Sliding Joint Constraints for the Analysis of Flexible Multibody Systems Using Intermediate Coordinates

2011 ◽  
Author(s):  
Ryo Honda ◽  
Hiroki Yamashita ◽  
Hiroyuki Sugiyama
Keyword(s):  
Multibody Dynamics ◽  
Absolute Nodal Coordinate Formulation ◽  
Rigid Bodies ◽  
Computer Algorithms ◽  
Arc Length ◽  
Flexible Bodies ◽  
Absolute Nodal Coordinate ◽  
Sliding Joint ◽  
Joint Constraints ◽  
The Absolute

In this investigation, formulations of sliding joint constraints for flexible bodies modeled using the absolute nodal coordinate formulation are developed using intermediate coordinates. Since modeling of prismatic and cylindrical joints for flexible bodies requires solutions to moving boundary problems in which joint definition points are moving on flexible bodies, arc-length coordinates are introduced for defining time-variant constraint definition points on flexible bodies. While this leads to a systematic modeling procedure for sliding joints, specialized formulations and implementations are required in general multibody dynamics computer algorithms. For this reason, intermediate coordinates are introduced to derive a mapping between the generalized gradient coordinates used in the absolute nodal coordinate formulation and the intermediate rotational coordinates used for defining the orientation constraints with rigid bodies. With this mapping, existing joint constraint libraries formulated for rigid bodies can be employed for the absolute nodal coordinate formulation without significant modifications. It is also demonstrated that the intermediate coordinates and arc-length coordinates introduced for modeling sliding joint constraints can be systematically eliminated from the equations of motion and standard differential algebraic equations used in general multibody dynamics computer algorithms can be obtained. Several numerical examples are presented in order to demonstrate the use of the formulation developed in this investigation.

Spatial Joint Constraints in Flexible Multibody Systems Using the Absolute Nodal Coordinate Formulation

2003 ◽  
Author(s):  
Hiroyuki Sugiyama ◽  
Jose´ L. Escalona ◽  
Ahmed A. Shabana
Keyword(s):  
Absolute Nodal Coordinate Formulation ◽  
Kinematic Constraint ◽  
Contact Parameter ◽  
Absolute Nodal Coordinate ◽  
Sliding Joint ◽  
Generalized Force ◽  
Floating Frame ◽  
Joint Constraints ◽  
The Absolute ◽  
New Formulation

This paper is concerned with the formulation and computer implementation of spatial joint constraints and generalized forces using the large deformation absolute nodal coordinate formulation. Unlike the floating frame of reference formulation that employs a mixed set of absolute reference and local elastic coordinates, in the absolute nodal coordinate formulation, global displacement and slope coordinates are used. The nonlinear kinematic constraint equations and generalized force expressions are expressed in terms of the absolute global displacements and slopes. In particular, a new formulation for the sliding joint between two very flexible bodies is developed. A contact parameter is introduced as an additional new variable in order to facilitate the formulation of this sliding joint. Numerical examples are presented in order to demonstrate the use of the formulations developed in the paper.

Describing Rigid-Flexible Multibody Systems Using Natural and Absolute Nodal Coordinates

2003 ◽  
Author(s):  
D. Garci´a-Vallejo ◽  
J. L. Escalona ◽  
J. Mayo ◽  
J. Domi´nguez ◽  
A. A´lvarez
Keyword(s):  
Absolute Nodal Coordinate Formulation ◽  
Mass Matrix ◽  
Linear Constraint ◽  
Rigid Bodies ◽  
Natural Coordinates ◽  
Flexible Bodies ◽  
Absolute Nodal Coordinate ◽  
Constraint Equations ◽  
Non Linear ◽  
The Absolute

