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Transversally higher-order interpolating polynomials for the two-dimensional shear deformable ANCF beam elements based on common coefficients

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Abstract

The polynomial representation for describing the displacement field of the elements is the main factor that determines the performance of the shear deformable beam elements based on the absolute nodal coordinate formulation (ANCF). In order to resolve the locking problem of the ANCF beam elements, the transversally higher-order polynomial representation has been investigated frequently and applied to the displacement field of the elements by increasing the nodal coordinates of the beam elements. In this paper, transversally higher-order interpolating polynomials are added into the polynomial displacement field of the elements by using common coefficients which mean that the coefficients between the higher-order longitudinal and transversal polynomial components are common. The implementation does not require the increase of the nodal coordinates. Two new kinds of two-dimensional transversally higher-order ANCF beam elements are formulated by common coefficients. The effect of transversally higher-order interpolating polynomials on the performance of the proposed ANCF beam elements is studied by means of certain static and dynamic problems. It is shown that the transversally quadratic order polynomial component \(y^{2}\) introduced by common coefficients can also relieve the problem of Poisson locking, and the proposed beam elements are effective and accurate in the static and dynamic analysis.

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Acknowledgements

This work is supported by the grants from the National Natural Science Foundation of China (No. 51775328).

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  1. School of Mechanical and Automotive Engineering, Shanghai University of Engineering Science, Shanghai, 201620, China

    Chun H. Zhao, Kang W. Bao & Yu L. Tao

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  1. Chun H. Zhao
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  2. Kang W. Bao
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Correspondence to Chun H. Zhao.

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Zhao, C.H., Bao, K.W. & Tao, Y.L. Transversally higher-order interpolating polynomials for the two-dimensional shear deformable ANCF beam elements based on common coefficients. Multibody Syst Dyn 51, 475–495 (2021). https://doi.org/10.1007/s11044-020-09768-4

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