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arXiv · 1511.02681

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

Jaroslav Haslinger·Sergey Repin·Stanislav Sysala
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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.

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Jaroslav Haslinger, Sergey Repin, Stanislav Sysala. 2015-11-09. A new incremental method of computing the limit load in deformation plasticity models. https://doi.org/10.1016/j.cam.2016.02.035

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