Use of Layout Optimization to Solve Large-Scale Limit Analysis and Design Problems
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.
KeywordsLayout Optimization Rigid Block Yield Constraint Truss Optimization Potential Discontinuity
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.
- 3.Chakrabarty J (2006) Theory of plasticity, 3rd edn. Butterworth-Heinemann, Oxford Google Scholar
- 5.Dorn WS, Gomory RE, Greenberg HJ (1964) Automatic design of optimal structures. J Mech 3:25–52 Google Scholar
- 6.Gilbert M, Smith CC (2010) Soil structure revolution. Struct Eng 88(3):18–22 Google Scholar
- 8.Gilbert M, Tyas A, Pritchard T (2003) An efficient linear programming based layout optimization method for pin-jointed frames. In: Proceedings of the 5th world congress on structural and multidisciplinary optimization, Venice. CD-ROM proceedings paper no 67 Google Scholar
- 10.Gilbert M, Smith CC, Haslam IW, Pritchard TJ (2010) Application of discontinuity layout optimization to geotechnical limit analysis problems. In: Proceedings of the 7th European conference on numerical methods in geotechnical engineering, Trondheim, Norway, pp 169–174 Google Scholar
- 11.Gilbert M, Smith CC, Pritchard TJ (2010) Masonry arch analysis using discontinuity layout optimisation. Proc Inst Civ Eng, Eng Comput Mech 163(3):155–166 Google Scholar
- 18.LimitState (2011) In: LimitState:RING masonry arch bridge analysis software. http://www.limitstate.com/ring
- 19.LimitState (2012) In: LimitState:GEO geotechnical analysis software. http://www.limitstate.com/geo
- 31.Wright SJ (1987) Primal-dual interior-point methods, vol 54. SIAM, Philadelphia Google Scholar