Dynamic Analysis of the Parabolic Leaf Spring Based on the Absolute Nodal Coordinate Formulation

2018 ◽  
Author(s):  
Tengfei Wang ◽  
Peng Lan ◽  
Yueqin Wang
Keyword(s):  
Dynamic Analysis ◽  
Absolute Nodal Coordinate Formulation ◽  
Leaf Spring ◽  
Absolute Nodal Coordinate ◽  
The Absolute ◽  
Parabolic Leaf Spring

scholarly journals Dynamic analysis of rotating shafts using the absolute nodal coordinate formulation

2019 ◽  
Vol 453 ◽  
pp. 214-236 ◽  
Author(s):  
Babak Bozorgmehri ◽  
Vesa-Ville Hurskainen ◽  
Marko K. Matikainen ◽  
Aki Mikkola
Keyword(s):  
Dynamic Analysis ◽  
Absolute Nodal Coordinate Formulation ◽  
Absolute Nodal Coordinate ◽  
Rotating Shafts ◽  
The Absolute

Dynamic Analysis of Offshore Oil Pipe Installation Using the Absolute Nodal Coordinate Formulation

2013 ◽  
Author(s):  
Jimmy D. Nielsen ◽  
Søren B. Madsen ◽  
Per Hyldahl ◽  
Ole Balling
Keyword(s):  
Dynamic Analysis ◽  
Large Deformation ◽  
Dynamic Behavior ◽  
Absolute Nodal Coordinate Formulation ◽  
Mass Matrix ◽  
Absolute Nodal Coordinate ◽  
Beam Elements ◽  
The Absolute ◽  
External Forces ◽  
Offshore Oil

The Absolute Nodal Coordinate Formulation (ANCF) has shown promising results in dynamic analysis of structures that undergo large deformation. The method relaxes the assumption of infinitesimal rotations. Being based in a fixed inertial reference frame leads to a constant mass matrix and zero centrifugal and Coriolis forces [12]. This makes the method attractive for multibody dynamics implementation. The focus in this paper is the application of ANCF beam elements and their performance on large deformation dynamic analysis. Large dynamic deformation is characteristic for the installation process of offshore submerged oil pipes using oceangoing vessels. In this investigation such an oil pipe is modeled using ANCF beam elements to simulate the dynamic behavior of the pipe during the installation process. Multiple physical effects such as gravity, buoyancy, seabed contact, and fluid damping, are included to mimic the external forces acting on the pipe during installation. The scope of this investigation is to demonstrate the ability using the ANCF to analyze the dynamic behavior of an offshore oil pipe during installation.

Development of Elastic Forces for a Large Deformation Plate Element Based on the Absolute Nodal Coordinate Formulation

2005 ◽  
Vol 1 (2) ◽  
pp. 103-108 ◽  
Author(s):  
Aki M. Mikkola ◽  
Marko K. Matikainen
Keyword(s):  
Finite Element ◽  
Dynamic Analysis ◽  
Continuum Mechanics ◽  
Absolute Nodal Coordinate Formulation ◽  
Three Dimensional ◽  
Plate Element ◽  
Absolute Nodal Coordinate ◽  
Elastic Forces ◽  
The Absolute ◽  
The Continuum

Dynamic analysis of large rotation and deformation can be carried out using the absolute nodal coordinate formulation. This formulation, which utilizes global displacements and slope coordinates as nodal variables, make it possible to avoid the difficulties that arise when a rotation is interpolated in three-dimensional applications. In the absolute nodal coordinate formulation, a continuum mechanics approach has become the dominating procedure when elastic forces are defined. It has recently been perceived, however, that the continuum mechanics based absolute nodal coordinate elements suffer from serious shortcomings, including Poisson’s locking and poor convergence rate. These problems can be circumvented by modifying the displacement field of a finite element in the definition of elastic forces. This allows the use of the mixed type interpolation technique, leading to accurate and efficient finite element formulations. This approach has been previously applied to two- and three-dimensional absolute nodal coordinate based finite elements. In this study, the improved approach for elastic forces is extended to the absolute nodal coordinate plate element. The introduced plate element is compared in static examples to the continuum mechanics based absolute nodal coordinate plate element, as well as to commercial finite element software. A simple dynamic analysis is performed using the introduced element in order to demonstrate the capability of the element to conserve energy.

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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