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Multiple-Load Truss Topology and Sizing Optimization: Some Properties of Minimax Compliance

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  • W. Achtziger

    (University of Erlangen–Nuremberg)

Abstract

This paper considers the mathematical properties of discrete or discretized mechanical structures under multiple loadings which are optimal w.r.t. maximal stiffness. We state a topology and/or sizing problem of maximum stiffness design in terms of element volumes and displacements. Multiple loads are handled by minimizing the maximum of compliance of all load cases, i.e., minimizing the maximal sum of displacements along an applied force. Generally, the problem considered may contain constraints on the design variables. This optimization problem is first reformulated in terms of only design variables. Elastic equilibrium is hidden in potential energy terms. It is shown that this transformed objective function is convex and continuous, including infinite values. We deduce that maximum stiffness structures are dependent continuously on the bounds of the element volumes as parameters. Consequently, solutions to sizing problems with small positive lower bounds on the design variables can be considered as good approximations of solutions to topology problems with zero lower bounds. This justifies heuristic approaches such as the well-known stress-rationing method for solving truss topology problems.

Suggested Citation

  • W. Achtziger, 1998. "Multiple-Load Truss Topology and Sizing Optimization: Some Properties of Minimax Compliance," Journal of Optimization Theory and Applications, Springer, vol. 98(2), pages 255-280, August.
    • Handle: RePEc:spr:joptap:v:98:y:1998:i:2:d:10.1023_a:1022637216104
    DOI: 10.1023/A:1022637216104
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    Cited by:

    1. Ada Amendola, 2020. "On the Optimal Prediction of the Stress Field Associated with Discrete Element Models," Journal of Optimization Theory and Applications, Springer, vol. 187(3), pages 613-629, December.
    2. Miguel Carrasco & Benjamin Ivorra & Angel Manuel Ramos, 2012. "A Variance-Expected Compliance Model for Structural Optimization," Journal of Optimization Theory and Applications, Springer, vol. 152(1), pages 136-151, January.
    3. Alemseged Gebrehiwot Weldeyesus & Jacek Gondzio, 2018. "A specialized primal-dual interior point method for the plastic truss layout optimization," Computational Optimization and Applications, Springer, vol. 71(3), pages 613-640, December.

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