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Topology Optimization of Structures Composed of One or Two Materials

  • J. Thomsen
Part of the International Centre for Mechanical Sciences book series (CISM, volume 332)

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

Design Variable Topology Optimization Design Domain Orthotropic Material Stiff Material 
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.

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References

  1. Avellaneda, M. 1987: Optimal Bounds and Microgeometries for Elastic Two-phase Composites. SIAM J. Appl. Math. 47, 1216–1228.MATHMathSciNetGoogle Scholar
  2. Bendsøe, M.P.; Kikuchi, N. 1988: Generating Optimal Topologies in Structural Design using a Homogenization Method. Computer Methods in Applied Mechanics and Engineering. 71, 197–224.CrossRefMathSciNetGoogle Scholar
  3. Bendsøe, M.P. 1989: Optimal Shape Design as a Material Distribution Problem. Structural Optimization. Vol. 1, No. 4, 193–202.CrossRefGoogle Scholar
  4. Bendsøe, M.P.; Rasmussen, J.; Rodrigues, H.C. 1990a: Topology and Boundary Shape Optimization as an Integrated Tool for Computer Aided Design. Engineering Optimization in Design Processes. 63, Proceedings, Springer-Verlag.Google Scholar
  5. Bendsøe, M.P.; Rodrigues, H.C. 1990b: Integrated Topology and Boundary Shape Optimization of 2-D Solids. Comput. Meth. Appl. Mech. Engrg. (to appear).Google Scholar
  6. Braibant, V.; Fleury, C. 1984: Shape Optimal Design using B-splines. Comp. Meth. Appl. Mech. Engrg. Vol. 44, 247–267.Google Scholar
  7. Díaz, A.R.; Bendsøe, M.P. 1990: Shape Optimization of Multipurpose Structures by a Homogenization Method. Report, Mechanical Engineering, Michigan State University, East Lansing, MI 48824, USA.Google Scholar
  8. Esping, B.J.D. 1984: Minimum Weight Design of Membrane Structures using eight node Isoparametric Elements and Numerical Derivatives. Computers & Structures, Vol. 19, No. 4, 591–604.CrossRefGoogle Scholar
  9. Esping, B.J.D. 1986: The OASIS Structural Optimization System. Computers & Structures, Vol. 23, 365–377.Google Scholar
  10. Haftka, R.T.; Gandhi, R.V. 1986: Structural Shape Optimization–a Survey. Comp. Meth. Appl. Mech. Engrg. 57, 91–106.CrossRefMATHGoogle Scholar
  11. Hemp, W.S. 1973: Optimum Structures. Clarendon Press, Oxford. 70–101.Google Scholar
  12. Jones, R.M. 1975: Mechanics of Composite Materials. 85–96, New York: McGraw-Hill.Google Scholar
  13. Kohn, R.; Strang, G. 1986: Optimal Design and Relaxation of Variational Problems I-III. Comm. Pure Appl. Math. 39, 113–138, 139–182, 353–377.Google Scholar
  14. Kohn, R. 1988a: Recent Progress in the Mathematical Modelling of Composite Materials. In: Composite Material Response: Constitutive Relations and Damage Mechanisms, G. Sih et. al. eds, Elsevier, 155–177.Google Scholar
  15. Kohn, R.; Lipton, R. 1988b: Optimal Bounds for the Effective Energy of a Mixture of Two Incompressible Materials. Arch. Rat. Mech. Anal. 102, 331–350.CrossRefMATHMathSciNetGoogle Scholar
  16. Kohn, R. 1990: Composite Materials and Structural Optimization. Proc. Workshop on Smart/Intelligent Materials and Systems. Honolulu, March 1990, (Thechonomic Press).Google Scholar
  17. Lurie, K.; Cherkaev, A. 1986: Effective Characteristics of Composites and Problems of Optimum Structural Design (in Russian). Uspekhi Mekhaniki 9, 1–81.MathSciNetGoogle Scholar
  18. MODULEF, 1983: Institut National de Recherche en Informatique et en Automatique. Bibliotheque D’Elasticite, 101.Google Scholar
