Structural and Multidisciplinary Optimization

, Volume 33, Issue 1, pp 13–26

Growth method for size, topology, and geometry optimization of truss structures

Research Paper

Abstract

The problem of optimally designing the topology of plane trusses has, in most cases, been dealt with as a size problem in which members are eliminated when their size tends to zero. This article presents a novel growth method for the optimal design in a sequential manner of size, geometry, and topology of plane trusses without the need of a ground structure. The method has been applied to single load case problems with stress and size constraints. It works sequentially by adding new joints and members optimally, requiring five basic steps: (1) domain specification, (2) topology and size optimization, (3) geometry optimization, (4) optimality verification, and (5) topology growth. To demonstrate the proposed growth method, three examples were carried out: Michell cantilever, Messerschmidt–Bölkow–Blohm beam, and Michell cantilever with fixed circular boundary. The results obtained with the proposed growth method agree perfectly with the analytical solutions. A Windows XP program, which demonstrates the method, can be downloaded from http://www.upct.es/~deyc/software/tto/.

Keywords

Optimal design of trusses Growth methods Size optimization Geometry optimization Topology optimization Stress constraints 

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References

  1. Achtziger W (1996) Truss topology optimization including bar properties different for tension and compression. Struct Optim 12(1):63–73CrossRefGoogle Scholar
  2. Achtziger W, Bendsøe MP, Ben-Tal A, Zowe J (1992) Equivalent based formulations for maximum strength truss topology design. Impact Comput Sci Eng 4(4):315–345MATHCrossRefGoogle Scholar
  3. Bendsøe MP, Mota Soares C (eds) (1992) Proceedings of NATO ARW on Topology design of structures. Kluwer, DordrechtGoogle Scholar
  4. Bendsøe MP, Ben-Tal A, Zowe J (1994) Optimization methods for truss geometry and topology design. Struct Optim 7(3):141–158CrossRefGoogle Scholar
  5. Ben-Tal A, Bendsøe MP (1993) A new method for optimal truss topology design. SIAM J Optim 3:322–355MATHMathSciNetCrossRefGoogle Scholar
  6. Ben-Tal A, Kočvara M, Zowe J (1993) Two non-smooth approaches to simultaneous geometry and topology design of trusses. In: Bendsøe MP, Mota Soares CA (eds) Topology design of structures, Kluwer, Dordrecht, pp 31–42Google Scholar
  7. Bojczuk D, Mróz Z (1999) Optimal topology and configuration design of trusses with stress and buckling constraints. Struct Optim 17:25–35CrossRefGoogle Scholar
  8. Cox HL (1965) The design of structures for least weight. Pergamon, OxfordGoogle Scholar
  9. da Silva Smith O (1996) An interactive system for truss topology design. Adv Eng Softw 27(1–2):167–178CrossRefGoogle Scholar
  10. Dorn W, Gomory R, Greenberg H (1964) Automatic design of optimal structures. J Mec 3:25–52Google Scholar
  11. Fleron P (1964) The minimum weight of trusses. Bygn Statiske Medd 35:81–96Google Scholar
  12. Hemp WS (1973) Optimum structures. Clarendon, OxfordGoogle Scholar
  13. Kirsch U (1989) Optimal topologies of structures. Appl Mech Rev 42:223–239CrossRefGoogle Scholar
  14. Kirsch U (1997) Reduction and expansion processes in topology optimization. In: Rozvany GIN (ed) Topology optimization in structural mechanics. Springer, Berlin Heidelberg New York, pp 197–206Google Scholar
  15. Lewiński T, Zhou M, Rozvany GIN (1994a) Extended exact solution for least-weight truss layout. Part I: cantilever with a horizontal axis of symmetry. Int J Mech Sci 36:375–398CrossRefMATHGoogle Scholar
  16. Lewiński T, Zhou M, Rozvany GIN (1994b) Extended exact solution for least-weight truss layout. Part II: unsymmetric cantilevers. Int J Mech Sci 36:399–419CrossRefGoogle Scholar
  17. Martínez P (2003) Simultaneous optimal design of topology and geometry of plane trusses by growing techniques (in Spanish). Ph.D. Thesis, Universidad Politécnica de Cartagena, SpainGoogle Scholar
  18. McKeown JJ (1998) Growing optimal pin-jointed frames. Struct Optim 15:92–100CrossRefGoogle Scholar
  19. Michell AGM (1904) The limit of economy of material in frame structures. Phila Mag 8(6):589–597MATHGoogle Scholar
  20. Nishino F, Duggal R (1990) Shape optimum design of trusses under multiple loading. Int J Solids Struct 26:17–27CrossRefGoogle Scholar
  21. Oberndorfer JM, Achtziger W, Hörnlein HREM (1996) Two approaches for truss topology optimization: a comparison for practical use. Struct Optim 11(3–4):137–144CrossRefGoogle Scholar
  22. Pedersen P (1970) On the minimum mass layout of trusses. Symposium on structural optimization. AGARD Conf Proc 36:189–192Google Scholar
  23. Pedersen P (1993) Topology optimization of three-dimensional trusses. In: Bendsøe MP, Mota Soares CA (eds) Topology design of structures. Kluwer, Dordrecht, pp 19–30Google Scholar
  24. Prager W (1985) Optimal design of grillages. In: Save M, Prager W (eds), Structural optimization. Plenum, New York, 153–200Google Scholar
  25. Prager W, Rozvany GIN (1977) Optimization of structural geometry. In: Bednarek A, Cesari L (eds) Dynamical systems. Academic, New YorkGoogle Scholar
  26. Rozvany GIN (1998) Exact analytical solutions for some popular benchmark problems in topology optimization. Struct Optim 15:42–48CrossRefGoogle Scholar
  27. Rozvany GIN, Bendsøe MP, Kirsch U (1995) Layout optimization of structures. Appl Mech Rev 48(1995):41–119CrossRefGoogle Scholar
  28. Rule WK (1994) Automatic truss design by optimized growth. J Struct Eng 120(10):3063–3070CrossRefGoogle Scholar
  29. Schittkowski K (1986) NLPQL: a FORTRAN subroutine solving constrained nonlinear programming problems. Ann Oper Res 5:485–500MathSciNetCrossRefGoogle Scholar
  30. Topping BHV (1983) Shape optimization of skeletal structures: a review. J Struct Eng 109:1933–1951CrossRefGoogle Scholar
  31. Zhou M, Rozvany GIN (1996) An improved approximation technique for the DCOC method of sizing optimization. Comput Struct 60(5):763–769MATHCrossRefGoogle Scholar

Copyright information

© Springer-Verlag 2006

Authors and Affiliations

  1. 1.Structures and Construction DepartmentTechnical University of CartagenaMurciaSpain
  2. 2.School of Mechanical EngineeringThe University of LeedsLeedsUK

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