A Complementary Energy Theorem for Composite Plates in Postbuckling

Abstract

A composite von Karman plate in postbuckling is considered. Using the first Piola stress tensor and the displacement gradient tensor, a complementary energy variational theorem is proven. The proof is given in the case of symmetric lay-up. According to the theorem, at the actual stress state of the plate the complementary energy (as a function of the internal forces and of the moments) reaches its stationary value. The stationary feature of the actual state is valid as compared to other states satisfying the static equilibrium and the static boundary conditions. It is shown how the theorem may be generalized to the case of a non-symmetric lay-up.

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