Slope constrained Topology Optimization

J. Petersson, Ole Sigmund

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    The problem of minimum compliance topology optimization of an elastic continuum is considered. A general continuous density-energy relation is assumed, including variable thickness sheet models and artificial power laws. To ensure existence of solutions, the design set is restricted by enforcing pointwise bounds on the density slopes. A finite element discretization procedure is described, and a proof of convergence of finite element solutions to exact solutions is given, as well as numerical examples obtained by a continuation/SLP (sequential linear programming) method. The convergence proof implies that checkerboard patterns and other numerical anomalies will not be present, or at least, that they can be made arbitrarily weak. (C) 1998 John Wiley & Sons, Ltd.
    Original languageEnglish
    JournalInternational Journal for Numerical Methods in Engineering
    Issue number8
    Pages (from-to)1417-1434
    Publication statusPublished - 1998


    • Topology optimization
    • Finite elements
    • Slope constraints

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