Theoretical and numerical studies of nonlinear shell equations

We study the solution field M of a parameter dependent nonlinear two-point boundary value problem presented by Troger and Steindl [H. Troger, A. Stein dl, Nonlinear Stability and Bifurcation Theory, Springer, Wien, New York, 1 991]. This problem models the buckling of a thin walled spherical shell und er a uniform external static pressure. The boundary value problem is formul ated as an abstract operator equation T(x,;lambda) = 0 in appropriate Banac h spaces. By exploiting the equivariance of T, we obtain detailed informati ons about the structure of M. These theoretical results are used to compute efficiently interesting parts of M with numerical standard techniques. Bif urcation diagrams, a stability diagram and pictures of deformed shells are presented. (C) 1999 Elsevier Science B.V. All rights reserved.