Algorithmic aspects of deformation dependent loads in non-linear static finite element analysis

摘要

The present study focuses on algorithmic aspects related to deformation dependent loads in non-linear static finite element analysis. If the deformation dependency is considered only on the right hand side, a considerable increase in the number of iterations follows. It may also cause failure of convergence in the proximity of critical points. If in turn the deformation dependent loading is included within the consistent linearization, an additional left hand side term emerges, the so-called load stiffness matrix. In this paper several numerical test cases are used to show and quantify the influence of the two different approaches on the iteration process. Consideration of the complete load stiffness matrix may result in a cumbersome coding effort, different for each load case, and in certain cases its derivation is even not practicable at all. Therefore also several formulations for approximated load stiffness matrices are presented. It is shown that these simplifications not only reduce the additional effort for linearizaiton and implementation, but also keep the iterative costs relatively small and still allow the calculation of the entire equibrium path.