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

卷:303

Article

Haslinger, Jaroslav^1,2  Repin, Sergey^3,4  Sysala, Stanislav² 

[1] Charles Univ Prague, Prague, Czech Republic

[2] Acad Sci Czech Republic, Inst Geon, CS-70300 Ostrava, Czech Republic

[3] Russian Acad Sci, St Petersburg Dept, VA Steklov Math Inst, Moscow 117901, Russia

[4] Univ Jyvaskyla, SF-40351 Jyvaskyla, Finland

关键词: Variational problems with linear growth energy;    Incremental limit analysis;    Elastic-perfectly plastic problems;    Finite element approximation;   

DOI  :  10.1016/j.cam.2016.02.035

来源: Elsevier

【 摘 要 】

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 zeta is an element of (0, zeta(lim)) where zeta(lim) is generally unknown. The enhanced incremental procedure is operated in terms of an inverse mapping psi : alpha bar right arrow zeta where the parameter a belongs to (0, +infinity) and its physical meaning is work of applied forces at the equilibrium state. The function psi is continuous, nondecreasing and its values tend to zeta(lim) as alpha -> +infinity. Reduction of the problem to a finite element subspace associated with a mesh T-h generates the discrete limit parameter and the discrete counterpart psi(h) to the function psi. We prove pointwise convergence psi(h) -> psi and specify a class of yield functions for which zeta(lim,h) -> zeta(lim). These convergence results enable to find reliable lower and upper bounds of zeta(lim). Numerical tests confirm computational efficiency of the suggested method. (C) 2016 Elsevier B.V. All rights reserved.

【 授权许可】

Free