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Optimization methods for truss geometry and topology design

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Abstract

Truss topology design for minimum external work (compliance) can be expressed in a number of equivalent potential or complementary energy problem formulations in terms of member forces, displacements and bar areas. Using duality principles and non-smooth analysis we show how displacements only as well as stresses only formulations can be obtained and discuss the implications these formulations have for the construction and implementation of efficient algorithms for large-scale truss topology design. The analysis covers min-max and weighted average multiple load designs with external as well as self-weight loads and extends to the topology design of reinforcement and the topology design of variable thickness sheets and sandwich plates. On the basis of topology design as an inner problem in a hierarchical procedure, the combined geometry and topology design of truss structures is also considered. Numerical results and illustrative examples are presented.

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Authors and Affiliations

  1. Mathematical Institute, The Technical University of Denmark, Building 303, DK-2800, Lyngby, Denmark

    M. P. Bendsøe

  2. Faculty of Industrial Engineering and Management, Technion-Israel Institute of Technology, 32000, Technion City, Haifa, Israel

    A. Ben-Tal

  3. Mathematisches Institut, Universität Bayreuth, D-95447, Bayreuth, Germany

    J. Zowe

Authors
  1. M. P. Bendsøe
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  2. A. Ben-Tal
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  3. J. Zowe
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Bendsøe, M.P., Ben-Tal, A. & Zowe, J. Optimization methods for truss geometry and topology design. Structural Optimization 7, 141–159 (1994). https://doi.org/10.1007/BF01742459

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  • DOI: https://doi.org/10.1007/BF01742459

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