A reliable incremental method of computing the limit load in deformation plasticity based on compliance : Continuous and discrete setting

The aim of this paper is to introduce an enhanced incremental procedure that can be used for the numerical evaluation and reliable estimation of the limit load. A conventional incremental method of limit analysis is based on parametrization of the respective variational formulation by the loading parameter ζ ∈ (0, ζlim), where ζlim is generally unknown. The enhanced incremental procedure is operated in terms of an inverse mapping ψ : α 7→ ζ where the parameter α belongs to (0, +∞) and its physical meaning is work of applied forces at the equilibrium state. The function ψ is continuous, nondecreasing and its values tend to ζlim as α → +∞. Reduction of the problem to a finite element subspace associated with a mesh Th generates the discrete limit parameter ζlim,h and the discrete counterpart ψh to the function ψ. We prove pointwise convergence ψh → ψ and specify a class of yield functions for which ζlim,h → ζlim. These convergence results enable to find reliable lower and upper bounds of ζlim. Numerical tests confirm computational efficiency of the suggested method.