Upper and lower bounds in limit analysis: adaptive meshing strategies and discontinuous loading

Author (s): Muñoz, J.J., Bonet, J., Huerta, A., Peraire, J.
Journal: International Journal for Numerical Methods in Engineering

Volume: 77, Issue 4
Pages: 471 – 501
Date: 2009

Abstract:
Upper and lower bounds of the collapse load factor are here obtained as the optimum values of two
discrete constrained optimisation problems. The membership constraints for Von Mises and Mohr-
Coulomb plasticity criteria are written as a set of quadratic constraints, which permits to solve
the optimisation problem using specific algorithms for Second Order Conic Program (SOCP). From
the stress field at the lower bound and the velocities at the upper bound, we construct a novel
error estimate, based on elemental and edge contributions to the bound gap. These contributions
are employed in an adaptive remeshing strategy that is able to reproduce fan-type mesh patterns
around points with discontinuous surface loading. The solution of this type of problems is analysed in
detail, and from this study some additional meshing strategies are also described. We particularise the
resulting formulation and strategies to two-dimensional problems in plane strain and we demonstrate
the effectiveness of the method with a set of numerical examples extracted from the literature.

Journal paper (from the publisher)  
UPCommons page Link  

Bibtex:

@article{JMR-MBHP:09,
  Author   = {Mu{\~n}oz, J. J. and Bonet, J. and Huerta, A. and Peraire, J.},
  Title    = {Upper and lower bounds in limit analysis: adaptive meshing strategies and discontinuous loading},
  Fjournal = {International Journal for Numerical Methods in Engineering},
  Journal  = {0029-5981},
  Volume   = {77},
  Number   = {4},
  Pages    = {471--501},
  Year     = {2009},
  Doi      = {10.1002/nme.2421},
  Url      = {http://dx.doi.org/10.1002/nme.2421}}