Reference Type:  Journal Article
Record Number: 1
Author: Li , Z. X. and Quoc, L. Vu.
Year: 2009
Title: A mixed co-rotational 3d beam element formulation for arbitrarily large rotations
Journal: Advanced Steel Construction
Volume: 6
Issue: 2
Pages: 21
Start Page: 767
Short Title: A mixed co-rotational 3d beam element formulation for arbitrarily large rotations
DOI: 10.18057/IJASC.2010.6.2.6
Keywords: Co-rotational method; vectorial rotational variable; 3D beam element; locking-free; Hellinger-Reissner functional; assumed strain.
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.
Author Address: Associate professor, Department of Civil Engineering, Zhejiang University, Hangzhou 310058, China