A co-rotational formulation for 3D beam element using vectorial rotational variables

Abstract

Based on a co-rotational framework, a 3-noded iso-parametric element formulation of 3D beam was presented, which was used for accurate modelling of frame structures with large displacements and large rotations. Firstly, a co-rotational framework was fixed at the internal node of the element, it translates and rotates with the node rigidly; then, vectorial rotational variables were defined, they are three smaller components of the cross-sectional principal vectors at each node, sometimes they represent different components of the cross-sectional principal vectors in incremental solution procedure so as to avoid the occurrence of ill-conditioned tangent stiffness matrix; thereafter, the internal force vector and tangent stiffness matrix in local system was derived from the strain energy of the element as its first partial derivative and second partial derivative with respect to local variables, respectively, and a symmetric tangent stiffness matrix was achieved; finally, several examples were analysed to illustrate the reliability and accuracy of this procedure.