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Topology optimization of truss structure considering kinematic stability based on mixed-integer programming approach

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Abstract

Kinematic instability due to unstable nodes is an often neglected but critical aspect of mathematical optimization models in truss topology optimization problems. On the one hand, kinematically unstable structures cannot be used in the actual structural design. On the other hand, unstable nodes within continuous parallel bars can make the calculation of bar length wrong and affect the optimization effect. To avoid kinematic instability, a computationally efficient nominal disturbing force (NDF) approach for truss topology optimization is presented in this paper. Using the NDF approach, the most favorable structure for the optimization goal can be selected in three schemes: (1) adding bracings at unstable nodes, (2) removing unstable nodes and replacing short bars with long ones, or (3) selecting a new topology form to avoid containing unstable nodes. Compared with the widely used nominal lateral force (NLF) approach in the literature, the NDF approach can not only improve the optimization efficiency but also obtain lighter optimization results. Moreover, using the NDF approach, a mixed-integer linear optimization model for minimizing the weight of truss with discrete cross-sectional areas subject to constraints on kinematic stability, bar buckling, allowable stress, nodal displacement, bar crossing, and overlap** is proposed in this study. Because the objective and constraint functions are linear expressions in terms of variables, the globally optimal structures can be obtained by using the proposed model. In addition, two necessary conditions for kinematic stability are proposed to speed up the computational efficiency and delete unnecessary nodes within consecutive tension bars. Finally, the effectiveness of the proposed NDF method and the necessary conditions for kinematic stability are studied on four truss topology optimization problems in two and three dimensions.

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Acknowledgements

This research was supported by the National Natural Science Foundation of China (Grant number: 51978151). The authors would like to thank Dr. Linwei He from the University of Sheffield for providing constructive suggestions which allowed us to improve the article significantly.

Funding

National Natural Science Foundation of China,51978151,Ruoqiang Feng, The Scientific Research Foundation of Graduate School of Southeast University, YBPY1958, QI CAI

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Authors and Affiliations

  1. Key Laboratory of Concrete and Prestressed Concrete Structures of Ministry of Education, Southeast University, Nan**g, 211189, Jiangsu Province, China

    Qi Cai, Ruoqiang Feng, Zhijie Zhang & ** Wang

  2. College of Mechanics and Engineering Science, Hohai University, Nan**g, 211189, Jiangsu Province, China

    Qi Cai

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  1. Qi Cai
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  2. Ruoqiang Feng
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  3. Zhijie Zhang
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  4. ** Wang
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Correspondence to Ruoqiang Feng.

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Cai, Q., Feng, R., Zhang, Z. et al. Topology optimization of truss structure considering kinematic stability based on mixed-integer programming approach. Struct Multidisc Optim 67, 112 (2024). https://doi.org/10.1007/s00158-024-03827-6

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  • DOI: https://doi.org/10.1007/s00158-024-03827-6

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