A KINEMATIC VARIATIONAL PRINCIPLE FOR THIN METALLIC AND COMPOSITE PLATES EXPERIENCING LARGE DEFLECTIONS ABOVE THE VON KARMAN LIMITS

Abstract

Thin elastic plates (metallic or composite) experiencing large deflections are considered. The plate deflections are much larger than the plate thickness. The geometrically nonlinear elasticity theory and the Kirchhoff assumptions are employed. The elongations, the shears and the in-plane rotations are assumed to be small. A kinematic variational principle leading to a boundary value problem for the plate is derived. It is shown that the principle gives proper equilibrium equations and boundary conditions. For moderate plate deflections the principle is transformed to the case of the von Karman plate.