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Acta Mechanica
Published in: Acta Mechanica 7/2023

28-02-2023 | Original Paper

A novel collocation beam element based on absolute nodal coordinate formulation

Authors: Jia Wang, Tengfei Wang, Hongyou Bian, Weijun Liu

Published in: Acta Mechanica | Issue 7/2023

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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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Metadata
Title
A novel collocation beam element based on absolute nodal coordinate formulation
Authors
Jia Wang
Tengfei Wang
Hongyou Bian
Weijun Liu
Publication date
28-02-2023
Publisher
Springer Vienna
Published in
Acta Mechanica / Issue 7/2023
Print ISSN: 0001-5970
Electronic ISSN: 1619-6937
DOI
https://doi.org/10.1007/s00707-023-03509-2

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