Effect of micromechanical models on stability of functionally graded conical panels resting on Winkler–Pasternak foundation in various thermal environments

Abstract

This work presents an analytical approach to investigate the mechanical buckling of functionally graded material (FGM) thin conical panels surrounded by Winkler–Pasternak foundation and exposed to thermal environments. The material properties of FGMs are assumed to be temperature-dependent and graded only in the thickness direction according to the power-law, sigmoid and the exponential distribution of volume fraction. Eight well-known types of micromechanical models, namely Voigt, Reuss, Mori–Tanaka, Hashin–Shtrikman, modified Wakashima–Tsukamoto, Halpin–Tsai, Tamura and LRVE estimations, are studied to determine the effective two-phase FGM material properties as a function of the particles’ volume fraction considering thermal effects. Further, it is been supposed that the FG conical panel is heated uniformly, linearly and nonlinearly through the thickness. The nonlinear temperature distribution is obtained based on Fourier’s law by applying a semi-analytical procedure. The fundamental relations and the basic equations are derived by using Love’s thin shell theory. Finally, the numerical results are provided to reveal the effect of explicit micromechanical model, FGM profile, temperature distribution with various thermal boundary conditions, foundation conditions and the geometric parameters on the stability of these panels. Additionally, the critical buckling load is compared with that of FG truncated conical shells, cylindrical panels and the cylindrical shells.