Symplectic Framework-Based New Analytic Solutions for Thermal Buckling of Temperature-Dependent Moderately Thick Functionally Graded Rectangular Plates

Abstract

This paper presents some new analytic thermal buckling solutions of temperature-dependent moderately thick functionally graded (FG) rectangular plates with non-Lévy-type constraints within the symplectic solution framework in the Hamiltonian system. An original problem is reduced to the superposition of two constructed subproblems that are analytically solved via the rigorous symplectic elasticity approach with mathematical techniques such as variable separation in the symplectic space and symplectic eigen expansion. The physical neutral surface is employed to remove the stretching-bending coupling in constitutive equations. The main characteristic of the present symplectic superposition strategy is on the rational derivation without assumption on solution forms, which, however, is hard to achieve by conventional semi-inverse methods. Comprehensive benchmark results are presented, including critical buckling temperatures as well as mode shapes of typical non-Lévy-type FG plates in uniform and nonlinear temperature fields, and are verified by available numerical results. The effects of boundary constraint, aspect ratio, volume fraction exponent, and thickness-to-width ratio on buckling temperatures are quantitatively investigated. The occurrence of thermal buckling is further studied by presenting a failure mode map covering a wide range of geometric parameters.