Structural optimization

, Volume 5, Issue 1–2, pp 108–115 | Cite as

Topology optimization of structures composed of one or two materials

  • J. Thomsen
Technical Papers

Abstract

Maximization of the integral stiffness of a structure composed of one or two isotropic materials of large stiffness is considered using the homogenization technique. Material is modelled by a second rank composite, and we use the concentrations and orientations of the composite as design variables. Numerical results are presented at the end of the paper.

Keywords

Civil Engineer Design Variable Topology Optimization Isotropic Material Homogenization Technique 

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References

  1. Avellaneda, M. 1987: Optimal bounds and microgeometries for elastic two-phase composites.SIAM J. Appl. Math. 47, 1216–1228Google Scholar
  2. Bendsøe, M.P.; Kikuchi, N. 1988: Generating optimal topologies in structural design using a homogenization method.Comp. Meth. Appl. Mech. Eng. 71, 197–224Google Scholar
  3. Bendsøe, M.P. 1989: Optimal shape design as a material distribution problem.Struct. Optim. 1, 193–202Google Scholar
  4. Bendsøe, M.P.; Rasmussen, J.; Rodrigues, H.C. 1990a: Topology and boundary shape optimization as an integrated tool for computer aided design.Eng. Optim. Des. 63, Berlin, Heidelberg, New York: SpringerGoogle Scholar
  5. Bendsøe, M.P.; Rodrigues, H.C. 1990b: Integrated topology and boundary shape optimization of 2-D solids.Comp. Meth. Appl. Eng. (to appear)Google Scholar
  6. Braibant, V.; Fleury, C. 1984: Shape optimal design using Bsplines.Comp. Meth. Appl. Mech. Eng. 44, 247–267Google Scholar
  7. Díaz, A.R.; Bendsøe, M.P. 1990: Shape optimization of multipurpose structures by a homogenization method.Report, Mechanical Engineering, Michigan State University Google Scholar
  8. Esping, B.J.D. 1984: Minimum weight design of membrane structures using eight node isoparametric elements and numerical derivatives.Comp. & Struct. 19, 519–604Google Scholar
  9. Esping, B.J.D. 1986: The OASIS strucutral optimization system.Comp. & Struct. 23, 365–377Google Scholar
  10. Haftka, R.T.; Gandhi, R.V. 1986: Structural shape optimization — a survey.Comp. Meth. Appl. Mech. Eng. 57, 91–106Google Scholar
  11. Hemp, W.S. 1973:Optimum structures. Oxford: Clarendon PressGoogle Scholar
  12. Jones, R.M. 1975:Mechanics of composite materials. New York: McGraw-HillGoogle Scholar
  13. Kohn, R. 1988: Recent progress in the mathematical modelling of composite materials. In: Sih, G.et al. (eds.)Composite material response: constitute relations and damage mechanisms. pp. 155–177. Amsterdam: ElsevierGoogle Scholar
  14. Kohn, R. 1990: Composite materials and structural optimization.Proc. Workshop “Smart/Intelligent Materials and Systems” (held in Honolulu, March 1990). Techonomic PressGoogle Scholar
  15. Kohn, R.; Lipton, R. 1988: Optimal bounds for the effective energy of a mixture of two incompressible materials.Arch. Rat. Mech. Anal. 102, 331–350Google Scholar
  16. Kohn, R.; Strang, G. 1986: Optimal design and relaxation of variational problems I–III.Comm. Pure Appl. Math. 39, 113–138, 139–182, 353–377Google Scholar
  17. Lurie, K.; Cherkaev, A. 1986: Effective characteristics of composite and problems of optimum strucural design.Uspekhi Mekhaniki 9, 1–81 (in Russian)Google Scholar
  18. MODULEF, 1983: Institut National de Recherche en Informatique et en Automatique.Bibliotheque D'Elasticite, 101Google Scholar
  19. Murat, F.; Tartar, L. 1985: Calcul des Variations et Homogenization. Le methodes de l'homogeneisation: Theorie et Application en Physique.Coll. de la Dir. des Etudes et Recherche d'Electricite de France, Eyrolles, 319–369Google Scholar
  20. Olhoff, N.; Bendsøe, M.P.; Rasmussen, J. 1991: On CAD-integrated strucutral topology and design optimization.Comp. Meth. Appl. Mech. Eng. 89, 259–279Google Scholar
  21. Papalambros, P.Y.; Chirehdast, M. 1990: An integrated environment for structural configuration design.J. Engrg. Des. 1, 73–96Google Scholar
  22. Pedersen, P. 1972: On the optimal layout of multi-purpose trusses.Comp. & Struct. 2, 695–712Google Scholar
  23. Pedersen, P. 1989: On optimal orientation of orthotropic materials.Struct. Optim. 1, 101–106Google Scholar
  24. Pedersen, P. 1990: Bounds on elastic energy in solids of orthotropic materials.Struct. Optim. 2, 55–63Google Scholar
  25. Pedersen, P. 1991: On thickness and orientational design with orthotropic materials.Struct. Optim. 3, 69–78Google Scholar
  26. Pedersen, P.; Bendsøe, M.P.; Nagendra, S. 1991: Note on the 2D-match of coaligned principal stresses and strains.Dept. of Solid Mechanics, Technical University of Denmark Google Scholar
  27. Rasmussen, J. 1990: The structural optimization system CAOS.Struct. Optim. 2, 109–115Google Scholar
  28. Rodrigues, H.C. 1988: Shape optimal design of elastic bodies using a mixed variational formulation.Comp. Meth. Appl. Mech. Engrg. 69, 29–44Google Scholar
  29. Rozvany, G.I.N.; Zhou M. 1991: Applications of the COC algorithm in layout optimization. In: Eschenauer, H.A.; Mattheck, C.;Olhoff, N. (eds.)Engineering optimization in design processes, pp. 59–70. Berlin, Heidelberg, New York: SpringerGoogle Scholar
  30. Rozvany, G.I.N.; Zhou M.; Birker, T. 1992: Generalized shape optimization withouth homogenization.Struct. Optim. 4 250–252Google Scholar
  31. Strang, G.; Kohn, R.V. 1986: Optimal design in elasticity and plasticity.Int. J. Num. Meth. Engrg. 22, 183–188Google Scholar
  32. Suzuki, K; Kikuchi, N. 1989: A homogenization method for shape and topology optimization.Dept. Mechanical Engeneering Applied Mechanics, The University of Michigan Google Scholar
  33. Svanberg, K. 1987: The method of moving asymptotes — a new method for structural optimization.Int. J. Num. Meth. Eng. 24, 359–373Google Scholar
  34. Thomsen, J.; Olhoff, N. 1990: Optimization of fiber orientation and concentration in composites.Control and Cybernetics 19 Google Scholar
  35. Thomsen, J. 1991: Optimization of composite discs.Struct. Optim. 3, 89–98Google Scholar
  36. Thomsen, J. 1992:Optimization of the properties of anisotropic materials and the topologies of structures. Ph.D. Thesis, Aalborg University (in English)Google Scholar
  37. Vinson, J.R.; Sierakowski, R.L. 1987:The behaviour of structures composed of composite materials. Dordrecht: Martinus NijhoffGoogle Scholar
  38. Zhou, M.; Rozvany, G.I.N. 1991: The COC algorithm. Part II: topological and generalized shape optimiization.Comp. Meth. Appl. Mech. Eng. 89, 309–336Google Scholar

Copyright information

© Springer-Verlag 1992

Authors and Affiliations

  • J. Thomsen
    • 1
  1. 1.Institute of Mechanical EngineeringThe University of AalborgAalborg EastDenmark

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