The axisymmetric branching behavior of complete spherical shells
Abstract : The purpose of the paper is to describe the axisymmetric branching behavior of complete spherical shells subjected to either external pressure or a centrally directed (dead) loading. By means of an asymptotic integration technique (based on the smallness of the ratio of the shell thickness to the shell radius) applied directly to a differential equation formulation, the authors are able to continue the solution branches from the immediate neighborhood of the branch points, where the solution has the functional form predicted by the linear buckling theory, to the region where the solution consists of either one or two dimples with the remainder of the shell remaining nearly spherical. The latter deflection states are the ones usually observed in experiments. The authors also deduce a number of results for the branching of solutions from the multiple eigenvalues. Finally, a boundary layer analysis is performed to determine the possible form of large deflection states. (Author)