Advertisement

Structural Optimization of a Linearly Elastic Structure using the Homogenization Method

  • Noboru Kikuchi
  • Katsuyuki Suzuki
Part of the Progress in Nonlinear Differential Equations and Their Applications book series (PNLDE, volume 5)

Abstract

We shall describe a brief review of the structural optimization of a linearly elastic structure, and we shall present a new method to solve the sizing, shape, and layout (topology) problems based on the theory of homogenization. Many numerical examples of the optimal design are also presented as well as a mathematical formulation of a relaxed design problem.

Keywords

Design Variable Design Problem Structural Optimization Design Domain Elasticity Tensor 
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.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [1]
    Banichuk, N.V., Problems and methods of optimal structural design, Plenum Press, New York (1983)Google Scholar
  2. [2]
    Cheng, K.T., and Olhoff, N., An investigation concerning optimal design of solid elastic plates, Int. J. Solids and Structures 17 (1981) 305–323MathSciNetMATHCrossRefGoogle Scholar
  3. [3]
    Lurie, K.A., Fedorov, A.V., and Cherkaev, A.V., Regularization of optimal design problems for bars and plates, Parts I and II, J. Optim. Theory Appl. 37(4) (1982) 4999–521Google Scholar
  4. [3a]
    Lurie, K.A., Fedorov, A.V., and Cherkaev, A.V., Regularization of optimal design problems for bars and plates, Parts I and II, J. Optim. Theory Appl. 37(4) (1982) 523–543MathSciNetMATHCrossRefGoogle Scholar
  5. [4]
    Bendsøe, M.P., Generalized plate models and optimal design, in J.L. Eriksen, D. Kinderlehrer, R. Kohn and J.L. Lions, eds., Homogenization and effect moduli of materials and media, The IMA Volumes in Mathematics and Its Applications, Spriger-Verlag, Berlin, 1986, 1–26CrossRefGoogle Scholar
  6. [5]
    Palmer, A.C., Dynamic Programing and Structural Optimization, in R.H. Gallagher and O.C. Zienkiewicz, eds., Optimum Structural Design, John Wiley & Sons, Chichester (1973) 179–200Google Scholar
  7. [6]
    Murat, F., and Tartar, L., Optimality conditions and homogenization, in A. Marino, L. Modica, S. Spagnolo, and M. Degiovanni, eds., Nonlinear variational problems, Pitman Advanced Publishing Program, Boston, 1985,1–8Google Scholar
  8. [7]
    Kohn, R., and Strang, G., Optimal Design and relaxation of variational problems, Parts I, II, and III, Communications on Pure and Applied Mathematics, XXXIX (1986) 113–137MathSciNetCrossRefGoogle Scholar
  9. [7a]
    Kohn, R., and Strang, G., Optimal Design and relaxation of variational problems, Parts I, II, and III, Communications on Pure and Applied Mathematics, XXXIX (1986) 139–182MathSciNetCrossRefGoogle Scholar
  10. [7b]
    Kohn, R., and Strang, G., Optimal Design and relaxation of variational problems, Parts I, II, and III, Communications on Pure and Applied Mathematics, XXXIX (1986) 353–378MathSciNetCrossRefGoogle Scholar
  11. [8]
    Bendsøe, M.P., and Kikuchi, N., Generating optimal topologies in structural design using a homogenization method, Comput. Mechs. Appl. Mech. Engrg., 71 (1988) 197–224CrossRefGoogle Scholar
  12. [9]
    Suzuki, K., and Kikuchi, N., Shape and topology optimization using the homogenization method, (in review) Comput. Mechs. Appl. Mech. Engrg. (1989)Google Scholar

Copyright information

© Birkhäuser Boston 1991

Authors and Affiliations

  • Noboru Kikuchi
    • 1
  • Katsuyuki Suzuki
    • 1
  1. 1.Department of Mechanical Engineering and Applied MechanicsThe University of MichiganAnn ArborUSA

Personalised recommendations