A nonlinear theory for thin elastic plates

Abstract

The purpose of this thesis is to derive a nonlinear theory of thin elastic rectangular plates including the effects of transverse normal stress, transverse shear stress, and transverse and rotary inertia. This nonlinear theory also includes the effects of the square of the rotation terms in the strain-displacement equations and the product of stress times rotation terms in the equilibrium equations. Using a -variation theorem due to Reissner, the equations of motion, the stress-strain relationships, and the associated natural and forced boundary conditions are simultaneously determined. The resulting equations may be applied to a certain group of rectangular plate problems where the applied dynamic loads produce deformations which are of such an order that only an appropriate nonlinear theory can account for them.