Variational Solutions of the Von Karman Plate Theory Based on a Mixed Formulation

by Wan-Lee Yin, Georgia Inst of Technology, Atlanta, United States,

Document Type: Proceeding Paper

Part of: Engineering Mechanics


A mixed formulation, involving the transverse deflection w(x,y) and the in-plane stress function F(x,y) as the unknown variables, will be used to obtain improved variational solutions of the von Karman theory of plates. The appropriate variational functional is obtained naturally from the total potential energy functional by using the partial Legendre transformation. Certain boundary conditions involving the in-plane displacements come out as natural boundary conditions and, therefore, are satisfied automatically in the solution process in the sense of weighted integrals. Rayleigh-Ritz solutions are obtained by the present method for the axisymmetric postbuckling problem of a clamped circular plate and superior accuracy and convergence trends are found when compared with similar solutions based on a purely displacement formulation.

Subject Headings: Plates | Displacement (mechanics) | Post buckling | Boundary conditions | Automation and robotics | Integrals | Energy methods | Axisymmetry

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