A nonlinear optimization procedure for limit analysis

We propose a nonlinear optimization algorithm for the general limit analysis problem, where plastic behavior is described by means of a multimodal nonlinear yield function. Four equivalent mathematical formulations of limit analysis are first considered. Then, the algorithm is developed as a sequence of Newtonian iterations on the set of optimality equalities, followed by a sort of line search consisting of step relaxations combined with stress scaling. The method is specially developed to take advantage of the structure of the limit analysis problem arising from most finite element discretizations. Several mixed and kinematical finite elements for limit analysis are also presented and tested in numerical applications involving large scale models.