Optimization strategies for discrete multi-material stiffness optimization

Christian Frier Hvejsel, Erik Lund, Mathias Stolpe

    Research output: Contribution to journalJournal articleResearchpeer-review


    Design of composite laminated lay-ups are formulated as discrete multi-material selection problems. The design problem can be modeled as a non-convex mixed-integer optimization problem. Such problems are in general only solvable to global optimality for small to moderate sized problems. To attack larger problem instances we formulate convex and non-convex continuous relaxations which can be solved using gradient based optimization algorithms. The convex relaxation yields a lower bound on the attainable performance. The optimal solution to the convex relaxation is used as a starting guess in a continuation approach where the convex relaxation is changed to a non-convex relaxation by introduction of a quadratic penalty constraint whereby intermediate-valued designs are prevented. The minimum compliance, mass constrained multiple load case problem is formulated and solved for a number of examples which numerically confirm the sought properties of the new scheme in terms of convergence to a discrete solution.
    Original languageEnglish
    JournalStructural and Multidisciplinary Optimization
    Issue number2
    Pages (from-to)149-163
    Publication statusPublished - 2011


    • Laminated composite materials
    • Sensitivity analysis
    • Solution strategies
    • Optimal design
    • Integer optimization

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