Membrane Theory for Layered Ellipsoidal Shells

The stress analysis of a laminated anisotropic ellipsoidal membrane shell of revolution is considered. A system of equations which is appropriate to the elastic behavior of anisotropic membrane shells of revolution is used as a basis. These equations are applied to the specific geometry of an ellipsoidal shell to develop the particular equations used in the analysis. Closed-form solutions are derived for the stresses and displacements. Methods for determining the extremely cumbersome integrals in the equations for the displacements are discussed as well. To illustrate the equations, solutions are presented for an ellipsoidal shell simply supported on one edge and subjected to internal pressure loading. Numerical results are presented for glass-epoxy and boron-epoxy material systems.