Upper and lower bounds in limit analysis: Adaptive meshing strategies and discontinuous loading
By Jose J. Muñoz, Javier Bonet, Antonio Huerta, Jaime Peraire. 2009
111 citations recorded by the source corpus.
Upper and lower bounds of the collapse load factor are here obtained as the optimum values of two discrete constrained optimization problems. The membership constraints for Von Mises and Mohr–Coulomb plasticity criteria are written as a set of quadratic constraints, which permits one to solve the optimization 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. Copyright © 2008 John Wiley & Sons, Ltd.
Subfields: Computational Mechanics, Safety, Risk, Reliability and Quality, Statistics and Probability
View Paper: https://www.semanticscholar.org/paper/8789cb0697fd726be45e06adb26161f6c1731a8f
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In Computational Mechanics
- Hung Nguyen-Xuan
- C. Le
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- Matthew Gilbert
- H. Nguyen‐Dang
- Trung Nguyen-Thoi
- Timon Rabczuk
- Guirong Liu
In Safety, Risk, Reliability and Quality
In Statistics and Probability
Citations in the corpus
- Adaptive element-free Galerkin method applied to the limit analysis of plates (2010, background): “Using solutions of the lower and upper bound problem in combination, another effective error estimate was proposed in [16,17].”
- Upper and lower bound limit analysis of plates using FEM and second-order cone programming (2010, background): “These limit analysis problems can then be solved by this efficient algorithm [21, 22, 23].”