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)ζ∈(0,ζlim), where ζlimζlim is generally unknown. The enhanced incremental procedure is operated in terms of an inverse mapping ψ:α↦ζψ:α↦ζ where the parameter αα belongs to (0,+∞)(0,+∞) and its physical meaning is work of applied forces at the equilibrium state. The function ψψ is continuous, nondecreasing and its values tend to ζlimζlim as α→+∞α→+∞. Reduction of the problem to a finite element subspace associated with a mesh ThTh generates the discrete limit parameter ζlim,hζlim,h and the discrete counterpart ψhψh to the function ψψ. We prove pointwise convergence ψh→ψψh→ψ and specify a class of yield functions for which ζlim,h→ζlimζlim,h→ζlim. These convergence results enable to find reliable lower and upper bounds of ζlimζlim. Numerical tests confirm computational efficiency of the suggested method.