Study on an assembling method of the 2-dimensional beam elements formulated by six absolute nodal coordinates

There are several formulations for beam elements in the multibody dynamics. Recently, the absolute nodal coordinate formulation (ANCF) is studied for such problems. In this formulation, the mass matrix and the stiffness matrix are described as simple equations, 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 formulation 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. But, this formulation had to use differential-algebraic equations for the assembling method. In this paper, the authors propose an assembling method of beam elements formulated by using 6 absolute nodal coordinates. In this method, beam elements can be assembled by superposition of the matrix like the conventional Finite element method. The usefulness of the proposed method is verified by the numerical simulations.