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Higher-order beam elements based on the absolute nodal coordinate formulation for three-dimensional elasticity

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Abstract

This study thoroughly examines various higher-order three and four-node beam elements for use in the absolute nodal coordinate formulation (ANCF). The paper carefully investigates which potential benefits and drawbacks the utilization of higher-order ANCF beam elements without in-slope vectors has in the case of the usage of full three-dimensional elasticity. When the elastic forces for shear-deformable ANCF beam elements are calculated using full three-dimensional elasticity—especially in the form of the St. Venant–Kirchhoff material law—Poisson locking severely deteriorates the accuracy of the numeric results. As shown in this paper, an existing approach to preventing this locking phenomenon for three-node beam elements can still produce unsatisfying results in load cases involving bidirectional bending. The results of this study show that enriching the polynomial basis used to approximate the beam kinematics provides a natural solution to this issue. As will be seen, these findings for three-node elements can also be extended to four-node elements. When using a sufficient approximation order in transverse directions, satisfying accuracy can be achieved both in conventional one-dimensional bending and in the above-mentioned bidirectional load case.

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Acknowledgements

The authors would like to thank the Academy of Finland (Application No. 259543 for the funding of Postdoctoral Researchers and Application No. 285064) for supporting Marko K. Matikainen.

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Authors and Affiliations

  1. Institute of Engineering and Computational Mechanics, University of Stuttgart, Pfaffenwaldring 9, 70569, Stuttgart, Germany

    Henrik Ebel

  2. Mechanical Engineering, Lappeenranta University of Technology, Skinnarilankatu 34, 53850, Lappeenranta, Finland

    Marko K. Matikainen, Vesa-Ville Hurskainen & Aki Mikkola

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  1. Henrik Ebel
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  2. Marko K. Matikainen
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  3. Vesa-Ville Hurskainen
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  4. Aki Mikkola
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Correspondence to Henrik Ebel.

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Ebel, H., Matikainen, M.K., Hurskainen, VV. et al. Higher-order beam elements based on the absolute nodal coordinate formulation for three-dimensional elasticity. Nonlinear Dyn 88, 1075–1091 (2017). https://doi.org/10.1007/s11071-016-3296-x

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