A discontinuous quasi-upper bound limit analysis approach with sequential linear programming mesh adaptation

In this paper, a simple discontinuous upper bound limit analysis approach with sequential linear programming mesh adaptation is presented. Rigid, infinitely strong triangular elements with both linear and Bezier curved edges are considered. A possible jump of velocities is allowed at the interfaces between contiguous elements, thus allowing plastic dissipation on curved interfaces. Bezier curved edges are used with the sole aim of improving the element performance when dealing with limit analysis problems involving curved sliding lines. The model performs poorly for unstructured meshes (i.e. at the initial iteration), being unable to reproduce the typical plastic deformation concentration on inclined slip lines. Therefore, an iterative mesh adaptation based on sequential linear programming is proposed. A simple linearization of the non-linear constraints is performed, allowing to treat the non-linear programming (NLP) problem with consolidated linear programming (LP) routines. The choice of inequalities constraints on elements nodes coordinates turns out to be crucial on the algorithm convergence.Several examples are treated, consisting in the determination of failure loads for ductile, purely cohesive and cohesive-frictional materials. The results obtained at the final iteration fit well, for all the cases analyzed, previously presented numerical approaches and analytical predictions.