An Efficient Three-Node Beam Element for Large Deformation Analysis Using Absolute Nodal Coordinate Formulation

An efficient formulation for dynamics of beams with large deformation and large rotation is presented. A large deformation three-node beam element is established, in which the position coordinate is selected as the generalized coordinates in middle node, and the position coordinate and lateral slope vectors are selected as the generalized coordinates in both end nodes. The inertia force and the constant mass matrix of beam element are obtained. Based on the principles of continuum mechanics, the elastic forces and the stiffness matrix are deduced, which are highly non-linear polynomials of the generalized coordinates. The generalize external forces is obtained by virtual work. The stretch, shear, bending, and torsion deformation of slender beams are considered. The Possion’s locking and shear locking do not exist in this formulation. Hilber-Hughes-Taylor (HHT) integration method involved the Jacobian matrix and right-hand side is used to obtain the dynamics results. Numerical example validates the presented approach. The proposed formulation provides an effective tool for dynamics analysis of flexible slender beams, which can be accurately applied to solve the dynamics problem of multibody system with large deformations.