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Sensitivity clustering-based multi-scale topology optimization method for metamaterial thermal actuators

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Abstract

Thermal elastic metamaterials with extreme positive or negative thermal expansion properties have great potential applications in designing and manufacturing thermal actuators. In this paper, a concurrent topology optimization method is proposed for metamaterial thermal actuator design. The actuator is composed of multiple metamaterials with different microstructures. The microstructures are composed of two common materials, aluminum and invar. The concurrent optimization method is capable of simultaneously designing the topology, the arrangement of the multiple metamaterials, and the microstructures of the metamaterials. The macro-topology and the multiple metamaterial microstructures are optimized simultaneously through density-based topology optimization method and multi-phase material optimization method. A sensitivity clustering-based method is proposed and used to partition the macrostructure into several sub-domains, each of which is occupied with appropriate individual metamaterial. The sensitivity of the optimization objective with respect to the thermal expansion coefficients is chosen as the criterion to generate data points for clustering, and the fuzzy c-means (FCM) method is adopted for data clustering. The grouped microstructures will greatly reduce the computational burden and at the same time improve the manufacturability and structural performance. Several numerical examples are presented, including the design with single output point and multiple output points. Optimization results show that both the macro-topology and the metamaterial microstructures are significantly affected by the actuation impedance adopted in the optimization. The effect of number of clusters on the optimization results is studied.

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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, 11821202), the 111 Project (B14013), and the Fundamental Research Funds for the Central Universities of China (DUT21GF101). The authors are also grateful to the anonymous reviewers for their valuable suggestions and comments.

Funding

Funding was provided by the National Natural Science Foundation of China (12272076), Overseas Expertise Introduction Project for Discipline Innovation (B14013), and Fundamental Research Funds for the Central Universities (DUT21GF101).

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

    Zheng Qiu, Quhao Li & Shutian Liu

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  1. Zheng Qiu
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  2. Quhao Li
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Correspondence to Shutian Liu.

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Qiu, Z., Li, Q. & Liu, S. Sensitivity clustering-based multi-scale topology optimization method for metamaterial thermal actuators. Struct Multidisc Optim 67, 9 (2024). https://doi.org/10.1007/s00158-023-03729-z

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