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A novel collocation beam element based on absolute nodal coordinate formulation

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Abstract

The computational efficiency has been largely hindering the application of the absolute nodal coordinate formulation (ANCF). To improve the computational efficiency of the absolute nodal coordinate formulation, the collocation strategy is employed to establish the ANCF beam element. A novel ANCF beam element based on multi-node collocation (ANCF_C) is proposed. Zero points of the second-order derivative of pth-order Legendre polynomial and the boundary points in the element domain are used as nodes to discretize the beam node-wisely. Accordingly, the \((p-1)\)th-order Lagrange interpolation is employed for the longitudinal displacement interpolation. The elastic force and stiffness matrix are deduced based on the enhanced continuum mechanics formulation (ECMF) to avoid the locking problem. By using p-point Lobatto quadrature for the numerical integration of the elastic force and the mass matrix, the quadrature points coincide with the discretized nodes in the element. The performance of the ANCF_C is verified by both static and dynamic examples.

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Funding

This research was supported by the National Science and Technology Major Project (2019-VII-0004-0144).

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Authors and Affiliations

  1. School of Mechanical Engineering, Shenyang University of Technology, NO.111, Shenliao West Road, Shenyang, China

    Jia Wang, Hongyou Bian & Weijun Liu

  2. State Key Laboratory for Strength and Vibration of Mechanical Structures, School of Aerospace Engineering, Xi’an Jiaotong University, Xi’an, 710049, Shaanxi, China

    Tengfei Wang

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  1. Jia Wang
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Correspondence to Weijun Liu.

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Wang, J., Wang, T., Bian, H. et al. A novel collocation beam element based on absolute nodal coordinate formulation. Acta Mech 234, 2695–2707 (2023). https://doi.org/10.1007/s00707-023-03509-2

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  • DOI: https://doi.org/10.1007/s00707-023-03509-2

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