Closed-form expression for nonlinear analysis of imperfect sigmoid-FGM plates with variable thickness resting on elastic medium

With the aim of reducing the weight of structures, functionally graded materials (FGM) plates with variable thickness have been widely used in various engineering applications such as aeronautical, mechanical and ocean structures. However so far, the analytical approaches for analyzing the instability behaviors of FGM plates with variable thickness are still somehow limited in the literature. The paper hence presents an analytical approach to investigate the influences of variable thickness on buckling and postbuckling behavior of imperfect sigmoid FGM (S-FGM) plates resting on elastic medium subjected to compressive loading. The material properties of S-FGM plates are assumed to be graded in the thickness direction according to a simple power law distribution in terms of the volume fractions of the constituents. Governing equations are based on the classical plate theory with von Karman-type geometric nonlinearity. The initial geometrical imperfections of plates are also accounted. By using the Galerkin procedure and the Airy stress function, the resulting equations are solved to obtain the closed form expressions for nonlinear equilibrium paths. The effects of power-law indices, coefficients of foundation, initial geometrical imperfections and geometrical parameters on nonlinear stability of plates are comprehensively investigated. The results reveal that the variable thickness of plate has a significant effect on the buckling behavior of S-FGM plates under compression loading.