Advertisement

Structural optimization

, Volume 7, Issue 1–2, pp 138–140 | Cite as

Optimization of material properties for improved frequency response

  • M. P. Bendsøe
  • A. R. Díaz
Brief Note

Abstract

The problem of maximizing the fundamental frequency of free vibrations of a structure is considered in the general setting of a simultaneous optimization of material and structure. As an extension of recent work by Bendsøeet al. (1993), the design variables include the constitutive tensors that characterize material properties. The analytical form of the extremal material problem is derived together with a considerably simplified auxiliary equivalent problem.

Keywords

Material Property Recent Work Civil Engineer General Setting Frequency Response 
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. Bendsøe, M.P.; Díaz, A.R. 1993: Optimization of material properties for Mindlin plate design.Struct. Optim. 6, 268–270Google Scholar
  2. Bendsøe, M.P.; Díaz, A.R.; Lipton, R.; Taylor, J.E. 1993a: Optimal design of material properties and material distribution for multiple loading conditions.DCAMM Report No. 469, The Danish Center for Applied Mathematics and Mechanics, The Technical University of DenmarkGoogle Scholar
  3. Bendsøe, M.P., Guedes, J.M., Haber, R.B., Pedersen, P., Taylor, J.E. 1993b: An analytical model to predict optimal material properties in the context of optimal structural design.J. Appl. Mech. (to appear)Google Scholar
  4. Díaz, A.; Kikuchi, N. 1992: Solutions to shape and topology eigenvalue problems using a homogenization method.Int. J. Num. Meth. Eng. 35, 1487–1502Google Scholar
  5. Ma, Z.-D.; Kikuchi, N.; Cheng, H.-C.; Hagiwara, I. 1993: Topology and shape optimization methods for structural dynamic problems. In: Pedersen, P. (ed.)Optimal design with advanced materials, pp. 247–261. Amsterdam: ElsevierGoogle Scholar
  6. Neves, M.M.; Guedes, J.M.; Rodrigues, H.C. 1993: Topology optimization of elastic 2D structures with critical load constraints. In: Herskovits, J. (ed.):Structural optimization 93 (Proc. World Congr. on Optimal Design of Structural Systems), Vol. 1, pp. 119–128. Rio de Janiero: Universidade Federal do Rio de JaneiroGoogle Scholar
  7. Sigmund, O. 1993: Materials with prescribed constitutive parameters: an inverse homogenization problem.DCAMM Report No. 470, The Danish Center for Applied Mathematics and Mechanics, The Technical University of DenmarkGoogle Scholar

Copyright information

© Springer-Verlag 1994

Authors and Affiliations

  • M. P. Bendsøe
    • 1
  • A. R. Díaz
    • 2
  1. 1.Mathematical InstituteThe Technical University of DenmarkLyngbyDenmark
  2. 2.Department of Mechanical EngineeringMichigan State UniversityEast LansingUSA

Personalised recommendations