A mixed co‐rotational formulation of 2D beam element using vectorial rotational variables

Abstract

AbstractBased on a co‐rotational framework, a three‐noded iso‐parametric mixed element formulation for large displacement analysis of 2D beam was presented, this formulation is free of membrane/shear locking problems. Firstly, the co‐rotational framework was fixed at the internal node of the element, which translates and rotates rigidly with this node, but does not deform with the element. Then, a set of vectorial rotational variables were defined to describe accurately the element deformation, these rotational variables may have different connotations in an incremental solution procedure. Thirdly, Green strain and independently assumed strain fields were introduced in calculating the mixed Hellinger–Reissner functional, and the internal force vector was derived by enforcing the stationarity to the mixed functional, thereafter, the element tangent stiffness matrix was calculated from the internal force vector by differentiating it with respect to local variables, and a symmetric element tangent stiffness matrix was achieved. Finally, several examples were analysed to illustrate the reliability and efficiency of the proposed procedure in modelling of 2D frame structures with large displacements and large rotations. Copyright © 2006 John Wiley & Sons, Ltd.