Symplectic Method-Based Analytical Solutions of Thermal Buckling for Shear Deformable Circular Functionally Graded Plates

Abstract

Thermal buckling of a shear deformable circular plate made of functionally graded materials (FGM) is studied using an exact analytical method in the Hamiltonian system. Fundamental equations for the thermal buckling of the plate under transversely nonuniform temperature rising are established based on the first-order shear deformation theory. Subsequently, by introducing the symplectic method, the differential equations are converted into canonical equations in the Hamiltonian system. Buckling loads and buckling modes correspond to symplectic eigenvalues and eigen solutions, respectively. The expressions of complete buckling modes in the form of special functions are achieved by solving canonical equations and boundary conditions analytically and exactly. The symplectic eigenvalues are obtained simultaneously and the buckling temperature increments are calculated using the inverse solution. Finally, the influences of the gradient characteristics, geometric parameters, boundary conditions, and type of thermal loading on the buckling temperature increments are discussed through parameter research.