Asymmetric Buckling of Spherical Caps With Asymmetrical Imperfections

Abstract

The title problem has been solved using the nonlinear relaxation technique to treat the finite-difference representation of the differential equations governing cap response. For clamped spherical caps designated by λ = 6, buckling loads are somewhat lower for the same imperfection magnitudes than those obtained previously for asymmetric and axisymmetric buckling. The three differential equations of the Marguerre type are set up in terms of three displacement quantities as the dependent variables. The equations are formulated so as to allow arbitrary initial imperfections, boundary conditions, and loading. The computer program setup to solve these equations was checked by successfully solving simpler problems, the solutions of which are in the literature. Although the buckling loads for spherical caps with asymmetric initial imperfections appear reasonable, it is not possible to ascertain at this point whether the cap results are indicative of what the full shell might do.