This paper deals with the dynamic description of interconnected rigid and flexible bodies. The absolute nodal coordinate formulation is used to describe the motion of flexible bodies and natural coordinates are used to describe the motion of the rigid bodies. The absolute nodal coordinate formulation is a non-incremental finite element procedure specially suitable for the dynamic analysis of flexible bodies exhibiting rigid body motion and large deformations. Nodal coordinates, that include global position vectors and global slopes, are all defined in a global inertial coordinate system. The advantages of using the absolute nodal coordinate formulation include constancy in the mass matrix, and the need for only a minimal set of non-linear constraint equations when connecting different flexible bodies with kinematic joints. When bodies within the system can be considered rigid, the above-mentioned advantages of the equations of motion can be preserved provided natural coordinates are used. In the natural coordinates method, the coordinates used to describe rigid bodies include global position vectors of basic points and global unit vectors. As in the absolute nodal coordinate formulation, rotational coordinates are avoided and the mass matrix is also constant. This paper provides computer implementation of this formulation that only uses absolute coordinates for general two-dimensional multibody systems. The constraint equations needed to define kinematic joints between different bodies can be linear or non-linear. The linear constraint equations, that include those needed to define rigid connections and revolute joints, are used to define constant connectivity matrices that reduce the size of the system coordinates. These constant connectivity matrices are also used to obtain the system mass matrix and the system generalized forces. However, the non-linear constraint equations that account for sliding joints, require the use of the Lagrange multipliers technique. Numerical examples are provided and compared to the results of other existing formulations.

Efficient Coupling of Absolute Nodal Coordinate Formulation Flexible Bodies With an Existing Multibody Dynamics Code

2012 ◽  
Author(s):  
Jeff Liu ◽  
Abdel-Nasser A. Mohamed
Keyword(s):  
Multibody Dynamics ◽  
Absolute Nodal Coordinate Formulation ◽  
Sparse Matrix ◽  
Equations Of Motion ◽  
Matrix Solution ◽  
State Equations ◽  
Combined System ◽  
Flexible Bodies ◽  
Absolute Nodal Coordinate ◽  
Efficient Coupling

A couple of issues are identified in the process to embed absolute nodal coordinate formulation (ANCF) flexible bodies in an existing multibody dynamics code. (1) The generalized coordinates of ANCF must be solved together with those of the rest of the mechanism in a combined system of the equations of motion. (2) The various constraints, joints, and forces elements supported in the multibody dynamics code must be extended to the ANCF flexible bodies without major code restructuring. This paper describes two novel techniques that were devised to solve these issues. The first is the idea of interface triad. We will demonstrate how to construct the interface triad such that all exiting constraints, joints, and forces elements are automatically supported. The second idea is to represent the equations of motion of the ANCF body as a user-defined subroutine element representing a set of implicit general state equations subroutine (GSESUB). By treating each ANCF body modularly as a user-defined subroutine, not only all existing integration options of its host solver, e.g., HHT or DAE index-1, 2, and 3, etc., are automatically supported, but also the existing features such as parallel computing and sparse matrix solution of the existing multibody dynamics software are supported with minimum programming. Numerical examples are presented to demonstrate the efficiency and the success of these two techniques.

Review on the Absolute Nodal Coordinate Formulation for Large Deformation Analysis of Multibody Systems

2013 ◽  
Vol 8 (3) ◽  
Author(s):  
Johannes Gerstmayr ◽  
Hiroyuki Sugiyama ◽  
Aki Mikkola
Keyword(s):  
Large Deformation ◽  
Multibody Systems ◽  
Absolute Nodal Coordinate Formulation ◽  
Efficient Solutions ◽  
Rotor Blades ◽  
Deformation Analysis ◽  
Computer Algorithms ◽  
Absolute Nodal Coordinate ◽  
Elasto Plasticity ◽  
The Absolute

The aim of this study is to provide a comprehensive review of the finite element absolute nodal coordinate formulation, which can be used to obtain efficient solutions to large deformation problems of constrained multibody systems. In particular, important features of different types of beam and plate elements that have been proposed since 1996 are reviewed. These elements are categorized by parameterization of the elements (i.e., fully parameterized and gradient deficient elements), strain measures used, and remedies for locking effects. Material nonlinearities and the integration of the absolute nodal coordinate formulation to general multibody dynamics computer algorithms are addressed with particular emphasis on visco-elasticity, elasto-plasticity, and joint constraint formulations. Furthermore, it is shown that the absolute nodal coordinate formulation has been applied to a wide variety of challenging nonlinear dynamics problems that include belt drives, rotor blades, elastic cables, leaf springs, and tires. Unresolved issues and future perspectives of the study of the absolute nodal coordinate formulation are also addressed in this investigation.

