Skip to main content
SpringerLink
Log in

An Outer Approximations Approach to Reliability-Based Optimal Design of Structures

  • Published:
Journal of Optimization Theory and Applications Aims and scope Submit manuscript

Abstract

We present a new formulation of the problem of minimizing the initial cost of a structure subject to a minimum reliability requirement, expressed in terms of the so-called design points of the first-order reliability theory, i.e., points on limit-state surfaces that are nearest to the origin in a transformed standard normal space, as well as other deterministic constraints. Our formulation makes it possible to use outer approximations algorithms for the solution of such optimal design problems, eliminating some of the major objections associated with treating them as bilevel optimization problems. A numerical example is presented that illustrates the reliability and efficiency of the algorithm.

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. Thoft-Christensen, P., 151 References in Reliability-Based Structural Optimization, Proceedings of the IFIP WG 7.5 Working Conference on Reliability and Optimization of Structural Systems, Munich, Germany, 1991.

  2. Hohenbichler, M., and Rackwitz, R., Non-Normal Dependent Vectors in Structural Safety, ASCE Journal of Engineering Mechanics, Vol. 107, pp. 1227–1238, 1981.

    Google Scholar 

  3. Liu, P. L., and Der Kiureghian, A., Multivariate Distribution Models with Prescribed Marginals and Covariances, Probabilistic Engineering Mechanics, Vol. 1, pp. 105–112, 1986.

    Google Scholar 

  4. Hohenbichler, M., and Rackwitz, R., First-Order Concepts in System Reliability, Journal of Structural Safety, Vol. 1, pp. 177–188, 1983.

    Google Scholar 

  5. Bertsekas, D. P., Nonlinear Programming, Athena Scientific, Belmont, Massachusetts, 1995.

    Google Scholar 

  6. Vincente, L. N., and Calamai, P. H., A Bibliography Review, Report, University of Waterloo, Waterloo, Ontario, Canada, 1995 [bilevel-review.bib and bilevel-review.tex, obtainable via email from phcalamai@dial.uwaterloo.ca.].

    Google Scholar 

  7. Mayne, D. Q., and Polak, E., Outer Approximations Algorithm for Nondifferentiable Optimization Problems, Journal of Optimization Theory and Applications, Vol. 42, pp. 19–30, 1984.

    Google Scholar 

  8. Polak, E., On the Mathematical Foundations of Nondifferentiable Optimization in Engineering Design, SIAM Review, Vol. 29, pp. 21–89, 1987.

    Google Scholar 

  9. Gonzaga, C., Polak, E., and Trahan, R., An Improved Algorithm for Optimization Problems with Functional Inequality Constraints, IEEE Transactions on Automatic Control, Vol. 25, pp. 49–54, 1979.

    Google Scholar 

  10. Gill, P. E., Murray, W., Saunders, M. A., and Wright, M. H., User's Guide for NPSOL: A Fortran Package for Nonlinear Programming, Technical Report 86–2, Department of Operations Research, Stanford University, 1986.

Download references

Author information

Authors and Affiliations

  1. Department of Electrical Engineering and Computer Sciences, University of California, Berkeley, California

    C. Kirjner-Neto (Graduate Student)

  2. Department of Electrical Engineering and Computer Sciences, University of California, Berkeley, California

    E. Polak (Professor in the Graduate School)

  3. Department of Civil and Environmental Engineering, University of California, Berkeley, California

    A. Der Kiureghian (Professor)

Authors
  1. C. Kirjner-Neto
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. E. Polak
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. A. Der Kiureghian
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Kirjner-Neto, C., Polak, E. & Kiureghian, A.D. An Outer Approximations Approach to Reliability-Based Optimal Design of Structures. Journal of Optimization Theory and Applications 98, 1–16 (1998). https://doi.org/10.1023/A:1022647728419

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1023/A:1022647728419

Search

Navigation