A nonlinear theory for thin elastic shells including the effects of transverse shear stress, transverse normal stress and transverse and rotary inertia

Abstract

The purpose of this thesis is to derive a nonlinear theory of thin elastic shells including the effects of transverse normal stress, transverse shear stress, and transverse and rotary inertia. Using a variation theorem due to Reissner, the equations of motion, the stress-strain relationships, and the associated natural boundary conditions are simultaneously determined. The resulting equations may be applied to a certain group of shell problems where the applied dynamic loads produce deformations which are of such an order that only an appropriate nonlinear theory can account for them.