Comparison of three-dimensional flexible beam elements for dynamic analysis

Classical finite element formulation and absolute nodal coordinate formulation

Journal article (2010)

Authors

A.L. Schwab Biomechatronics & Human-Machine Control - Mechanical, Maritime and Materials Engineering
J.P. Meijaard University of Twente
Research Group
Biomechatronics & Human-Machine Control (Mechanical, Maritime and Materials Engineering) (TU Delft)
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Published Date

2010

Language

English

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Faculty

Mechanical, Maritime and Materials Engineering

Department

Biomechanical Engineering

Research Group

Biomechatronics & Human-Machine Control

Abstract

Three formulations for a flexible spatial beam element for dynamic analysis are compared: a Timoshenko beam with large displacements and rotations, a fully parametrized element according to the absolute nodal coordinate formulation (ANCF), and an ANCF element based on an elastic line approach. In the last formulation, the shear locking of the antisymmetric bending mode is avoided by the application of either the two-field Hellinger-Reissner or the three-field Hu-Washizu variational principle. The comparison is made by means of linear static deflection and eigenfrequency analyses on stylized problems. It is shown that the ANCF fully parametrized element yields too large torsional and flexural rigidities, and shear locking effectively suppresses the antisymmetric bending mode. The presented ANCF formulation with the elastic line approach resolves most of these problems.