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Truss topology optimization with discrete design variables by outer approximation

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Abstract

Several variants of an outer approximation method are proposed to solve truss topology optimization problems with discrete design variables to proven global optimality. The objective is to minimize the volume of the structure while satisfying constraints on the global stiffness of the structure under the applied loads. We extend the natural problem formulation by adding redundant force variables and force equilibrium constraints. This guarantees that the designs suggested by the relaxed master problems are capable of carrying the applied loads, a property which is generally not satisfied for classical outer approximation approaches applied to optimal design problems. A set of two- and three-dimensional benchmark problems are solved and the numerical results suggest that the proposed approaches are competitive with other special-purpose global optimization methods for the considered class of problems. Numerical comparisons indicate that the suggested outer approximation algorithms can outperform standard approaches suggested in the literature, especially on difficult problem instances.

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Acknowledgments

I extend sincere thanks to Professor Wolfgang Achtziger for valuable comments and suggestions on an early draft of this article. I would also like to thank the two anonymous reviewers for constructive comments and suggestions that improved the article.

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Authors and Affiliations

  1. Department of Wind Energy, Technical University of Denmark, Frederiksborgvej 399, 4000 , Roskilde, Denmark

    Mathias Stolpe

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  1. Mathias Stolpe
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Correspondence to Mathias Stolpe.

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The computing resources were funded by the Danish Center for Scientific Computing under the grant Optimal design of composite structures. The research is partially funded by The Danish Council for Independent Research—Technology and Production Sciences through the research project Optimal Design of Composite Structures under Manufacturing Constraints.

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Stolpe, M. Truss topology optimization with discrete design variables by outer approximation. J Glob Optim 61, 139–163 (2015). https://doi.org/10.1007/s10898-014-0142-x

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  • DOI: https://doi.org/10.1007/s10898-014-0142-x

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