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Topology Optimization Method for Microscale Structures Described with Integral Nonlocal Theory

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Abstract

The integration of additive manufacturing and topology optimization makes it possible to fabricate complex configurations, especially for microscale structures, which can guarantee the realization of high-performance structural designs. However, topology results often contain microstructures (several multicellular scales) similar to the characteristic length of local macrostructures, leading to errors in structural performance analysis based on classical theories. Therefore, it is necessary to consider the size effect in topology optimization. In this paper, we establish a novel topology optimization model utilizing the integral nonlocal theory to account for the size effect. The approach consists of an integral constitutive model that incorporates a kernel function, enabling the description of stress at a specific point in relation to strain in a distant field. Topology optimization structures based on nonlocal theory are presented for some benchmark examples, and the results are compared with those based on classical medium theory. The material layout exhibits significant differences between the two approaches, highlighting the necessity of topology optimization based on nonlocal theory and the effectiveness of the proposed method.

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The datasets generated or analyzed during this study are available from the corresponding author upon reasonable request.

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Acknowledgements

The authors gratefully acknowledge the financial support to this work by the National Natural Science Foundation of China (Grant Nos. 12272076 and 11802164) and the 111 Project (B14013).

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Authors and Affiliations

  1. State Key Laboratory of Structural Analysis, Optimization and CAE Software for Industrial Equipment, Dalian University of Technology, Dalian, 116024, China

    Jiayu Li, Quhao Li & Shutian Liu

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  1. Jiayu Li
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  2. Quhao Li
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  3. Shutian Liu
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Contributions

JL provided all the data for this paper and contributed significantly to writing this paper. SL conceived the main idea of this paper and put forward valuable suggestions for revision. QL provided the large memory server needed for the calculation and modified the English.

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Correspondence to Shutian Liu.

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Li, J., Li, Q. & Liu, S. Topology Optimization Method for Microscale Structures Described with Integral Nonlocal Theory. Acta Mech. Solida Sin. 37, 63–71 (2024). https://doi.org/10.1007/s10338-023-00438-4

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  • DOI: https://doi.org/10.1007/s10338-023-00438-4

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