6533b820fe1ef96bd12792d3
RESEARCH PRODUCT
A reliable incremental method of computing the limit load in deformation plasticity based on compliance : Continuous and discrete setting
Sergey RepinJ. HaslingerStanislav Sysalasubject
Pointwise convergenceReduction (recursion theory)Applied MathematicsMathematical analysista111Inverse010103 numerical & computational mathematics02 engineering and technologyFunction (mathematics)variational problems with linear growth energyfinite element approximation01 natural sciencesincremental limit analysisComputational Mathematics020303 mechanical engineering & transports0203 mechanical engineeringLimit analysisConvergence (routing)elastic-perfectly plastic problemsLimit loadLimit (mathematics)0101 mathematicsta216Mathematicsdescription
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 ? ? ( 0 , ? l i m ) , where ? l i m is generally unknown. The enhanced incremental procedure is operated in terms of an inverse mapping ? : α ? ? where the parameter α belongs to ( 0 , + ∞ ) and its physical meaning is work of applied forces at the equilibrium state. The function ? is continuous, nondecreasing and its values tend to ? l i m as α ? + ∞ . Reduction of the problem to a finite element subspace associated with a mesh T h generates the discrete limit parameter ? l i m , h and the discrete counterpart ? h to the function ? . We prove pointwise convergence ? h ? ? and specify a class of yield functions for which ? l i m , h ? ? l i m . These convergence results enable to find reliable lower and upper bounds of ? l i m . Numerical tests confirm computational efficiency of the suggested method.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2016-09-01 | Journal of Computational and Applied Mathematics |