Theory and model implementation for analyzing line structures subject to dynamic motions of large deformation and elongation using the absolute nodal coordinate formulation (ANCF) approach

2020 ◽  
Vol 101 (1) ◽  
pp. 333-359 ◽  
Author(s):  
Fangfang Sheng ◽  
Zhengyong Zhong ◽  
Keh-Han Wang
Keyword(s):  
Large Deformation ◽  
Absolute Nodal Coordinate Formulation ◽  
Absolute Nodal Coordinate ◽  
The Absolute ◽  
Theory And Model

A new higher-order locking-free beam element based on the absolute nodal coordinate formulation

2017 ◽  
Vol 232 (19) ◽  
pp. 3410-3423 ◽  
Author(s):  
Haidong Yu ◽  
Chunzhang Zhao ◽  
Bin Zheng ◽  
Hao Wang
Keyword(s):  
Large Deformation ◽  
Cross Section ◽  
Absolute Nodal Coordinate Formulation ◽  
Beam Element ◽  
Higher Order ◽  
Continuity Condition ◽  
Large Rotation ◽  
Absolute Nodal Coordinate ◽  
The Absolute ◽  
The Cross

The beam elements based on the absolute nodal coordinate formulation are widely used in large deformation and large rotation problems. Some of them lead to shear and Poisson locking problems when the continuum mechanics method is employed to deduce the generalized elastic force of the element. To circumvent these locking problems, a new higher-order beam element is proposed that may capture the warping and non-uniform stretching distribution of the cross-section by introducing the trapezoidal cross-section deformation mode and increasing the order of interpolation polynomials in transverse direction. The curvature vectors are chosen as the nodal coordinates of the new element that improve the continuity condition at the element interface. Static and dynamic analyses are conducted to investigate the performance of the new element. Poisson locking phenomena may be eliminated effectively for the new element even when Poisson’s ratio is greater than zero. Meanwhile, the distortion deformation of the cross-section may be described directly. The new element has a better convergence performance compared with the spatial absolute nodal coordinate formulation beam element for that shear locking issue is eliminated. The results also show that the new element fulfills energy conservation and may be applied to the dynamics of both straight and initial curved structures with large deformation.

scholarly journals Several dynamic models of a large deformation flexible beam based on the absolute nodal coordinate formulation

2016 ◽  
Vol 65 (9) ◽  
pp. 094501
Author(s):  
Zhang Xiao-Shun ◽  
Zhang Ding-Guo ◽  
Chen Si-Jia ◽  
Hong Jia-Zhen
Keyword(s):  
Large Deformation ◽  
Dynamic Models ◽  
Absolute Nodal Coordinate Formulation ◽  
Flexible Beam ◽  
Absolute Nodal Coordinate ◽  
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.

A Large Deformation Finite Element for Pipes Conveying Fluid Based on the Absolute Nodal Coordinate Formulation

2007 ◽  
Author(s):  
Michael Stangl ◽  
Johannes Gerstmayr ◽  
Hans Irschik
Keyword(s):  
Finite Element ◽  
Large Deformation ◽  
Absolute Nodal Coordinate Formulation ◽  
Equations Of Motion ◽  
Directional Derivatives ◽  
Absolute Nodal Coordinate ◽  
Lagrange’S Equations ◽  
The Absolute ◽  
Lagrange's Equations ◽  
Conveying Fluid

A novel pipe finite element conveying fluid, suitable for modeling large deformations in the framework of Bernoulli Euler beam theory, is presented. The element is based on a third order planar beam finite element, introduced by Berzeri and Shabana, on basis of the absolute nodal coordinate formulation. The equations of motion for the pipe-element are derived using an extended version of Lagrange’s equations of the second kind for taking into account the flow of fluids, in contrast to the literature, where most derivations are based on Hamilton’s Principle or Newtonian approaches. The advantage of this element in comparison to classical large deformation beam elements, which are based on rotations, is the direct interpolation of position and directional derivatives, which simplifies the equations of motion considerably. As an advantage Lagrange’s equations of the second kind offer a convenient connection for introducing fluids into multibody dynamic systems. Standard numerical examples show the convergence of the deformation for increasing number of elements. For a cantilever pipe, the critical flow velocities for increasing number of pipe elements are compared to existing works, based on Euler elastica beams and moving discrete masses. The results show good agreements with the reference solutions applying only a small number of pipe finite elements.

A Large Deformation Planar Finite Element for Pipes Conveying Fluid Based on the Absolute Nodal Coordinate Formulation

2009 ◽  
Vol 4 (3) ◽  
Author(s):  
Michael Stangl ◽  
Johannes Gerstmayr ◽  
Hans Irschik
Keyword(s):  
Finite Element ◽  
Large Deformation ◽  
Absolute Nodal Coordinate Formulation ◽  
Equations Of Motion ◽  
Directional Derivatives ◽  
Absolute Nodal Coordinate ◽  
Lagrange’S Equations ◽  
The Absolute ◽  
Lagrange's Equations ◽  
Conveying Fluid

A novel planar pipe finite element conveying fluid with steady flow, suitable for modeling large deformations in the framework of the Bernoulli–Euler beam theory, is presented. The element is based on a third order planar beam finite element, introduced by Berzeri and Shabana (2000, “Development of Simple Models for the Elastic Forces in the Absolute Nodal Co-Ordinate Formulation,” J. Sound Vib., 235(4), pp. 539–565), applying the absolute nodal coordinate formulation. The equations of motion of the pipe finite element are derived using an extended version of Lagrange’s equations of the second kind taking into account the flow of fluid; in contrast, most derivations in the literature are based on Hamilton’s principle or the Newtonian approaches. The advantage of this element in comparison to classical large deformation beam elements, which are based on rotations, is the direct interpolation of position and directional derivatives, which simplifies the equations of motion considerably. As an advantage, Lagrange’s equations of the second kind offer a convenient connection for introducing fluids into multibody dynamic systems. Standard numerical examples show the convergence of the deformation for increasing number of elements. For a cantilever pipe, the critical flow velocities for increasing number of pipe elements are compared with existing works, based on Euler elastica beams and moving discrete masses. The results show good agreement with the reference solutions applying only a small number of pipe finite elements.

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]

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