Abstract
Numerical techniques for the computation of strict bounds in limit analyses have been developed for more than thirty years. The efficiency of these techniques have been substantially improved in the last ten years, and have been successfully applied to academic problems, foundations and excavations. We here extend the theoretical background to problems with anchors, interface conditions, and joints. Those extensions are relevant for the analysis of retaining and anchored walls, which we study in this work. The analysis of three-dimensional domains remains as yet very scarce. From the computational standpoint, the memory requirements and CPU time are exceedingly prohibitive when mesh adaptivity is employed. For this reason, we also present here the application of decomposition techniques to the optimisation problem of limit analysis. We discuss the performance of different methodologies adopted in the literature for general optimisation problems, such as primal and dual decomposition, and suggest some strategies that are suitable for the parallelisation of large three-dimensional problems. The proposed decomposition techniques are tested against representative problems.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Similar content being viewed by others
References
MOSEK ApS (2005) The MOSEK optimization tools version 3.2 (revision 8). User’s manual and reference. http://www.mosek.com
Benders JF (1962) Partitioning procedures for solving mixed-variables programming problems. Numer Math 4:238–252
Bertsekas DP (2003) Convex analysis and optimization, 3rd edn. Athena Scientific, Cambridge
Boyd S, Vandenberghe L (2004) Convex optimization. Cambridge University Press, Cambridge
Boyd S, **ao L, Mutapcic A, Mattingley J (2007) Notes on decomposition methods. Technical report, Stanford University. Notes of EE364B course
Christiansen E (1996) Limit analysis of collapse states. In: Handbook of numerical analysis, vol IV. North Holland, Amsterdam, pp 193–312
Ciria H, Peraire J, Bonet J (2008) Mesh adaptive computation of upper and lower bounds in limit analysis. Int J Numer Methods Eng 75:899–944
Conejo AJ, Castillo E, Mínguez R, García-Bertrand R (2006) Decomposition techniques in mathematical programming. Springer, The Netherlands
Geoffrion AM (1972) Generalized Benders decomposition. J Optim Theory Appl 10(4):238–252
Kammoun Z, Pastor F, Smaoui H, Pastor J (2010) Large static problem in numerical limit analysis: a decomposition approach. Int J Numer Anal Methods Geomech 34:1960–1980
Kaneko I (1983) A decomposition procedure for large-scale optimum plastic design problems. Int J Numer Methods Eng 19:873–889
Lyamin AV, Sloan SW, Krabbenhøft K, Hjiaj M (2005) Lower bound limit analysis with adaptive remeshing. Int J Numer Methods Eng 63:1961–1974
Muñoz JJ, Bonet J, Huerta A, Peraire J (2009) Upper and lower bounds in limit analysis: adaptive meshing strategies and discontinuous loading. Int J Numer Methods Eng 77:471–501
Muñoz JJ, Bonet J, Huerta A, Peraire J (2012) A note on upper bound formulations in limit analysis. Int J Numer Methods Eng 91(8):896–908
Muñoz JJ, Lyamin A, Huerta A (2012) Stability of anchored sheet wall in cohesive-frictional soils by FE limit analysis. Int J Numer Anal Methods Geomech. doi:10.1002/nag.2090
Salençon J (2002) De l’élasto-plasticité au calcul à la rupture. Les Éditions de l’Ècole Polytechnique, Paris
Sturm JF (1999) Using SeDuMi 1.02, a MATLAB toolbox for optimization over symmetric cones. Optim Methods Softw 11–12:625–653. Version 1.05 available from http://sedumi.ie.lehigh.edu
Tütüncü RH, Toh KC, Todd MJ (2003) Solving semidefinite-quadratic-linear programs using SDPT3. Math Program, Ser B 95:189–217. http://www.math.nus.edu.sg/~mattohkc/sdpt3.html
Vossoughi KC (2001) Étude numérique du comportement des ouvrages de soutènement à la rupture. PhD thesis, Ecole Centrale Paris, Paris, France
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2014 Springer Science+Business Media Dordrecht
About this chapter
Cite this chapter
Muñoz, J.J., Rabiei, N., Lyamin, A., Huerta, A. (2014). Computation of Bounds for Anchor Problems in Limit Analysis and Decomposition Techniques. In: Spiliopoulos, K., Weichert, D. (eds) Direct Methods for Limit States in Structures and Materials. Springer, Dordrecht. https://doi.org/10.1007/978-94-007-6827-7_4
Download citation
DOI: https://doi.org/10.1007/978-94-007-6827-7_4
Publisher Name: Springer, Dordrecht
Print ISBN: 978-94-007-6826-0
Online ISBN: 978-94-007-6827-7
eBook Packages: EngineeringEngineering (R0)