Journal Article

A new flexible multibody beam element based on the absolute nodal coordinate formulation using the global shape function and the analytical mode shape function

Kobayashi, N, Iwai, R

2004

Overview

Several techniques for the reduced dimensionality of finite element formulations were considered as component mode reduction methods in the middle sixties. These techniques are widely used in flexible multibody simulations for solving small deformation problems. The absolute nodal coordinate formulation for solving large rotation and deformation problems has been established as a full finite element method instead of using similar kinds of reduction techniques. In this paper, a reduced order absolute nodal coordinate formulation is newly established by introducing the global beam shape function and the analytical deformation modes as a full finite element. This formulation leads to a constant and symmetric mass matrix as the conventional absolute nodal coordinate formulation, and makes it possible to reduce the number of elements and system coordinates of the beam structure which undergoes large rotations and large deformations. Numerical examples show that the excellent agreements between the present formulation and the conventional absolute nodal coordinate formulation using a large number of elements are examined. These results demonstrate that the present formulation has high accuracy in the sense that the present solutions are similar to the conventional ones with fewer system coordinates, and high efficiency in computation.