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 $\zeta \in [0,{\zeta }_{lim})$, where ${\zeta }_{lim}$ is generally unknown. In the new method, the incremental procedure is operated in terms of an inverse mapping and the respective parameter $\alpha$ is changing in the interval $(0,+\infty )$. Theoretically, in each step of this algorithm, we obtain a guaranteed lower bound of ${\zeta }_{lim}$. Reduction of the problem to a finite element subspace associated with a mesh ${\mathcal{T}}_h$ generates computable bound ${\zeta }_{lim,h}$. Under certain assumptions, we prove that ${\zeta }_{lim,h}$ tends to ${\zeta }_{lim}$ as $h\to 0_{+}$. Numerical tests confirm practical efficiency of the suggested method.

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