An Optimization Problem for Predicting the Maximal Effect of Degradation of Mechanical Structures

W. Achtziger, Martin P. Bendsøe, J. E. Taylor

    Research output: Contribution to journalJournal articleResearchpeer-review

    Abstract

    This paper deals with a nonlinear nonconvex optimization problem that models prediction of degradation in discrete or discretized mechanical structures. The mathematical difficulty lies in equality constraints of the form Σ(i=1)(m) 1/yi A(i) x=b, where A(i) are symmetric and positive semidefinite matrices, b is a vector, and x, y are the vectors of unknowns. The linear objective function to be maximized is (x, y) bar right arrow b(T)x.

    In a first step we investigate the problem properties such as existence of solutions and the differentiability of related marginal functions. As a by-product, this gives insight in terms of a mechanical interpretation of the optimization problem. We derive an equivalent convex problem formulation and a convex dual problem, and for dyadic matrices A(i) a quadratic programming problem formulation is developed. A nontrivial numerical example is included, based on the latter formulation.
    Original languageEnglish
    JournalS I A M Journal on Optimization
    Volume10
    Issue number4
    Pages (from-to)982-998
    ISSN1052-6234
    DOIs
    Publication statusPublished - 18 Jun 2000

    Keywords

    • nonlinear optimization
    • structural optimization
    • variational methods

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