On some fundamental properties of structural topology optimization problems

    Research output: Book/ReportReportResearchpeer-review

    Abstract

    We study some fundamental mathematical properties of classical structural topology optimization problems. Either compliance is minimized with an upper bound on the volume of the structure, or volume is minimized with an upper bound on the compliance. The design variables are either continuous or 0--1. We show, by examples which can be solved by hand calculations, that the optimal solutions in general are not unique and possibly do not have an active volume constraint. These observations have immediate consequences on the theoretical convergence properties of penalization approaches. Furthermore, we illustrate that the optimal solutions to the considered problems in general are not symmetric even if the design domain, the external loads, and the boundary conditions are symmetric around an axis. The presented examples can be used as teaching material in graduate and undergraduate courses on structural topology optimization.
    Original languageEnglish
    Publication statusPublished - 2009
    SeriesDCAMM Report
    Number741
    ISSN0903-1685

    Keywords

    • Minimum compliance optimization
    • Topology optimization
    • Minimum volume optimization

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