Abstract
Absolute Nodal Coordinate Formulation(ANCF) is applied for multibody dynamics problems of flexible bodies. The mass matrix and the stiffness matrix are described as simple equations in this formulation, even in the case of the large deformation and displacement problem. However, degree of freedom of the beam element of ANCF increases from conventional finite element method, since the beam element is formulated by 8 absolute nodal coordinates. In order to reduce the degree of freedom of this beam element, authors have tried a new formuation by using 6 absolute nodal coordinates. The shape function of the beam element has been expressed in terms of the quadratic function, and the equation of motion has been described simply. This paper reports characteristics of the numerical computation for the dynamics analyses of the beam element formulated by ANCF. The formulation using 6 absolute nodal coordinates for the 2-dimensional beam element is shown in order to compare the formulation using 8 absolute nodal coordinates. The shape function of the formulation using eight coordinates is expressed as a cubic equation. And, the shape function of the formulation using six coordinates is expressed as a quadratic equation. In order to investigate numerical characteristics, several situations of problems are consider for numerical examples.
