties. The properties of FGMs are assumed to be constant in xy–plane and vary through thickness by a power law function in terms of volume fraction of the constituents. The mathematical model includes the quadratic variation of transverse shear stresses within each layer of the plate. The principle of virtual displacements (PVD) is used to derive Euler–Lagrange differential equations of linearized buckling problem. Closed form solution is derived following the Navier’s technique and solving the eigenvalue problem. The original MATLAB computer program is coded for the numerical solution. The results reveal that the effects of side–to–thickness ratio, power–low index and modulus ratio have significant effect on critical buckling loads of FGM plates.