Advanced Steel Construction

Vol. 6, No. 2, pp. 767-787 (2010)


A MIXED CO-ROTATIONAL 3D BEAM ELEMENT FORMULATION FOR ARBITRARILY LARGE ROTATIONS

 

Z.X. Li 1,* and L. Vu-Quoc 2

1 Associate professor, Department of Civil Engineering, Zhejiang University, Hangzhou 310058, China

2 Professor, Department of Mechanical and Aerospace Engineering, University of Florida, Gainesville FL 32611, USA

*(Corresponding author: E-mail: This email address is being protected from spambots. You need JavaScript enabled to view it. )

 

Received: 16 May 2009; Revised: 8 August 2009; Accepted: 11 August 2009

DOI:10.18057/IJASC.2010.6.2.6

 

ABSTRACT:

A new 3-node co-rotational element formulation for 3D beam is presented. The present formulation differs from existing co-rotational formulations as follows: 1) vectorial rotational variables are used to replace traditional angular rotational variables, thus all nodal variables are additive in incremental solution procedure; 2) the Hellinger-Reissner functional is introduced to eliminate membrane and shear locking phenomena, with assumed membrane strains and shear strains employed to replace part of conforming strains; 3) all nodal variables are commutative in differentiating Hellinger-Reissner functional with respect to these variables, resulting in a symmetric element tangent stiffness matrix; 4) the total values of nodal variables are used to update the element tangent stiffness matrix, making it advantageous in solving dynamic problems. Several examples of elastic beams with large displacements and large rotations are analysed to verify the computational efficiency and reliability of the present beam element formulation.

 

Keywords:Co-rotational method; vectorial rotational variable; 3D beam element; locking-free; Hellinger-Reissner functional; assumed strain.

 

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