Asymmetric thermal buckling of annular plates on a partial elastic foundation

Abstract

ABSTRACTIn this investigation, the asymmetrical buckling behavior of isotropic homogeneous annular plates resting on a partial Winkler-type elastic foundation under uniform temperature elevation is investigated. First-order shear deformation plate theory is used to obtain the governing equations and the associated boundary conditions. Prebuckling deformations and stresses of the plate are obtained under the solution of a plane stress formulation, neglecting the rotations and lateral deflection. Applying the adjacent equilibrium criterion, the linearized stability equations are obtained. The governing equations are divided into two sets. The first set, which is associated with the in-contact region, and the second set, which is related to contact-less region. The resulting equations are solved using a hybrid method, including the analytical trigonometric functions through the circumferential direction and generalized differential quadratures method through the radial direction. The resulting system of eigenvalue problem is solved to obtain the critical conditions of the plate and the associated circumferential mode number. Benchmark results are given in tabular and graphical presentations for combinations of simply supported and clamped types of boundary conditions. Numerical results are given to explore the effects of elastic foundation, foundation radius, plate thickness, plate hole size, and the boundary conditions.