Performance of the Incremental and Non-Incremental Finite Element Formulations in Flexible Multibody Problems

1999 ◽  
Vol 122 (4) ◽  
pp. 498-507 ◽  
Author(s):  
Marcello Campanelli ◽  
Marcello Berzeri ◽  
Ahmed A. Shabana
Keyword(s):  
Finite Element ◽  
Multibody Systems ◽  
Absolute Nodal Coordinate Formulation ◽  
Flexible Multibody Systems ◽  
Large Displacement ◽  
Body Motion ◽  
Absolute Nodal Coordinate ◽  
Flexible Multibody ◽  
The Absolute ◽  
Finite Element Formulations

Many flexible multibody applications are characterized by high inertia forces and motion discontinuities. Because of these characteristics, problems can be encountered when large displacement finite element formulations are used in the simulation of flexible multibody systems. In this investigation, the performance of two different large displacement finite element formulations in the analysis of flexible multibody systems is investigated. These are the incremental corotational procedure proposed in an earlier article (Rankin, C. C., and Brogan, F. A., 1986, ASME J. Pressure Vessel Technol., 108, pp. 165–174) and the non-incremental absolute nodal coordinate formulation recently proposed (Shabana, A. A., 1998, Dynamics of Multibody Systems, 2nd ed., Cambridge University Press, Cambridge). It is demonstrated in this investigation that the limitation resulting from the use of the infinitesmal nodal rotations in the incremental corotational procedure can lead to simulation problems even when simple flexible multibody applications are considered. The absolute nodal coordinate formulation, on the other hand, does not employ infinitesimal or finite rotation coordinates and leads to a constant mass matrix. Despite the fact that the absolute nodal coordinate formulation leads to a non-linear expression for the elastic forces, the results presented in this study, surprisingly, demonstrate that such a formulation is efficient in static problems as compared to the incremental corotational procedure. The excellent performance of the absolute nodal coordinate formulation in static and dynamic problems can be attributed to the fact that such a formulation does not employ rotations and leads to exact representation of the rigid body motion of the finite element. [S1050-0472(00)00604-8]

Elastic Forces and Coordinate Systems in the Finite Element Formulations

1999 ◽  
Author(s):  
Marcello Berzeri ◽  
Marcello Campanelli ◽  
A. A. Shabana
Keyword(s):  
Finite Element ◽  
Absolute Nodal Coordinate Formulation ◽  
Frame Of Reference ◽  
Coordinate Systems ◽  
Absolute Nodal Coordinate ◽  
Floating Frame Of Reference ◽  
Elastic Forces ◽  
Floating Frame ◽  
The Absolute ◽  
Finite Element Formulations

Abstract The equivalence of the elastic forces of finite element formulations used in flexible multibody dynamics is the focus of this investigation. Two conceptually different finite element formulations that lead to exact modeling of the rigid body dynamics will be used. These are the floating frame of reference formulation and the absolute nodal coordinate formulation. It is demonstrated in this study that different element coordinate systems, which are used for the convenience of describing the element deformations in the absolute nodal coordinate formulation, lead to similar results as the element size is reduced. The equivalence of the elastic forces in the absolute nodal coordinate and the floating frame of reference formulations is shown. The result of this analysis clearly demonstrates that the instability observed in high speed rotor analytical models due to the neglect of the geometric centrifugal stiffening is not a problem inherent to a particular finite element formulation but only depends on the beam model that is used. Fourier analysis of the solutions obtained in this investigation also sheds new light on the fundamental problem of the choice of the deformable body coordinate system in the floating frame of reference formulation. A new method is presented and used to obtain a simple expression for the elastic forces in the absolute nodal coordinate formulation. This method, which employs a nonlinear elastic strain-displacement relationship, does not result in an unstable solution when the angular velocity is increased.

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