Control in the coefficients with variational crimes: Application to topology optimization of Kirchhoff plates

Anton Evgrafov, Kun Saptohartyadi Marhadi

    Research output: Contribution to journalJournal articleResearchpeer-review

    Abstract

    We study convergence of discontinuous Galerkin-type discretizations of the problems of control in the coefficients of uniformly elliptic partial differential equations (PDEs). As a model problem we use that of the optimal design of thin (Kirchhoff) plates, where the governing equations are of the fourth order. Methods which do not require approximation subspaces to conform to the smoothness requirements dictated by the PDE are very attractive for such problems. However, variational formulations of such methods normally contain boundary integrals whose dependence on the small, with respect to “volumetric” Lebesgue norm, changes of the coefficients is generally speaking not continuous. We utilize the lifting formulation of the discontinuous Galerkin method to deal with this issue.Our main result is that limit points of sequences of designs verifying discrete versions of stationarity can also be expected to satisfy stationarity for the limiting continuum mechanics problem. We illustrate the practical behaviour of our discretization strategy on some benchmark-type examples.
    Original languageEnglish
    JournalComputer Methods in Applied Mechanics and Engineering
    Volume237-240
    Pages (from-to)27-38
    ISSN0045-7825
    DOIs
    Publication statusPublished - 2012

    Keywords

    • Control in the coefficients
    • Topology optimization
    • Discontinuous Galerkin methods
    • Thin plates
    • Convergence analysis

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