Asymptotic forms of a simplified version of the non-linear Reissner equations for clamped elastic spherical caps under outward pressure

Abstract

A new, simplified version of Reissner's equations for the torsionless, axisymmetric deformation of elastically isotropic shells of revolution suffering small strains but large angles of rotation is specialized to clamped spherical caps under uniform outward pressure. The non-dimensional equations contain a thickness parameter, a shallowness parameter, and a load parameter. The latter two are written as powers of the former and the dependent variables scaled so that as the thickness parameter goes to zero, meaningful limit equations emerge. Seventeen distinct sets of simplified equations are found. In thirteen cases these are linear and the solutions are listed. These results should provide a useful set of benchmarks for testing the efficacy of numerical codes which often have difficulties with very thin shells.