Skip to main content
SpringerLink
Log in

A novel computational method for dynamic analysis of flexible sandwich plates undergoing large deformation

  • Technical notes
  • Published:
Archive of Applied Mechanics Aims and scope Submit manuscript

Abstract

To account for the nonlinear dynamic effects of flexible sandwich plates undergoing large deformation, a computational method for dynamic analysis of flexible sandwich plates is studied. According to the characteristics of sandwich plates, a simplified plate model is proposed based on the Kirchhoff plate theory, in which the shear stiffness of the core plate is neglected and the stiffness for the whole plate is derived. For the dynamic problem of flexible multibody systems, a thin plate element has been studied based on the absolute nodal coordinate formulation (ANCF). Meanwhile, a method based on invariant tensors is proposed for calculating elastic forces and their Jacobians, which can be calculated during preprocessing and applied for programmed calculation. Using examples, the proposed computational method is verified to be feasible and accurate. In addition, a benchmark example and a double-pendulum model are used to verify the applicability and feasibility of our analytical method for flexible sandwich plates in flexible multibody systems. Therefore, this method lays a foundation for the study of flexible dynamics problems regarding multibody systems with sandwich plates.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6

Availability of data and material

The data sets supporting the results of this article are included within the article and its additional files.

References

  1. Vu-Quoc, L., Deng, H.: Dynamics of geometrically-exact sandwich beams/1-D plates computational aspects. Comput. Methods Appl. Mech. 146(1–2), 135–172 (1996). https://doi.org/10.1016/S0045-7825(96)01226-1

    Article  MATH  Google Scholar 

  2. Vu-Quoc, L., Deng, H., Tan, X.G.: Geometrically exact sandwich shells: the dynamic case. Comput. Methods Appl. Mech. 190(22–23), 2825–2873 (2001). https://doi.org/10.1016/S0045-7825(00)00181-X

    Article  MathSciNet  MATH  Google Scholar 

  3. Galucio, A.C., Deü, J.F., Ohayon, R.: Finite element formulation of viscoelastic sandwich beams using fractional derivative operators. Comput. Mech. 33(4), 282–291 (2004). https://doi.org/10.1007/s00466-003-0529-x

    Article  MATH  Google Scholar 

  4. Arikoglu, A., Ozkol, I.: Vibration analysis of composite sandwich beams with viscoelastic core by using differential transform method. Compos. Struct. 92(12), 3031–3039 (2010). https://doi.org/10.1016/j.compstruct.2010.05.022

    Article  Google Scholar 

  5. Shabana, A.A.: Computer implementation of the absolute nodal coordinate formulation for flexible multibody dynamics. Nonlinear Dyn. 19(3), 293–306 (1998). https://doi.org/10.1023/A:1008072517368

    Article  MathSciNet  MATH  Google Scholar 

  6. Mikkola, A.M., Shabana, A.A.: A non-incremental finite element procedure for the analysis of large deformation of plates and shells in mechanical system applications. Multi-body Syst. Dyn. 9(3), 283–309 (2003). https://doi.org/10.1023/A:1022950912782

    Article  MathSciNet  MATH  Google Scholar 

  7. Dmitrochenko, O.N., Pogorelov, D.Y.: Generalization of plate finite elements for absolute nodal coordinate formulation. Multi-body Syst. Dyn. 10(1), 17–43 (2003). https://doi.org/10.1023/A:1024553708730

    Article  MATH  Google Scholar 

  8. Dufva, K., Shabana, A.A.: Analysis of thin plate structures using the absolute nodal coordinate formulation. Proc. Inst. Mech. Eng. Part K J. Multi-body Dyn. 219(4), 345–355 (2005). https://doi.org/10.1243/146441905x50678

    Article  Google Scholar 

  9. Dufva, K., Kerkkänen, K., Maqueda, L.G., Shabana, A.A.: Nonlinear dynamics of three-dimensional belt drives using the finite-element method. Nonlinear Dyn. 48(4), 449–466 (2007). https://doi.org/10.1007/s11071-006-9098-9

    Article  MATH  Google Scholar 

  10. Liu, C., Tian, Q., Hu, H.Y.: Dynamics of a large scale rigid–flexible multibody system composed of composite laminated plates. Multi-body Syst. Dyn. 26(3), 283–305 (2011). https://doi.org/10.1007/s11044-011-9256-9

