A finite element beam model including cross-section distortion in the absolute nodal coordinate formulation

Zhenxing Shen, Pei Li, Cheng Liu, Gengkai Hu*

*Corresponding author for this work

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Abstract

A new class of beam finite elements is proposed in a three-dimensional fully parameterized absolute nodal coordinate formulation, in which the distortion of the beam cross section can be characterized. The linear, second-order, third-order, and fourth-order models of beam cross section are proposed based on the Pascal triangle polynomials. It is shown that Poisson locking can be eliminated with the proposed higher-order beam models, and the warping displacement of a square beam is well described in the fourth-order beam model. The accuracy of the proposed beam elements and the influence of cross-section distortion on structure deformation and dynamics are examined through several numerical examples. We find that the proposed higher-order models can capture more accurately the structure deformation such as cross-section distortion including warping, compared to the existing beam models in the absolute nodal coordinate formulation.

Original languageEnglish
Pages (from-to)1019-1033
Number of pages15
JournalNonlinear Dynamics
Volume77
Issue number3
DOIs
Publication statusPublished - Aug 2014
Externally publishedYes

Keywords

  • Absolute nodal coordinate formulation
  • Cross-section distortion
  • Higher-order beam models
  • Warping displacement

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Shen, Z., Li, P., Liu, C., & Hu, G. (2014). A finite element beam model including cross-section distortion in the absolute nodal coordinate formulation. Nonlinear Dynamics, 77(3), 1019-1033. https://doi.org/10.1007/s11071-014-1360-y