ELASTIC BUCKLING OF CIRCULAR PLATES ALLOWING FOR PREBUCKLING DEFORMATION

The effect of prebuckling deformation on the elastic buckling of circu lar plates is studied. Based on Trefftz's initial stress theory, the e nergy functional is obtained from which the governing differential equ ation for equilibrium can be derived via calculus of variations. Exact and simple approximate closed-form critical-load expressions are obta ined after solving the two-point boundary value problem. The effect of the nonlinear terms involving in-plane displacements in the Green-Lag range strain expressions on the solutions is also investigated. For ci rcular plates with relatively large thickness-to-radius ratios, the al lowance for prebuckling deformation affects the critical load of clamp ed plates more than simply supported plates. This occurs because the p rebuckling deformation is greater in clamped plates, since they underg o higher loads before buckling.