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Topology optimization of frame structures with stress and stability constraints

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Abstract

At present, most of the researches on topology optimization focus on continuum structures, but few on frame structures. This paper presents a methodology for topology optimization of frame structures with stress and stability constraints under a prescribed volume. In order to solve the pseudo buckling mode issues and calculation efficiency caused by low-density elements, new smooth penalty functions of the element elastic stiffness matrix and stress stiffness matrix are constructed, and an effective pseudo buckling mode identification measure is adopted to solve the corresponding problems. Moreover, a comprehensive measure, including the stress relaxation and the constraint aggregation method and the varying constraint limit scheme, to deal with stress and stability constraints is proposed. Furthermore, the Heaviside mapping scheme is introduced to obtain a clear solid/empty beam layout. Then, the sensitivities of stress and stability constraints with respect to design variables are given, and the proposed topology optimization problem is solved by the method of moving asymptotes. Finally, several numerical examples are given to demonstrate the feasibility and effectiveness of the proposed approach.

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Acknowledgements

This work is supported by the National Natural Science Foundation of China (Grant Nos. 12102066, 12172065), Cooperation Research Project of China Construction Fifth Engineering Division Corp. LTD of China (2019RG088), the Young Teachers Growth Program Project of CSUST of China (2019QJCZ032). Very thanks reviewers for their comments on the paper.

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Authors and Affiliations

  1. School of Civil Engineering, Changsha University of Science and Technology, Changsha, 410076, Hunan, People’s Republic of China

    Lei Zhao, Zihang Zhang & Yan Han

  2. School of Automotive and Mechanical Engineering, Changsha University of Science and Technology, Changsha, 410076, Hunan, People’s Republic of China

    Jijun Yi & Jianhua Rong

  3. School of Civil Engineering, Changsha University, Changsha, 410076, Hunan, People’s Republic of China

    Zhijun Zhao

Authors
  1. Lei Zhao
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  2. Jijun Yi
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  4. Zihang Zhang
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  5. Yan Han
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  6. Jianhua Rong
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Correspondence to Jianhua Rong.

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The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Replication of results

The topology optimization model described in Sect. 5 is implemented in Matlab with Structure Mechanics Module, Optimization Module. The details, such as material properties, loads, boundary conditions, constraints, and objectives, for the validation cases have been defined in Sect. 7. The numerical model of this paper can be obtained from the corresponding author with a reasonable request.

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Zhao, L., Yi, J., Zhao, Z. et al. Topology optimization of frame structures with stress and stability constraints. Struct Multidisc Optim 65, 268 (2022). https://doi.org/10.1007/s00158-022-03361-3

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  • DOI: https://doi.org/10.1007/s00158-022-03361-3

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