A two-dimensional shear deformable beam element based on the absolute nodal coordinate formulation

In this study, a new two-dimensional shear deformable beam element is proposed for large deformation problems. The kinematics of the beam are defined using an exact displacement field, where the rotation angles of the cross-section caused by bending and shear deformations are described separately. Cubic interpolation is used for determining the curvature of the beam due to bending, while linear interpolation polynomials are used for the shear strain. The absolute nodal coordinate formulation, in which global displacements and slopes are used as the nodal coordinates, is employed for the finite element discretization of the beam. The capability of the element to predict static deformation is studied using numerical examples. The results imply that the element is free of a phenomenon called shear-locking. The capability of the element to model highly nonlinear behaviour is established using a bending test where the cantilever is bent into a full circle using only four elements. A flexible pendulum and a spin-up manoeuvre are modelled in order to study the behaviour of the element in dynamical problems. The proposed element is also compared with an existing shear deformable beam element based on the absolute nodal coordinate formulation. Finally, the simple linearization of the beam curvature based on the assumption of small strain will be discussed.