scholarly journals Development of flexible telescopic boom model using absolute nodal coordinate formulation sliding joint constraints with LuGre friction

2012 ◽  
Vol 2 (6) ◽  
pp. 063005 ◽  
Author(s):  
Hiroki Fujita ◽  
Hiroyuki Sugiyama
Keyword(s):  
Absolute Nodal Coordinate Formulation ◽  
Absolute Nodal Coordinate ◽  
Sliding Joint ◽  
Lugre Friction ◽  
Joint Constraints

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.

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.

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]

Nonlinear Analysis of L-shaped Pipe Conveying Fluid with the Aid of Absolute Nodal Coordinate Formulation

2021 ◽  
Author(s):  
K. Zhou ◽  
H.R. Yi ◽  
Huliang Dai ◽  
H Yan ◽  
Z.L. Guo ◽  
...  
Keyword(s):  
Theoretical Model ◽  
Flow Velocity ◽  
Absolute Nodal Coordinate Formulation ◽  
Strong Relationship ◽  
Excitation Amplitude ◽  
Pipe Conveying Fluid ◽  
Base Excitation ◽  
Absolute Nodal Coordinate ◽  
Nonlinear Behaviors ◽  
Conveying Fluid

Abstract By adopting the absolute nodal coordinate formulation, a novel and general nonlinear theoretical model, which can be applied to solve the dynamics of combined straight-curved fluid-conveying pipes with arbitrary initially configurations and any boundary conditions, is developed in the current study. Based on this established model, the nonlinear behaviors of the cantilevered L-shaped pipe conveying fluid with and without base excitations are systematically investigated. Before starting the research, the developed theoretical model is verified by performing three validation examples. Then, with the aid of this model, the static deformations, linear stability, and nonlinear self-excited vibrations of the L-shaped pipe without the base excitation are determined. It is found that the cantilevered L-shaped pipe suffers from the static deformations when the flow velocity is subcritical, and will undergo the limit-cycle motions as the flow velocity exceeds the critical value. Subsequently, the nonlinear forced vibrations of the pipe with a base excitation are explored. It is indicated that the period-n, quasi-periodic and chaotic responses can be detected for the L-shaped pipe, which has a strong relationship with the flow velocity, excitation amplitude and frequency.

Numerical Investigation of Dynamics of the Flexible Riser by Applying Absolute Nodal Coordinate Formulation

2021 ◽  
Vol 55 (5) ◽  
pp. 179-195
Author(s):  
Luu Quang Hung ◽  
Zhuang Kang ◽  
Li Shaojie
Keyword(s):  
Absolute Nodal Coordinate Formulation ◽  
Flexible Structures ◽  
Beam Model ◽  
Environmental Load ◽  
The Finite Element Method ◽  
Ocean Engineering ◽  
Flexible Riser ◽  
Absolute Nodal Coordinate ◽  
Static And Dynamic Characteristics ◽  
Load Conditions

Abstract In this paper, the dynamics of the flexible riser are investigated based on the absolute nodal coordinate formulation (ANCF). The stiffness, generalized elastic force, external load, and mass matrixes of the element are deduced based on the principle of energy conversion and assembled with the finite element method. The motion equation of the flexible riser is established. The influence of the environmental load conditions on the flexible riser model is studied in the MATLAB environment. Moreover, the accuracy and reliability of the programs are verified for a beam model with theoretical solutions. Finally, the static and dynamic characteristics of the flexible riser are analyzed, systematically adopting the ANCF method, which in turn proves the effectiveness and feasibility of the ANCF. Therefore, the proposed method is a powerful scheme for investigating the dynamics of flexible structures with large deformation in ocean engineering.

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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