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Multiscale eigenfrequency optimization of multimaterial lattice structures based on the asymptotic homogenization method

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Abstract

Ultralight lattice structures exhibit excellent mechanical performance and have been used widely. In structural design, the fundamental frequency is highly important. Therefore, a multiscale topology optimization method was utilized to optimize the fundamental frequency of multimaterial lattice structures in this study. Two types of optimization problems were studied, namely, maximizing the natural fundamental frequency with mass constraints and minimizing compliance with frequency constraints. The Heaviside-penalty-based discrete material optimization method was adopted for the optimal selection of candidate materials. The asymptotic homogenization method was used to evaluate the equivalent macroscale properties according to the microstructure of the lattice material. To enable gradient optimization, sensitivities were outlined in detail. A density filter with a volume-preserving Heaviside projection was used to eliminate the risk of a checkerboard pattern and reduce the number of gray elements. A polynomial penalization scheme was employed to eliminate localized spurious eigenmodes in the low-density region. Finally, several numerical examples were performed to validate the proposed method. These numerical examples resulted in novel microstructural configurations with remarkably improved vibration resistance.

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Funding

This research was financially supported by the National Natural Science Foundation of China (No. 11672057, 11711530018, 51975087), the National Key R&D Program of China (2017YFC0307203), Program (LR2017001) for Excellent Talents at Colleges and Universities in Liaoning Province, the 111 project (B14013), the Lightweight Optimization and High Reliability 3D Printing Technology for Aeroengine Parts, Scientific Research Program of Shanghai Science and Technology Commissio (17DZ1120000), the STINT Project of Lund University and China Scholarship Council (CSC).

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Authors and Affiliations

  1. State Key Laboratory of Structural Analysis for Industrial Equipment, Department of Engineering Mechanics, International Research Center for Computational Mechanics, Dalian University of Technology, Dalian, 116024, China

    Zhirui Fan, Jun Yan & Guozhong Zhao

  2. Division of Solid Mechanics, Lund University, Box 118, 22100, Lund, Sweden

    Zhirui Fan, Mathias Wallin & Matti Ristinmaa

  3. Yunnan Mechanical Research & Design Institute, Kunming, 650031, China

    Jun Yan

  4. School of Mechanical Engineering, Dalian University of Technology, Dalian, 116024, China

    Bin Niu

Authors
  1. Zhirui Fan
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  2. Jun Yan
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  3. Mathias Wallin
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  4. Matti Ristinmaa
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  5. Bin Niu
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  6. Guozhong Zhao
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Correspondence to Jun Yan.

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Fan, Z., Yan, J., Wallin, M. et al. Multiscale eigenfrequency optimization of multimaterial lattice structures based on the asymptotic homogenization method. Struct Multidisc Optim 61, 983–998 (2020). https://doi.org/10.1007/s00158-019-02399-0

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  • DOI: https://doi.org/10.1007/s00158-019-02399-0

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