The Large Deformation Curved Beam Element In Multibody Dynamics And Its Application

In recent years, absolute nodal coordinate formulation becomes very popular in the field of flexible multibody dynamics. In this formulation absolute nodal coordinates and their material derivatives are applied as generalized coordinates to represent both deformation and rigid body motion. In contrast to conventional incremental finite element approach, absolute nodal coordinate formulation allows a fully nonlinear representation of rigid body motion and can provide the exact rigid body inertia in the case of large rotation, and at the same time reduces the nonlinearity of the dynamics equation greatly. The methodology is suited not only for simulation of beams, but for modeling of plates, shells, and solids.In this thesis, a curved Euler-Bernoulli beam element based on the absolute nodal coordinate formulation is presented in the frame of multibody system. The curved beam element here adopts nodal coordinates and their material derivatives as well as one of the Euler angles as nodal variables, and describes the element configuration based on Hermite interpolation of nodal coordinates and linear interpolation of Euler angles, which allows the curved element to simulate large displacement, large rotation and large deformation problem. The flexible curved beam can be degenerated to a straight beam or a more simple flexible cable element. To consider the singularity problem, involved in calculating the Euler angles with certain orientation, another set of Euler angles is introduced, and the singularity problem which the curved beam may encounter during large rotation in space can be avoided through swapping between the two sets of Euler angles. In this paper, several numerical examples are provided, including static, mode and dynamic analysis, to verify the validity of the large deformation curved beam element.Another main part of the paper is to study the coupling between the large deformation curved beam element and the rigid body element. The coupling behaves as the form of constraint and contact. This paper presents detailed theories in these two aspects, and shows several numerical examples of contact between curved elements and rigid bodies. In addition, an engineering application of the large deformation curved beam element in modeling the steel plate is proposed. From this application, the flexible curved beam element base on absolute nodal coordinate formulation shows great advantages in contrast to the conventional finite segment beam element in multibody system, because it describes both accurate exact rigid motion and large deformation. As a result, the model of flexible curved beam element to the steel plate needs much less elements and computational time. This application gives another evidence to testify excellent capability of the flexible curved beam element shown in this paper.