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

The present study focusses on algorithmic aspects related to deformation de pendent loads in non-linear static finite element analysis. If the deformat ion dependency is considered only on the right hand side, a considerable in crease in the number of iterations follows. It may also cause failure of co nvergence in the proximity of critical points. If in turn the deformation d ependent loading is included within the consistent linearization, an additi onal left hand side term emerges, the so-called load stiffness matrix. In t his paper several numerical test cases are used to show and quantify the in fluence of the two different approaches on the iteration process. Considera tion of the complete load stiffness matrix may result in a cumbersome codin g effort, different for each load case, and in certain cases its derivation is even not practicable at all. Therefore also several formulations for ap proximated load stiffness matrices are presented It is shown that these sim plifications not only reduce the additional effort for linearization and im plementation, but also keep the iterative costs relatively small and still allow the calculation of the entire equilibrium path.