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A new curved gradient deficient shell element of absolute nodal coordinate formulation for modeling thin shell structures

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Abstract

A curved gradient deficient shell element for the Absolute Nodal Coordinate Formulation (ANCF) is proposed for modeling initially thin curved structures. Unlike the fully parameterized elements of ANCF, a full mapping of the gradient vectors between different configurations is not available for gradient deficient elements, therefore it is cumbersome to work in a rectangular coordinate system for an initially curved element. In this study, a curvilinear coordinate system is adopted as the undeformed Lagrangian coordinates, and the Green–Lagrange strain tensor with respect to the curvilinear frame is utilized to characterize the deformation energy of the shell element. As a result, the strain due to the initially curved element shape is eliminated naturally, and the element formulation is obtained in a concise mathematical form with a clear physical interpretation. For thin structures, the simplified formulations for the evaluation of elastic forces are also given. Moreover, an approach to deal with the on-surface slope discontinuity is also proposed for modeling general curved shell structures. Finally, the developed element of ANCF is validated by several numerical examples.

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Acknowledgements

This work was supported in part by National Natural Science Foundation of China under Grant Nos. 10972036, 10832002, 11221202, 11202025 and 11290151.

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Authors and Affiliations

  1. Key Laboratory of Dynamics and Control of Flight Vehicle, Ministry of Education, School of Aerospace Engineering, Beijing Institute of Technology, Beijing, 100081, China

    D. Yan, C. Liu, Q. Tian, K. Zhang, X. N. Liu & G. K. Hu

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  1. D. Yan
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  2. C. Liu
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  3. Q. Tian
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  4. K. Zhang
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  5. X. N. Liu
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Correspondence to X. N. Liu.

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Yan, D., Liu, C., Tian, Q. et al. A new curved gradient deficient shell element of absolute nodal coordinate formulation for modeling thin shell structures. Nonlinear Dyn 74, 153–164 (2013). https://doi.org/10.1007/s11071-013-0955-z

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  • DOI: https://doi.org/10.1007/s11071-013-0955-z

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