Computation of Dynamic Stress in Flexible Multi-Body Dynamics Using Absolute Nodal Coordinate Formulation

Recently, the finite element absolute nodal coordinate formulation (ANCF) was developed for the large deformation analysis of flexible bodies in multi-body dynamics. This formulation is based on the finite element method and the general continuum mechanics theory to represent the elastic forces. In this paper, a computational method of dynamic stress in flexible multi-body dynamics using absolute nodal coordinate formulation is proposed. Numerical examples, based on the Euler-Bernoulli beam theory, are shown to verify the efficiency of the proposed method. This method can be applied to predict the fatigue life of a mechanical system. In conclusion, it is possible to improve the reliability of a product by analyzing the dynamic stress time history in the design stage of product development using computer simulation. Moreover, this study demonstrates that structural and multi-body dynamic models can be unified into one numerical system. Introduction In various fields of mechanics, a part’s periodic or non-periodic elastic deformation resulting from the system’s light weight and high speed is considered to be the main cause of fatigue crack. In order to solve this problem, there have been many studies to calculate the dynamic stress, a main factor of fatigue, through dynamic analysis of the mechanical system considering a part’s elastic deformation [1-2]. In particular, computer simulation techniques have proven useful as a more economical means of predicting a product’s fatigue life than durability tests. These include the flexible multi-body dynamics analysis method [3-4] adopting modal coordinates, and the use of the commercial finite analysis program. The flexible multi-body dynamics analysis method, which employs modal coordinates, considers only a small number of a system’s generalized coordinates and thus offers numerical efficiency. However, it cannot adequately express large deformable motion, which takes into account rotational freedom. Furthermore, in order to find the body’s elastic deformation modes, a finite element analysis has to be carried out as well and the dynamic stress time history, which is required to predict fatigue life, must be calculated, proving to be a tedious process. The commercial finite element analysis program not only provides vibration and static analysis, but may also include dynamic analysis for a nonlinear mechanical system, and can be used to calculate a comparatively accurate dynamic stress, although much time and effort is required for analysis. Recently, a dynamic analysis method using absolute nodal coordinates applicable to even large deformation problems was introduced [5-6]. Due to the limitations of the existing flexible multi-body dynamics method using modal coordinates, this method employs nodal coordinates, and its reliability is being verified by large deformation experiments [7]. Key Engineering Materials Online: 2004-08-15 ISSN: 1662-9795, Vols. 270-273, pp 1427-1433 doi:10.4028/www.scientific. net/KEM.270-273.1427 © 2004 Trans Tech Publications Ltd, Switzerland All rights reserved. No part of contents of this paper may be reproduced or transmitted in any form or by any means without the written permission of Trans Tech Publications Ltd, www.scientific. net. (Semanticscholar.org-13/03/20,17:38:07) Title of Publication (to be inserted by the publisher) In this study, a method for calculating the structural properties of strain and dynamic stress, as well as solving for a body’s position, velocity, acceleration, force, and other dynamic properties, through a single dynamic analysis employing the verifiably reliable absolute nodal coordinates, is proposed, and compared with results from the commercial analysis program ABAQUS [8]. This study is significant, in that it raises the possibility of a merging of the two fields of multi-body dynamics and structural dynamics, and perhaps even fatigue analysis as well, into one numerical model. Introduction of Absolute Nodal Coordinate Formulation Displacement Kinematics. Fig.1 shows the position and slope of the absolute nodal coordinates on both ends of the global reference frame for 2-D beam elements j making up the deformable body i. Fig. 1. The global position of an arbitrary point on beam element j on the deformable body i. In absolute nodal coordinate formulation, since the coordinates of the material points are defined in the global reference frame, there is no reason to use a transformation matrix for coordinate transformation [5-6]. The location of an arbitrary point on finite element ij can be defined in terms of the element shape function and the vector of nodal coordinates as Eq.1. ) ( ) ( ) , ( t x r r t x ij ij ij y ij x ij e S r =         = (1) Where, ij r is the global position vector of an arbitrary point on element ij, ij S is a global shape function that includes a complete set of rigid body modes, and ij e is the vector of absolute nodal coordinates and slopes of the element ij. A cubic polynomial is employed to describe both components of longitudinal and transversal displacements. Therefore, the global shape function ij S can be written as Eq.2.