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Acta Mechanica
Published in: Acta Mechanica 12/2023

07-10-2023 | Original Paper

A novel plate element based on absolute nodal coordinate formulation with collocation strategy

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

Published in: Acta Mechanica | Issue 12/2023

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Abstract

In this paper, a novel multi-node plate element with absolute node coordinate formulation (ANCF) is proposed. The nodes of the element are collocated to coincide with the in-plane integral quadrature points, which are used to calculate the elastic and inertia functions. The unevenly distributed nodes of the element are the zero points of the second-order derivative of Legendre polynomial and the boundary ends of the element. The tensor product of the two-direction univariate Lagrange interpolation is used to define the displacement field. To alleviate the locking problem, the gradient deficient setup and the second-order gradient of the thickness direction are used as the nodal coordinates. The standard continuum mechanic formulation is used to deduce the elastic forces. The proposed plate element based on the ANCF with collocated nodes is denoted as ANCF\(\_\)C element. The performance of the ANCF\(\_\)C element is verified by static, eigenfrequency and dynamic examples. The results show that the ANCF\(\_\)C element is more accurate and computationally efficient.
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Metadata
Title
A novel plate element based on absolute nodal coordinate formulation with collocation strategy
Authors
Jia Wang
Tengfei Wang
Yulong Zhang
Hongyou Bian
Weijun Liu
Publication date
07-10-2023
Publisher
Springer Vienna
Published in
Acta Mechanica / Issue 12/2023
Print ISSN: 0001-5970
Electronic ISSN: 1619-6937
DOI
https://doi.org/10.1007/s00707-023-03730-z

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