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

0465662 - ÚGN 2017 RIV NL eng J - Journal Article
Haslinger, Jaroslav - Repin, S. - Sysala, Stanislav
A reliable incremental method of computing the limit load in deformation plasticity based on compliance: Continuous and discrete setting.
Journal of Computational and Applied Mathematics. Roč. 303, September 2016 (2016), s. 156-170. ISSN 0377-0427. E-ISSN 1879-1778
R&D Projects: GA MŠMT LQ1602; GA ČR GA13-18652S
Institutional support: RVO:68145535
Keywords : variational problems with linear growth energy * incremental limit analysis * elastic-perfectly plastic problems * finite element approximation
Subject RIV: BA - General Mathematics
Impact factor: 1.357, year: 2016
http://www.sciencedirect.com/science/article/pii/S0377042716300917

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.
Permanent Link: http://hdl.handle.net/11104/0264110