A nonlinear theory for thin elastic shells

Abstract

The purpose of this thesis is to derive a nonlinear theory of thin elastic shells including the effects of transverse shear stress, in-plane stability forces, and transverse and rotary inertia. Using a variational theorem due to E. Reissner, the equations of motion, the stress-strain relationships, and the associated boundary conditions are simultaneously determined. The resulting equations may be applied to a particular group of shell problems where the applied statics and dynamic loads produce deformations which are of such an order that only appropriate nonlinear theory accounts for them. The resulting equations are simplified for the special case of a thin circular plate subjected to the above stress and loading conditions. An analogy is made with the problem of a thin rectangular elastic plate using rectangular cartesian co-ordinate analyzed by R. D. Mindlin.