Adaptive Analysis of Bifurcation Points of Shell Structures

In recent years many procedures for stability investigations based on the Finite Element Method have been developed to compute the so-called stability points of structures in order to judge the stability. However, in engineering practice predominantly knock-down factors based on experiments are used for the design loads. The reason for such a procedure is the hard to quantify sensitivity of shell structures – especially of cylindrical shells – against perturbations like geometrical and loading imperfections or imperfections in boundary conditions. The standard procedure as also proposed in design rules is based on the computation of the limit load taking into account the modification of the bifurcation load resp. the snap-through load due to geometrical imperfections. Thus, the eigenvalueproblem for stability points have to be computed very accurately. In the present contribution an adaptive h-refinement procedure is taken for the solution using low order shell elements. The algorithm is partially based on the well-known a-posteriori error estimator of Zienkiewicz and Zhu [Zie92] with the stresses computed using the eigenvectors instead of displacement vectors, as e.g. proposed by Stein et al. [Stein94].