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.

A 3-Node Co-Rotational Triangular Elasto-Plastic Shell Element Using Vectorial Rotational Variables

“…In general, the two smallest components of one orientation vector and one smaller component of another orientation vector at a node can be selected as global rotational variables, and these vectors can be oriented to three global coordinate axes in the initial configuration or defined as those of the beam element presented in [83][84][85].…”

A Mixed Co-Rotational 3d Beam Element Formulation for Arbitrarily Large Rotations

“…Crisfield [2] and Simo [21] also predicted that a symmetric tangent stiffness matrix could be achieved if a certain set of additive rotational variables were employed in a co-rotational element formulation. In the present co-rotational beam element formulation, such additive rotational variables are used, and the versatile vectorial rotational variables had also been employed in a co-rotational 2D beam element formulation [22], a co-rotational 3D beam conforming element formulation [23], a co-rotational curved triangular shell element formulation [24], and a co-rotational curved quadrilateral shell element formulation [25], respectively.…”

Model-Predictive Gust Load Alleviation Controller for a Highly Flexible Aircraft

“…This is accomplished by attaching a local element reference frame to each element; this rotates and translates with the beam element. A more detailed description can be found in the nonlinear finite-element literature [27,28,29].…”