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

作者：Haslinger Jaroslav; Repin Sergey; Sysala Stanislav^*

来源：Journal of Computational and Applied Mathematics, 2016, 303: 156-170.

DOI：10.1016/j.cam.2016.02.035

• Variational problems with linear growth energy
• Incremental limit analysis
• Elastic-perfectly plastic problems
• Finite element approximation

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.

• 出版日期2016-9