On applications of parallel solution techniques for highly nonlinear problems involving static and dynamic buckling

Within this contribution the efficient finite element analysis of shell structures with highly nonlinear behavior is presented. The coupled nonlinear system of equations resulting from the FE discretization is solved using Newton-like procedures, thus the solution of a linear system of equations is needed in each Newton iteration. For fine discretizations the resulting linear systems of equations become very large and their solution dominates the computational effort. Consequently, parallel computers offer major capabilities to reduce the CPU time needed. A geometrical approach for parallelization is used, standard methods for the graph partitioning are employed. It is well known that iterative methods for the solution of linear equation systems are much more suitable for parallelizing compared to direct methods. Therefore in a first step the use of such methods is investigated for the application to badly conditioned problems typical for shell problems in particular in failure situations with almost singular matrices. In the analysis of shell structures with tendencies to buckle a static and a dynamic approach are discussed considering both physical and computational aspects.