  19. Murat, F; Tartar, L. 1985. Calcul des Variations et Homogenization. Le Methodes de l’Homogeneisation: Theorie et Applications en Physique, Coll. de la Dir. des Etudes et Recherche d’Electricite de France, Eyrolles, 319–369.Google Scholar
  20. Olhoff, N.; Bendsøe, M.P.; Rasmussen, J. 1991: On CAD-integrated Structural Topology and Design Optimization. Computer Methods in Applied Mechanics and Engineering 89, North-Holland, 259–279.Google Scholar
  21. Papalambros, P.Y.; Chirehdast, M. 1990: An Integrated Environment for Structural Configuration Design. J. Engrg. Design. 1, 73–96.CrossRefGoogle Scholar
  22. Pedersen, P. 1972: On the Optimal Layout of Multi-Purpose Trusses. Computers & Structures, Vol. 2, 695–712.Google Scholar
  23. Pedersen, P. 1990: Bounds on Elastic Energy in Solids of Orthotropic Materials, Structural Optimization, Vol. 2, No. 1, 55–63.CrossRefGoogle Scholar
  24. Pedersen, P. 1989: On Optimal Orientation of Orthotropic Materials. Structural Optimization. 1, 101–106, Lyngby, Denmark, pp. 127.Google Scholar
  25. Pedersen, P. 1991a: On Thickness and Orientational Design with Orthotropic Materials. Structural Optimization. Vol. 3, No. 2, 69–78.CrossRefGoogle Scholar
  26. Pedersen, P.; Bendsøe, M.P.; Nagendra, S. 1991b: Note on the 2D-Match of Coaligned Principal Stresses and Strains. Dept. of Solid Mechanics, Technical University of Denmark, Lyngby, Denmark.Google Scholar
  27. Rasmussen, J. 1990: The Structural Optimization System CAOS. Structural Optimization, Vol. 2, No. 2, 109–115.CrossRefMathSciNetGoogle Scholar
  28. Rodrigues, H.C. 1988: Shape Optimal Design of Elastic Bodies using a Mixed Variational Formulation. Comp. Meth. Appl. Mech. Engrn., Vol. 69, 29–44, 1988.CrossRefMATHGoogle Scholar
  29. Rozvany, G.I.N.; Zhou M. 1990: Applications of the COC Algorithm in Layout Optimization. Engineering Optimization in Design Processes, Proceedings of the International Conference, Karlsruhe Nuclear Research Center, Germany, September 3–4, 1990. Springer-Verlag.Google Scholar
  30. Strang, G.; Kohn, R.V. 1986: Optimal Design in Elasticity and Plasticity. International Journal for Numerical Methods in Engineering. Vol. 22, 22, 183–188.CrossRefMATHMathSciNetGoogle Scholar
  31. Suzuki, K.; Kikuchi, N. 1989: A Homogenization Method for Shape and Topology Optimization. Department of Mechanical Engineering and Applied Mechanics, The University of Michigan, Ann Arbor, Michigan 48–109, USA.Google Scholar
  32. Svanberg, K. 1987: The Method of Moving Asymptotes - a New Method for Structural Optimization. Int. J. Num. Meth. Eng., Vol. 24, 359–373.Google Scholar
  33. Thomsen, J.; Olhoff, N. 1990: Optimization of Fiber Orientation and Concentration in Composites. Control and Cybernetics, Vol. 19, No. 3–4.Google Scholar
  34. Thomsen, J. 1991: Optimization of Composite Discs. Structural Optimization. Vol. 3, No. 2, 89–98.CrossRefGoogle Scholar
  35. Thomsen, J. 1992: Optimization of the Properties of Anisotropic Materials and the Topologies of Structures. (in English). Ph.D. thesis. Institute of Mechanical Engineering, Aalborg University, Denmark.Google Scholar
  36. Vinson, J.R.; Sierakowski R.L. 1987. The Behavior of Structures Composed of Composite Materials. Martinus Nijhoff Publishers, Dordrecht.Google Scholar

Copyright information

© Springer-Verlag Wien 1993

Authors and Affiliations

  • J. Thomsen
    • 1
  1. 1.The University of AalborgAalborgDenmark

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