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

1432-0924

Springer Online Journal Archives 1860-2000

Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics

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.

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