Skip to main content
SpringerLink
Log in

Minimization of the expected compliance as an alternative approach to multiload truss optimization

  • Research Paper
  • Published:
Structural and Multidisciplinary Optimization Aims and scope Submit manuscript

Abstract

We show that a problem of finding the truss of minimum expected compliance under stochastic loading conditions is equivalent to the dual of a special convex minimax problem, and therefore may be efficiently solved. This equivalence makes it possible to provide classic multiload compliance minimization problems with interpretations in a probabilistic setting. In fact, we prove that minimizing the expected compliance amounts to solving a multiload-like problem associated with a particular finite set of loading scenarios, which depend on the mean and the variance of the perturbations.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Ac97 Achtziger W (1997) Topology optimization of discrete structures: an introduction in view of computational and nonsmoth aspects. In: Rozvany GIN (ed) Topology optimization in structural mechanics, CISm courses and lectures, No. 374, Springer-Verlag, Vienna, Austria, 57–100

  2. Ac98 Achtziger W (1998) Multiple-load truss topology and sizing optimization: Some propierties of minimax compliance, J Optim Theory Appl 98(2):255–280

  3. AcBeBeZo92 Achtziger W, Bendsøe MP, Ben-Tal A, Zowe J (1992) Equivalent displacement based formulations for maximun strength truss topology design. Impact Comput Sci Eng 4:315–345

  4. Al96 Alvarez F (1996) Métodos continuos en optimización paramétrica y aplicaciones a la optimización estructural. Engineering Degree Thesis, Universidad de Chile

  5. BeBe93 Ben-Tal A, Bendsøe MP (1993) A new method for optimal truss topology design. SIAM J Optim 3(2):322–358

  6. BeJaKoNeZo00 Ben-Tal A, Jarre F, Kočvara M, Nemirovski A, Zowe J (2000) Optimal design of trusses under a nonconvex global buckling constraint. Optim Eng 1:189–213

  7. BeKoZo93 Ben-Tal A, Kočvara M, Zowe J (1993) Two nonsmooth appoaches to simultaneous geometry and topology Design of trusses. Topology design of structures. Kluwer Academic, Netherlands, pp31–34

  8. BeNe97 Ben-Tal A, Nemirovski A (1997) Robust truss topology design via semidefinite programing. SIAM J Optim 7:991–1016

  9. BeZi97 Ben-Tal A, Zibulevsky M (1997) Penalty/barrier multiplier methods for convex programming problems. SIAM J Optim 7(2):347–366

  10. BeSi03 Bendsøe MP, Sigmund O (2003) Topology Optimization. Theory, Methods and Applications. Springer, Berlin Heidelberg New York

  11. BoSh00 Bonnans JF, Shapiro A (2000) Perturbation analysis of optimization problems, Springer series in operations research. Springer, Berlin Heidelberg New York

  12. Ca03 Carrasco M (2003) Diseño óptimo de estructuras reticulares en elasticidad lineal vía teoría de la dualidad. Estudio teórico y numérico. Engineering Degree Thesis, Universidad de Chile

  13. DoGoGr64 Dorn W, Gomory R, Greenberg M (1964) Automatic design of optimal structures. J Mechanique 3:25–52

  14. EvPaPe03 Evgrafov A, Patriksson M, Petersson J (2003) Stochastic structural topology optimization: existence of solutions and sensitivity analyses. ZAMM 83(7):479–492

  15. JaKoZo93 Jarre F, Kočvara M, Zowe J (1998) Optimal truss design by interior-point method. Topology design of structures. SIAM J Optim 8(4):1084–1107

  16. MaSt99 Marti K, Stöckl G (1999) Optimal (topology) design under stochastic uncertainty. In: Schueller GI, Kafka P (eds) Safety and reliability, Vol. 2, AA Balkema, Rotterdam-Brookfield, pp1597–1602

  17. Ro74 Rockafellar RT (1974) Conjugate duality and optimization. conference series in applied mathematics, No. 16, Society for industrial and applied mathematics, Philadelphia, Pa.

  18. RoWe98 Rockafellar RT, Wets RJ-B (1998) Variational analysis Grundlehren der Mathematischen Wissenschaften. Fundamental principles of mathematical sciences 317. Springer, Berlin Heidelberg New York

  19. Se77 Seber GAF (1977) Linear regression analysis. Wiley, New York

Download references

Author information

Authors and Affiliations

  1. Departamento de Ingeniería Matemática and Centro de Modelamiento Matemático (CNRS UMR 2071), Universidad de Chile, Casilla 170/3, Correo 3, Santiago, Chile

    F. Alvarez & M. Carrasco

Authors
  1. F. Alvarez
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. M. Carrasco
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to M. Carrasco.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Alvarez, F., Carrasco, M. Minimization of the expected compliance as an alternative approach to multiload truss optimization. Struct Multidisc Optim 29, 470–476 (2005). https://doi.org/10.1007/s00158-004-0488-7

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00158-004-0488-7

Keywords

Search

Navigation