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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Vydáno v:	Communications in numerical methods in engineering Ročník 24; číslo 11; s. 1107 - 1119
Hlavní autoři:	Krabbenhøft, K., Lyamin, A. V., Sloan, S. W.
Médium:	Journal Article
Jazyk:	angličtina
Vydáno:	Chichester, UK John Wiley & Sons, Ltd 01.11.2008 Wiley
Témata:	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
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Abstract	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.
AbstractList	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. Recently, Krabbenhoft 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. 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.
Author	Krabbenhøft, K. Lyamin, A. V. Sloan, S. W.
Author_xml	– sequence: 1 givenname: K. surname: Krabbenhøft fullname: Krabbenhøft, K. email: kristian.krabbenhoft@newcastle.edu.au organization: Centre for Geotechnical and Materials Modelling, School of Engineering, University of Newcastle, Callaghan, NSW 2308, Australia – sequence: 2 givenname: A. V. surname: Lyamin fullname: Lyamin, A. V. organization: Centre for Geotechnical and Materials Modelling, School of Engineering, University of Newcastle, Callaghan, NSW 2308, Australia – sequence: 3 givenname: S. W. surname: Sloan fullname: Sloan, S. W. organization: Centre for Geotechnical and Materials Modelling, School of Engineering, University of Newcastle, Callaghan, NSW 2308, Australia
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Keywords	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
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References_xml	– reference: Krabbenhoft K, Lyamin AV, Sloan SW, Wriggers P. An interior-point method for elastoplasticity. International Journal for Numerical Methods in Engineering 2007; 69:592-626. – reference: Lyamin AV, Sloan SW. Lower bound limit analysis using non-linear programming. International Journal for Numerical Methods in Engineering 2002; 55:573-611. – reference: Krabbenhoft K, Lyamin AV, Hjiaj M, Sloan SW. A new discontinuous upper bound limit analysis formulation. International Journal for Numerical Methods in Engineering 2005; 63:1069-1088. – reference: Alizadeh F, Haeberly JA, Overton M. Primal-dual interiorpoint methods for semidefinite programming: convergence rates, stability and numerical results. SIAM Journal on Optimization 1998; 8:746-768. – reference: Krabbenhoft K, Damkilde L. A general nonlinear optimization algorithm for lower bound limit analysis. 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Snippet	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... Recently, Krabbenhøft et al . ( Int. J. Solids Struct . 2007; 44 :1533–1549) have presented a formulation of the three‐dimensional Mohr–Coulomb criterion in... Recently, Krabbenhoft et al. (Int. J. Solids Struct. 2007; 44:1533-1549) have presented a formulation of the three-dimensional Mohr-Coulomb criterion in terms...
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SubjectTerms	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
Title	Three-dimensional Mohr-Coulomb limit analysis using semidefinite programming
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