A new incremental method of computing the limit load in deformation plasticity models

Abstract

The aim of this paper is to introduce a new incremental procedure that can be used for numerical evaluation of the limit load. Existing incremental type methods are based on parametrization of the energy by the loading parameter $ζ\in[0,ζ_{lim})$, where $ζ_{lim}$ is generally unknown. In the new method, the incremental procedure is operated in terms of an inverse mapping and the respective parameter $α$ is changing in the interval $(0,+\infty)$. Theoretically, in each step of this algorithm, we obtain a guaranteed lower bound of $ζ_{lim}$. Reduction of the problem to a finite element subspace associated with a mesh $\mathcal T_h$ generates computable bound $ζ_{lim,h}$. Under certain assumptions, we prove that $ζ_{lim,h}$ tends to $ζ_{lim}$ as $h\rightarrow0_+$. Numerical tests confirm practical efficiency of the suggested method.