Parallel multilevel solution of nonlinear shell structures
Thin-walled-structures discretized by finite elements lead to ill-conditioned matrices, and therefore the performance of iterative solvers is generally poor. This situation further deteriorates when the thickness change of the shell is taken into account. Here a preconditioner for this challenging class of problems is presented combining two approaches in a parallel framework. The first approach is a mechanically motivated improvement called `scaled director conditioning' (SDC), and is able to remove the extra-ill conditioning that appears with three-dimensional shell formulations as compared to formulations that neglect thickness change of the shell. It is introduced at the element level and harmonizes well with the second approach utilizing a multilevel algorithm. The authors demonstrate that shell models based on relative displacements including thickness change beside their numerous advantages tend to be even worse conditioned than those based on rotational degrees of freedom. It is shown that this parametrization-dependent disadvantage of three-dimensional models can be eliminated by the scaled director conditioning approach. This means that the `spectral gap' between different models can easily be closed. The SDC approach is introduced into a three-dimensional, geometrically and materially nonlinear shell formulation and is applied along with a hybrid finite element discretization. The SDC approach is combined with a semi-algebraic multilevel preconditioner based on an aggregation concept. The combination of the two methods results in a stable iterative solution process capable of achieving good performance for a wide range of large-scale problems in nonlinear shell dynamics and statics.
scientific article; zbMATH DE number 5009883