Reduction of degrees of Freedom in three-dimensional ANCF beam of 24-DOF beam element by component mode synthesis

Abstract

This paper describes how to reduce degrees of freedom for the absolute nodal coordinate formulation (ANCF) of three-dimensional beam made up of 24 degrees of freedom beam elements by applying the component mode synthesis. The stiffness matrix of the ANCF Bernoulli-Euler beam is introduced to the equation of motion of 24 dof ANCF beam element. Since the bending stiffness matrix of the ANCF Bernoulli-Euler beam is constant, the Craig-Bampton method is applicable to the equation of motion to reduce degrees of freedom of beam structure which is composed of 24 dof ANCF elements. To examine the effectiveness and the efficiency of the presented method, three numerical examples were performed with comparing the results obtained by the conventional ANCF beam elements. In examples of the pure torsional deformation and the free-fall behavior under the gravity field, the presented method was verified to be capable of expressing the torsional deformation and large deformation precisely as well as the conventional ANCF, in spite of the dof of the presented method being reduced to be the half of the conventional ANCF. In the example of the cantilevered beam subjected by the screw driving constraint under the gravity, the presented method was also verified to express the large bending and torsion coupled deformation well.