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 $h\rightarrow0_+$. Numerical tests confirm practical efficiency of the suggested method.
Categories: math.NA