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Large deformations of hyperelastic curved beams based on the absolute nodal coordinate formulation

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Abstract

Compared with traditional linear elastic materials, the soft structure composed of incompressible hyperelastic materials has not only geometrical nonlinearity but also material nonlinearity during deformation. In this paper, the absolute nodal coordinate formulation (ANCF) is used to study the large deformations and large overall motions of incompressible hyperelastic curved beams. A novel large deformation dynamic modeling method for curved beams made of hyperelastic materials is proposed, in which a simplified Neo-Hookean model is combined with the one-dimensional ANCF beam element. The elastic force vector is calculated according to the exact expression of curvature. The dynamic equations are derived by using the virtual work principle. The dynamic responses of a cantilever silica gel beam under gravity are calculated based on the present method and compared with those of the improved low-order beam element (ILOBE), high-order beam element (HOBE), and commercial finite element analysis software (ANSYS). Simulation results show that the proposed method can accurately describe the large deformation and large overall motion of the beam, and has better computational efficiency. Research in this paper provides an efficient dynamic model for the dynamics analysis of soft robot arms.

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Data Availability

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

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Funding

This research is supported by grants from the National Natural Science Foundation of China (Project Nos. 12072159 and 12232012) and the Fundamental Research Funds for the Central Universities (Project No. 30922010314).

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Authors and Affiliations

  1. School of Science, Nanjing University of Science and Technology, Nanjing, People’s Republic of China

    Liang Li, Yaolun Wang, Yongbin Guo & Dingguo Zhang

  2. School of Aerospace Engineering and Applied Mechanics, Tongji University, Shanghaig, People’s Republic of China

    Yaolun Wang

Authors
  1. Liang Li
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  2. Yaolun Wang
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  3. Yongbin Guo
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  4. Dingguo Zhang
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Contributions

All authors contributed to the study conception and design. Formal analysis and investigation were performed by [Liang Li] and [Yaolun Wang]. Conceptualization by [Yongbin Guo]. Funding acquisition performed by [Liang Li] and [Dingguo Zhang]. The first draft of the manuscript was written by [Liang Li] and [Yaolun Wang] and all authors commented on previous versions of the manuscript. All authors read and approved the final manuscript.

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Correspondence to Dingguo Zhang.

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Li, L., Wang, Y., Guo, Y. et al. Large deformations of hyperelastic curved beams based on the absolute nodal coordinate formulation. Nonlinear Dyn 111, 4191–4204 (2023). https://doi.org/10.1007/s11071-022-08076-0

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  • DOI: https://doi.org/10.1007/s11071-022-08076-0

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