Notes on Nonlinear Shell Theory

Exact tensor equations of equilibrium are derived for nonlinear membrane shell theory and small perturbations of pressurized membrane shells. Approximate equations (for sufficiently small initial strains and rotations) for small perturbations of pressurized membrane shells are also given. Exact equations for the general nonlinear shell theory (including bending) are discussed, and approximate equations (again for small initial strains and rotations) are derived for the small perturbations, buckling, and vibration of stressed shells. These last equations are given in an Appendix in lines-of-curvature coordinates in classical notation.