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

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Direct Methods for Limit States in Structures and Materials

Abstract

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.

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Notes

  1. 1.

    Note that adaptive model refinement procedures will generally be most effective when interior point methods are used. This is because the collapse fields generated are more ‘physically correct’ [1] than when extreme-point methods, such as the traditional Simplex method, are used.

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Acknowledgements

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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Authors and Affiliations

  1. Department of Civil and Structural Engineering, University of Sheffield, Mappin Street, Sheffield, S1 3JD, UK

    Matthew Gilbert, Colin C. Smith, Samuel J. Hawksbee & Andrew Tyas

Authors
  1. Matthew Gilbert
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  2. Colin C. Smith
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  3. Samuel J. Hawksbee
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  4. Andrew Tyas
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Correspondence to Matthew Gilbert .

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Editors and Affiliations

  1. Department of Structural Engineering, National Technical University of Athens School of Civil Engineering, Athens, Greece

    Konstantinos Spiliopoulos

  2. Institute of General Mechanics, RWTH-Aachen University, Aachen, Germany

    Dieter Weichert

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Gilbert, M., Smith, C.C., Hawksbee, S.J., Tyas, A. (2014). Use of Layout Optimization to Solve Large-Scale Limit Analysis and Design Problems. 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_8

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  • DOI: https://doi.org/10.1007/978-94-007-6827-7_8

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-94-007-6826-0

  • Online ISBN: 978-94-007-6827-7

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