Comparison of Fully Parameterized and Gradient Deficient Elements in the Absolute Nodal Coordinate Formulation

2017 ◽  
Author(s):  
Johannes Gerstmayr ◽  
Peter Gruber ◽  
Alexander Humer
Keyword(s):  
Finite Elements ◽  
Absolute Nodal Coordinate Formulation ◽  
Dynamic Test ◽  
Test Problems ◽  
Rotational Parameter ◽  
Absolute Nodal Coordinate ◽  
Beam Elements ◽  
Spatial Beams ◽  
Numerical Instabilities ◽  
The Absolute

The aim of the present paper is to evaluate six particular beam finite elements based on the absolute nodal coordinate formulation (ANCF). Specifically, accuracy, computational efficiency and numerical stability are compared for those beam finite elements. The finite elements under consideration are planar as well as spatial beams, which are formulated both for the Bernoulli-Euler case as well as for shear and cross-section deformation. While all of the investigated elements have been exposed to specific numerical tests already before, a comparative test has not been performed in the past. The numerical examples cover large deformation static and dynamic problems, which represent typical applications of such beam elements. Finally, the dynamic test problems show that the thin spatial beam formulation, which includes a rotational parameter, leads to well-known numerical instabilities.

Three-Dimensional Solid Brick Element Using Slopes in the Absolute Nodal Coordinate Formulation

2013 ◽  
Vol 9 (2) ◽  
Author(s):  
Alexander Olshevskiy ◽  
Oleg Dmitrochenko ◽  
Chang-Wan Kim
Keyword(s):  
Finite Element ◽  
Finite Elements ◽  
Absolute Nodal Coordinate Formulation ◽  
Mass Matrix ◽  
Equations Of Motion ◽  
Test Problems ◽  
Absolute Nodal Coordinate ◽  
Highly Nonlinear ◽  
Brick Element ◽  
The Absolute

The present paper contributes to the field of flexible multibody systems dynamics. Two new solid finite elements employing the absolute nodal coordinate formulation are presented. In this formulation, the equations of motion contain a constant mass matrix and a vector of generalized gravity forces, but the vector of elastic forces is highly nonlinear. The proposed solid eight node brick element with 96 degrees of freedom uses translations of nodes and finite slopes as sets of nodal coordinates. The displacement field is interpolated using incomplete cubic polynomials providing the absence of shear locking effect. The use of finite slopes describes the deformed shape of the finite element more exactly and, therefore, minimizes the number of finite elements required for accurate simulations. Accuracy and convergence of the finite element is demonstrated in nonlinear test problems of statics and dynamics.

Experimental Validation of Flexible Multibody Dynamics Beam Formulations

2013 ◽  
Author(s):  
Olivier A. Bauchau ◽  
Shilei Han ◽  
Aki Mikkola ◽  
Marko K. Matikainen ◽  
Johannes Gerstmayr
Keyword(s):  
Experimental Data ◽  
Absolute Nodal Coordinate Formulation ◽  
Flexible Multibody Dynamics ◽  
Absolute Nodal Coordinate ◽  
Beam Elements ◽  
Beam Experiment ◽  
Geometrically Exact Beam ◽  
Cantilevered Beam ◽  
The Absolute ◽  
Geometrically Exact Beam Formulation

In this paper, the accuracy of the geometrically exact beam formulation and absolute nodal coordinate formulation are studied by comparing their predictions against experimental data referred to as the “Princeton beam experiment.” The experiment deals with a cantilevered beam experiencing coupled flap, lag, and twist deformations. In the absolute nodal coordinate formulation, two different beam elements are used. The first is based on a shear deformable approach in which the element kinematics are described using two nodes. The second is based on a recently proposed approach in which three nodes are used. The numerical results for the geometrically exact beam formulation and the recently proposed three-node absolute nodal coordinate formulation agree well with the experimental data. The two-node beam element predictions are similarly to linear theory. This study suggests that the latest developments of the absolute nodal coordinate formulation must be used to ensure accuracy under complicated loading conditions involving by twist 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 Linear Beam Finite Element Based on the Absolute Nodal Coordinate Formulation

2004 ◽  
Vol 127 (4) ◽  
pp. 621-630 ◽  
Author(s):  
Kimmo S. Kerkkänen ◽  
Jussi T. Sopanen ◽  
Aki M. Mikkola
Keyword(s):  
Absolute Nodal Coordinate Formulation ◽  
Longitudinal Direction ◽  
Beam Element ◽  
Computational Effort ◽  
Two Dimensional ◽  
Absolute Nodal Coordinate ◽  
Beam Elements ◽  
Shear Deformable Beam ◽  
The Absolute ◽  
Shear Deformable

