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Digital Twin Data-Driven Multi-Disciplinary and Multi-Objective Optimization Framework for Automatic Design of Negative Stiffness Honeycomb

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Abstract

The honeycomb structures perform well in shock and vibration isolation with a light weight and small material. They cannot reuse due to plastic buckling after a deformation. To overcome this disadvantage, many researchers have actively studied the development of a reusable honeycomb structure using the elastic buckling mechanism. They proposed a new shape for honeycombs: one that can absorb and dissipate energy through a negative stiffness (NS) effect caused by the elastic buckling phenomenon. However, existing studies have focused on the concept design of the NS curved beam, and the research on how to design products in detail is insufficient. Therefore, this study proposes a digital twin data-driven design framework for the detailed design of the semi-symmetric NS curved beam. For this, multi-disciplinary and multi-objective optimization of the virtual NS beam model is performed by maximizing the energy absorption in the elastic buckling discipline through geometric design variables and analytical parameters, and enhancing its similarity to accurate theoretical models in the digital twin discipline through coupling variables. For the optimization, the specific energy absorption (SEA) and error rate are modeled as regression models, and convergence is modeled as a classification model using an artificial intelligence (AI) model. The optimum results improved the energy absorption and reduced the relative error rates while ensuring convergence of the virtual model.

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Acknowledgements

This work was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIT) (No. 2021R1A2C1013557 and 2020R1A5A8018822).

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Authors and Affiliations

  1. School of Mechanical Engineering, Pusan National University, Busan, South Korea

    Juyoung Choi, Hyungdo Kim, Taemin Noh & Yoojeong Noh

  2. Research Institute of Mechanical Technology, Pusan National Univsity, Busan, South Korea

    Young-** Kang

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  1. Juyoung Choi
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Contributions

JC: Conceptualization, investigation, formal analysis, writing – original draft. HK: investigation, formal analysis. TN: investigation, formal analysis. YJK: conceptualization, methodology, validation, visualization, project administration, writing – original draft. YN: conceptualization, funding acquisition, project administration, supervision, writing – review & editing. All authors read and approved the final manuscript.

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Correspondence to Young-** Kang or Yoojeong Noh.

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Appendix

Appendix

The convergence classification model in Sect. 4.3 is determined very sensitively by the design variables and analysis parameters. In particular, In particular, in FE models with strong nonlinearity in analysis, convergence/nonconvergence varies sensitively depending on the combination of analysis parameters. Figure 21 is a scatterplot showing three reduced features and convergence/non-convergence labels using t-distributed static neighbor embedding (t-SNE) and principal component analysis (PCA), which are representative methods of dimension reduction and data visualization [40]. Here, 0 represents non-convergence, and 1 represents convergence. The results of t-SNE, a nonlinear dimensionality reduction method, show that nonlinearity is very serious for the reduced three features, and that most of the regions have a mixture of convergent/non-convergent classes. Looking at PCA, a linear dimension reduction method, convergence/non-convergence data are mixed with each other with a large variation. This result clearly shows that it is very difficult to distinguish convergence/nonconvergence according to changes in design variables and analysis parameters in NSH curved beams, and means that even a slight change in input values can change the classification results.

Fig. 21
figure 21

Difficulty of classification of convergene/non-convergence

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Choi, J., Kim, H., Noh, T. et al. Digital Twin Data-Driven Multi-Disciplinary and Multi-Objective Optimization Framework for Automatic Design of Negative Stiffness Honeycomb. Int. J. Precis. Eng. Manuf. 24, 1453–1472 (2023). https://doi.org/10.1007/s12541-023-00816-5

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