Elastic buckling of circular plates allowing for prebuckling deformation

Abstract

The effect of prebuckling deformation on the elastic buckling of circular plates is studied. Based on Treffz's initial stress theory, the energy functional is obtained from which the governing differential equation for equilibrium can be derived via calculus of variations. Exact and simple approximate closed-from critical-load expressions are obtained after solving the two-point boundary value problem. The effect of the nonlinear terms involving in-plane displacements in the Green-Lagrange strain expressions on the solutions is also investigated. For circular plates with relatively large thickness-to-radius ratios, the allowance for prebuckling deformation affects the critical load of clamped plates more than simply supported plates. This occurs because the prebuckling deformation is greater in clamped plates, since they undergo higher loads before buckling.