In this paper, a new two-dimensional shear deformable beam element based on the absolute nodal coordinate formulation is proposed. The nonlinear elastic forces of the beam element are obtained using a continuum mechanics approach, without employing a local element coordinate system. In this study, linear polynomials are used to interpolate both the transverse and longitudinal components of the displacement. This is different from other absolute nodal-coordinate-based beam elements where cubic polynomials are used in the longitudinal direction. The use of linear interpolation polynomials leads to the phenomenon known as shear locking. This defect is avoided through the adoption of selective integration within the numerical integration method. The proposed element is verified using several numerical examples. The results of the proposed element are compared to analytical solutions and the results for an existing shear deformable beam element. It is shown that by using the proposed element, accurate linear and nonlinear static deformations, as well as realistic dynamic behavior including the capturing of the centrifugal stiffening effect, can be achieved with a smaller computational effort than by using existing shear deformable two-dimensional beam elements.

Three Dimensional Absolute Nodal Coordinate Formulation for Beam Elements: Implementation and Applications

2000 ◽  
Vol 123 (4) ◽  
pp. 614-621 ◽  
Author(s):  
Refaat Y. Yakoub ◽  
Ahmed A. Shabana
Keyword(s):  
High Speed ◽  
Absolute Nodal Coordinate Formulation ◽  
Mass Matrix ◽  
Three Dimensional ◽  
Large Rotation ◽  
Absolute Nodal Coordinate ◽  
Incremental Methods ◽  
Beam Elements ◽  
High Speed Forming ◽  
The Absolute

This part of these two companion papers demonstrates the computer implementation of the absolute nodal coordinate formulation for three-dimensional beam elements. Two beam elements that relax the assumptions of Euler-Bernoulli and Timoshenko beam theories are developed. These two elements take into account the effect of rotary inertia, shear deformation and torsion, and yet they lead to a constant mass matrix. As a consequence, the Coriolis and centrifugal forces are identically equal to zero. Both beam elements use the same interpolating polynomials and have the same number of nodal coordinates. However, one of the elements has two nodes, while the other has four nodes. The results obtained using the two elements are compared with the results obtained using existing incremental methods. Unlike existing large rotation vector formulations, the results of this paper show that no special numerical integration methods need to be used in order to satisfy the principle of work and energy when the absolute nodal coordinate formulation is used. These results show that this formulation can be used in manufacturing applications such as high speed forming and extrusion problems in which the element cross section dimensions significantly change.

scholarly journals Analysis of beam elements of circular cross section using the absolute nodal coordinate formulation

2012 ◽  
Vol 59 (3) ◽  
pp. 283-296 ◽  
Author(s):  
Grzegorz Orzechowski
Keyword(s):  
Cross Section ◽  
Absolute Nodal Coordinate Formulation ◽  
Gaussian Quadrature ◽  
Circular Cross Section ◽  
Beam Cross Section ◽  
Element Analysis ◽  
Absolute Nodal Coordinate ◽  
Beam Elements ◽  
The Absolute ◽  
The Cross

Abstract The beam elements, which are widely used in the absolute nodal coordinate formulation (ANCF) can be treated as isoparametric elements, and by analogy to the classical finite element analysis (FEA) are integrated with standard, spatial Gauss- Legendre quadratures. For this reason, the shape of the ANCF beam cross section is restricted only to the shape of rectangle. In this paper, a distinct method of integration of ANCF elements based on continuum mechanics approach is presented. This method allows for efficient analysis of the ANCF beam elements with circular cross section. The integration of element vectors and matrices is performed by separation of the quadrature into the part that integrate along beam axis and the part that integrate in the beam cross section. Then, an alternative quadrature is used to integrate in the circular shape of the cross section. Since the number of integration points in the alternative quadrature corresponds to the number of points in the standard Gaussian quadrature the change in the shape of the cross section does not affects negatively the element efficiency. The presented method was verified using selected numerical tests. They show good relatively agreement with the reference results. Apart from the analysis of the beams with the circular cross section, a possibility of further modifications in the methods of the element integration is also discussed. Due to the fact that locking influence on the convergence of the element is also observed, the methods of locking elimination in the proposed elements are also considered in the paper.

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