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A 101-line MATLAB code for topology optimization using binary variables and integer programming

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Abstract

This paper presents a MATLAB code with the implementation of the Topology Optimization of Binary Structures (TOBS) method first published by Sivapuram and Picelli (Finite Elem Anal Des 139: pp. 49–61, 2018). The TOBS is a gradient-based topology optimization method that employs binary design variables and formal mathematical programming. Besides its educational purposes, the 101-line code is provided to show that topology optimization with integer linear programming can be efficiently carried out, contrary to the previous reports in the literature. Compliance minimization subject to a volume constraint is first solved to highlight the main features of the TOBS method. The optimization parameters are discussed. Then, volume minimization subject to a compliance constraint is solved to illustrate that the method can efficiently deal with different types of constraints. Finally, simultaneous volume and displacement constraints are investigated in order to expose the capabilities of the optimizer and to serve as a tutorial of multiple constraints. The 101-line MATLAB code and some simple enhancements are elucidated, keeping only the integer programming solver unmodified so that it can be tested and extended to other numerical examples of interest.

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Funding

The first author would like to thank the support of FAPESP (São Paulo Research Foundation), grants 2018/05797-8 and 2019/01685-3 under the Young Investigators Awards program.

Author information

Authors and Affiliations

  1. Department of Mining and Petroleum Engineering, University of São Paulo, Praça Narciso de Andrade s/n, Vila Mathias, Santos - SP, 11013-560, Brazil

    Renato Picelli

  2. Structural Engineering Department, University of California San Diego, 9500 Gilman Drive, La Jolla, CA, 92093, USA

    Raghavendra Sivapuram

  3. Center for Innovative Structures and Materials, School of Engineering, RMIT University, Melbourne, 3001, Australia

    Yi Min Xie

Authors
  1. Renato Picelli
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  2. Raghavendra Sivapuram
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  3. Yi Min Xie
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Corresponding author

Correspondence to Renato Picelli.

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The authors declare that they have no conflict of interest.

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Responsible Editor: Ming Zhou

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Replication of results

The 101-line code is provided in the Appendix A. The code and its modified versions to run all examples in this paper are also provided as supplementary material. A more detailed implementation of the TOBS method is available upon request by email or for download at https://github.com/renatopicelli/tobs.

Electronic supplementary material

Below is the link to the electronic supplementary material.

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Appendix A: 101-line TOBS code

Appendix A: 101-line TOBS code

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Picelli, R., Sivapuram, R. & Xie, Y.M. A 101-line MATLAB code for topology optimization using binary variables and integer programming. Struct Multidisc Optim 63, 935–954 (2021). https://doi.org/10.1007/s00158-020-02719-9

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  • DOI: https://doi.org/10.1007/s00158-020-02719-9

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