Kinematic Stability of Variable Cross-section Beam with Large Deformation by using the Absolute Nodal Coordinate Formulation

2016 ◽  
Vol 2016.8 (0) ◽  
pp. 13_1282602
Author(s):  
Haidong YU ◽  
Jingjing LUO ◽  
Chunzhang ZHAO ◽  
Hao WANG
Keyword(s):  
Large Deformation ◽  
Cross Section ◽  
Absolute Nodal Coordinate Formulation ◽  
Variable Cross Section ◽  
Variable Cross ◽  
Absolute Nodal Coordinate ◽  
The Absolute

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.

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 Higher-Order Variable Cross-Section Viscoelastic Beam Element Via ANCF for Kinematic and Dynamic Analyses of Two-Link Flexible Manipulators

2017 ◽  
Vol 09 (08) ◽  
pp. 1750116 ◽  
Author(s):  
Haidong Yu ◽  
Chunzhang Zhao ◽  
Hui Zheng
Keyword(s):  
Large Deformation ◽  
Cross Section ◽  
Variable Cross Section ◽  
Beam Element ◽  
Higher Order ◽  
Flexible Manipulator ◽  
Variable Cross ◽  
Viscoelastic Beam ◽  
Shear Locking ◽  
Large Deformation Problems

A new viscoelastic beam element with variable cross-sections is developed based on the absolute nodal coordinate formulation, in which the higher-order slope coordinates are used to describe the variable geometric boundaries and circumvent possible shear-locking problem. The mass and stiffness matrices of the new element are derived by considering the variable geometrical boundary in the integration functions. The modified Kelvin–Voigt viscoelastic constitutive model for large deformation problems is introduced into the stiffness matrix. The dynamic model of a typical two-link manipulator with variable cross-section links is established where the constraint equations of revolute joints are considered with Lagrange multipliers. The kinematic trajectories of the manipulator with various materials and geometrical parameters are numerically studied. It is shown that the new element could circumvent shear-locking problem and yield improved accuracy and convergence compared with the conventional beam elements for solving large deformation problems. Also, the viscosity of the structural material helps to reduce the deformation of the links and improve the kinematic precision of the manipulator, hence the trajectory of the flexible manipulator could be controlled by changing the geometrical shape of the cross-section of links under the constraint of same mass.

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.

Non-Linear Strain Description for Two-Dimensional Shear Deformable Beam Element Based on the Absolute Nodal Coordinate Formulation

2009 ◽  
Author(s):  
Jussi Sopanen ◽  
Marko Matikainen ◽  
Aki Mikkola
Keyword(s):  
Shear Deformation ◽  
Cross Section ◽  
Absolute Nodal Coordinate Formulation ◽  
Beam Element ◽  
Two Dimensional ◽  
Linear Strain ◽  
Absolute Nodal Coordinate ◽  
Elastic Forces ◽  
Longitudinal Slope ◽  
The Absolute

In the absolute nodal coordinate formulation, the transverse shear deformation can be accounted for by using a fully parametrized element or, alternatively, by replacing longitudinal slope coordinates by a vector that describes the orientation of the cross-section. The use of a fully parametrized element allows the description of cross-section deformations in the case of beams and, correspondingly, fiber deformations in the case of plates and shells. It is noteworthy, however, that cross-section or fiber deformations are usually associated with high natural frequencies complicating the time integration of a fully parametrized element. A procedure to replace longitudinal slope coordinates by the vector that describes cross-section orientation was recently applied to a two-dimensional beam element based on the absolute nodal coordinate formulation. In this study, the procedure to account for shear deformation using the vector that describes cross-section orientation is extended to account for the nonlinear strain-displacement relationship in the definition of the elastic forces of the beam element. To accomplish this, the exact displacement field is used in the description of element kinematical and strain measures. This makes it straightforward to implement the non-linear strain-displacement relationship in the description of the elastic forces. Numerical results demonstrate that the enhanced beam element yields accurate results in eigenfrequency analysis. Results obtained in large deformation cases are in line with previously proposed elements based on the absolute nodal coordinate formulation.

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