Numerical solution of an elastic boundary layer problem using a multiple shooting technique

A model is described for large axisymmetric deformations of a linearly elastic spherical shell compressed between two rigid plates. The deformation of the free region may be determined from a two-point boundary value problem, but the presence of a boundary layer makes the solution difficult by standard techniques. Solutions found by a multiple shooting method with some special features are presented here for a number of cases. Numerical evidence suggests that the onset of buckling in the contact region is controlled by a single nondimensional parameter.