Use of Layout Optimization to Solve Large-Scale Limit Analysis and Design Problems

  • Matthew Gilbert
  • Colin C. Smith
  • Samuel J. Hawksbee
  • Andrew Tyas


Direct methods can be used to rapidly verify the safety of solid bodies and structures against collapse, and also to assist engineers wishing to rapidly identify structurally efficient designs for a specified load carrying capacity. Layout optimization is a direct method that can be used to solve very large-scale problems when adaptive solution schemes are employed, and the same underlying mathematical formulation is applicable to both analysis and design problems. Here the truss layout optimization formulation is applied to various benchmark design problems and the discontinuity layout optimization formulation applied to various plane strain limit analysis problems. It is observed that highly accurate solutions can be obtained, close to known analytical solutions. Finally future directions in the field of layout optimization are briefly considered.


Layout Optimization Rigid Block Yield Constraint Truss Optimization Potential Discontinuity 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.



The authors acknowledge the assistance provided by Dr Wael Darwich, Dr Thomas Pritchard and Dr Iain Haslam, who assisted with the development of the software used in this Chapter. Also acknowledged are the mathematical insights provided by Dr Aleksey Pichugin of Brunel University. Finally the financial support provided by EPSRC (Advanced Research Fellowship grant ref: GR/S53329/01) is gratefully acknowledged.


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Copyright information

© Springer Science+Business Media Dordrecht 2014

Authors and Affiliations

  • Matthew Gilbert
    • 1
  • Colin C. Smith
    • 1
  • Samuel J. Hawksbee
    • 1
  • Andrew Tyas
    • 1
  1. 1.Department of Civil and Structural EngineeringUniversity of SheffieldSheffieldUK

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