Sensitivity Investigations Concerning the Stability of Thin-Walled Shell Structures
In stability investigations with finite element methods standard procedures are based on the static approach. However, when investigating shell structures, many numerical problems occur, e.g. “bad” convergence behaviour in the vicinity of bifurcation points and in the post-buckling regime. Furthermore, the physical meaning of unstable paths computed with static methods such as arc-length procedures is questionable, as buckling is in reality a dynamic process. Thus, using transient FE-analysis not only the real behaviour is captured but in addition the pre- and post-buckling states can be computed with improved convergence behaviour, due to the “better” condition number of the effective system matrix. As a result of progression in computers and computational techniques, nowadays such transient analyses can be performed with moderate computational effort. The applications in this contribution include cylindrical silo shells under axial loading and external pressure, first with the goal to detect the minimum post-buckling load. Then a sensitivity analysis of stable equilibrium states in the pre-buckling region follows using finite perturbations. The latter allows a quantitative judgement of stable equilibrium states concerning stability. Finally some considerations are added for a possible use in design.