Three-dimensional Mohr-Coulomb limit analysis using semidefinite programming

Recently, Krabbenhøft et al. (Int. J. Solids Struct. 2007; 44:1533–1549) have presented a formulation of the three‐dimensional Mohr–Coulomb criterion in terms of positive‐definite cones. The capabilities of this formulation when applied to large‐scale three‐dimensional problems of limit analysis are...

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Bibliographic Details
Published in:Communications in numerical methods in engineering Vol. 24; no. 11; pp. 1107 - 1119
Main Authors: Krabbenhøft, K., Lyamin, A. V., Sloan, S. W.
Format: Journal Article
Language:English
Published: Chichester, UK John Wiley & Sons, Ltd 01.11.2008
Wiley
Subjects:
Computational techniques
Earth sciences
Earth, ocean, space
Engineering and environment geology. Geothermics
Engineering geology
Exact sciences and technology
Fundamental areas of phenomenology (including applications)
Inelasticity (thermoplasticity, viscoplasticity...)
limit analysis
Mathematical methods in physics
Mohr-Coulomb
optimization
Physics
plasticity
semidefinite programming
Solid mechanics
Structural and continuum mechanics
High performance
conic programming
limit analysis
Algorithmics
Interior point method
geophysics
plasticity
Mohr-Coulomb
Distributed computing
Mohr circle
semidefinite programming
Inelasticity
optimization
Dimensional analysis
cones
Positive definite matrix
Primal dual method
Ultimate load
ISSN:1069-8299, 1099-0887
Online Access:Get full text
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Summary:Recently, Krabbenhøft et al. (Int. J. Solids Struct. 2007; 44:1533–1549) have presented a formulation of the three‐dimensional Mohr–Coulomb criterion in terms of positive‐definite cones. The capabilities of this formulation when applied to large‐scale three‐dimensional problems of limit analysis are investigated. Following a brief discussion on a number of theoretical and algorithmic issues, three common, but traditionally difficult, geomechanics problems are solved and the performance of a common primal–dual interior‐point algorithm (SeDuMi (Appl. Numer. Math. 1999; 29:301–315)) is documented in detail. Although generally encouraging, the results also reveal several difficulties which support the idea of constructing a conic programming algorithm specifically dedicated to plasticity problems. Copyright © 2007 John Wiley & Sons, Ltd.
Bibliography:ark:/67375/WNG-XS1HB7J0-W
ArticleID:CNM1018
istex:335AA48020299EC5861265CFA4529A6704ACB00F
ObjectType-Article-2
SourceType-Scholarly Journals-1
ObjectType-Feature-1
content type line 23
ISSN:1069-8299
1099-0887
DOI:10.1002/cnm.1018