    Article  MATH  Google Scholar 

  11. Tian, Q., Chen, L.P., Zhang, Y.Q., Yang, J.Z.: An efficient hybrid method for multibody dynamics simulation based on absolute nodal coordinate formulation. J. Comput. Nonlinear Dyn. (2009). https://doi.org/10.1115/1.3079783

    Article  Google Scholar 

  12. García-Vallejo, D., Mayo, J., Escalona, J.L., Dominguez, J.: Efficient evaluation of the elastic forces and the Jacobian in the absolute nodal coordinate formulation. Nonlinear Dyn. 35(4), 313–329 (2004). https://doi.org/10.1023/B:NODY.0000027747.41604.20

    Article  MATH  Google Scholar 

  13. Ventsel, E., Krauthammer, T.: Thin Plates and Shell Theory, Analysis, and Applications. Marcel Dekker, New York (2001)

    Google Scholar 

  14. Kollár, L.P., George, S.: Mechanics of Composite Structures. Cambridge University Press, New York (2003)

    Book  Google Scholar 

  15. Dmitrochenko, O., Mikkola, A.: Two simple triangular plate elements based on the absolute nodal coordinate formulation. J. Comput. Nonlinear Dyn. 3(4), 041012 (2008). https://doi.org/10.1115/1.2960479

    Article  Google Scholar 

  16. Gerstmayr, J., Shabana, A.A.: Efficient integration of the elastic forces and thin three-dimensional beam elements in the absolute nodal coordinate formulation. In: ECCOMAS Thematic Conference, Madrid, Spain, 21–24 June (2005)

  17. Liu, C., Tian, Q., Hu, H.Y.: Efficient computational method for dynamics of flexible multibody systems based on absolute nodal coordinate. Chin. J. Theor. Appl. Mech. 42(6), 1197–1204 (2010)

    Google Scholar 

  18. Leissa, A.W.: Vibration of Plates. Ohio State University, Columbus (1969)

    Google Scholar 

  19. Mikkola, A.M., Matikainen, M.K.: Development of elastic forces for a large deformation plate element based on the absolute nodal coordinate formulation. J. Comput. Nonlinear Dyn. 1(2), 103 (2006). https://doi.org/10.1115/1.1961870

    Article  Google Scholar 

Download references

Acknowledgements

National Natural Science Foundation of China [51975567], Strategic Priority Research Program on Space Science of Chinese Academy of Sciences [XDA1502030505], Foundation of State Key Laboratory of Robotics [2019-Z06].

Author information

Authors and Affiliations

  1. University of Chinese Academy of Sciences, Beijing, 100049, China

    Zhaowei Zhang

  2. State Key Laboratory of Robotics, Shenyang Institute of Automation, Chinese Academy of Sciences, Shenyang, 110016, China

    Zhaowei Zhang, Weijia Zhou, Sheng Gao, Minhong Wan & Wei Zhang

  3. Institutes for Robotics and Intelligent Manufacturing, Chinese Academy of Sciences, Shenyang, 110016, China

    Zhaowei Zhang, Weijia Zhou, Sheng Gao, Minhong Wan & Wei Zhang

Authors
  1. Zhaowei Zhang
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Weijia Zhou
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Sheng Gao
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Minhong Wan
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Wei Zhang
    View author publications

    You can also search for this author in PubMed Google Scholar

Contributions

Z.W. Zhang and W.J. Zhou conceived and designed the study. Z.W. Zhang wrote the paper. S. Gao and M.H. Wan analyzed the data and interpreted the results. W. Zhang developed the idea for the study. All authors discussed the results and revised the manuscript.

Corresponding author

Correspondence to Zhaowei Zhang.

Ethics declarations

Conflict of interest

Not applicable.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Zhang, Z., Zhou, W., Gao, S. et al. A novel computational method for dynamic analysis of flexible sandwich plates undergoing large deformation. Arch Appl Mech 91, 4069–4080 (2021). https://doi.org/10.1007/s00419-021-02022-z

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00419-021-02022-z

Keywords

Search

Navigation