des DFG-Sonderforschungsbereichs 393

Numerische Simulation auf massiv parallelen Rechnern

Zeit: Freitag, 6.12.2002, 11:30 Uhr
Ort: Reichenhainer Straße 70, B 202
Vortragender: U.-J. Goerke, A. Bucher, R. Kreissig (SFB, D2)
Thema: Adaptive FEM for Geometrically and Physically Nonlinear Problems in Solid Mechanics

Real stress states are frequently characterized by large stress gradients. They occur in damage areas, near cracks, at the boundary of plastic regions or in contact zones of components and structures modelling, for instance, forming processes. A realistic numerical simulation of large stress gradients by Finite Element Methods essentially depends on a suitable FE mesh in the corresponding regions of the component. Especially for the incremental solution of geometrically and physically nonlinear problems commonly accompanied by a large number of load steps adaptive remeshing algorithms in contrast to global remeshing procedures or the generation of unnecessary fine coarse grids provide an efficient method for an effective simulation of critical states.

The authors present the application of an adaptive strategy for refining and coarsening of FE-meshes developed at the Chemnitz University of Technology for linear problems to the nonlinear solid mechanics problem of the simulation of anisotropic elastic-plastic material behaviour in case of large deformations. Crucial point is the useful embedding of the adaptive remeshing algorithms into the incremental solution of the boundary value problem with a restart of the current load step after remeshing to improve the convergence rate of the equilibrium iterations. In this context details of the transfer of displacements, strains, stresses and internal variables to newly generated nodes and integration points are presented. In contrast to usual nonlinear Finite Element strategies the integration of the deformation law has to be carried out additionally in the nodes of the FE mesh. The authors give special attention to the application of residual a posteriori error estimators for the indication of edges for subdividing which proved to be problematic in case of nonlinear analysis for several reasons. Particularly the problem of choosing a suitable criterion of convergence of the refining process could not yet be settled completely and universally valid. Finally, some examples are shown.

Das Seminar wird von Prof. Meyer geleitet. Interessenten sind herzlich eingeladen.

Gerd Kunert,