A new incremental method of computing the limit load in deformation plasticity models
For researchers in computational plasticity, this method offers a theoretically grounded approach to compute limit loads with guaranteed lower bounds, though it is an incremental improvement over existing incremental methods.
The paper introduces a new incremental method for computing the limit load in deformation plasticity models, which provides guaranteed lower bounds and converges to the true limit load as mesh size decreases. Numerical tests demonstrate practical efficiency.
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.