Dynamic Analysis of High-Speed Rotating Shafts Using the Flexible Multibody Approach

2018 ◽  
Author(s):  
Vesa-Ville Hurskainen ◽  
Babak Bozorgmehri ◽  
Marko K. Matikainen ◽  
Aki Mikkola
Keyword(s):  
Dynamic Analysis ◽  
Cross Section ◽  
High Speed ◽  
Capture Cross Section ◽  
Absolute Nodal Coordinate Formulation ◽  
Beam Element ◽  
Capture Cross ◽  
Rotating Shaft ◽  
Absolute Nodal Coordinate ◽  
Rotating Shafts

In this study, a higher-order finite element based on the absolute nodal coordinate formulation (ANCF) is applied in the dynamic analysis of high-speed rotating shafts. Static and modal tests are carried out to analyze the performance and accuracy of the introduced ANCF element. Also, via a transient dynamic benchmark test involving a rotating flexible shaft, the accuracy of the examined beam element in high-speed applications is analyzed. According to the results, the introduced beam element can adequately capture cross-section deformationin high-speed rotating shaft analysis.

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

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.

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.

A new thin beam element with cross-section distortion of the absolute nodal coordinate formulation

2021 ◽  
pp. 095440622110200
Author(s):  
Zhenxing Shen ◽  
Xiaofeng Xing ◽  
Boyu Li
Keyword(s):  
Cross Section ◽  
Absolute Nodal Coordinate Formulation ◽  
Laminated Composite ◽  
Shell Element ◽  
Beam Element ◽  
Cross Sectional ◽  
Thin Beam ◽  
Absolute Nodal Coordinate ◽  
The Absolute ◽  
The Cross

A novel modelling approach to beams with thin cross-sections is proposed in the absolute nodal coordinate formulation (ANCF), where the Lagrange interpolating and curve fitting techniques of numerical analysis are utilized for construction of the thin beam cross-section contour. Although the slope vector with respect to the coordinate line on cross-section contour is not considered in nodal coordinates, the cross-section distortion could be adequately captured through selecting an appropriate degree of polynomial. The main advantages of the present ANCF thin beam element are that the computational costs are more inexpensive than the ANCF shell element due to less generalized coordinates, there is very small amount of input data because slope vectors of the cross-section are eliminated, and the cross-sectional stress distribution may always be continuous on account of the fact that the cross-section is not discretized into a set of finite elements. Moreover, the formulations of elastic forces and Jacobian of thin laminated composite beam are also derived based on the continuum mechanics. Finally, several examples including both static and dynamic problems are performed to verify the new element and meanwhile demonstrate its general characteristics.

Studies on the Stiffness Properties of the Absolute Nodal Coordinate Formulation for Three-Dimensional Beams

2003 ◽  
Author(s):  
Jussi T. Sopanen ◽  
Aki M. Mikkola
Keyword(s):  
Cross Section ◽  
Absolute Nodal Coordinate Formulation ◽  
Three Dimensional ◽  
Beam Element ◽  
Element Formulation ◽  
Absolute Nodal Coordinate ◽  
Numerical Examples ◽  
Elastic Forces ◽  
Nodal Coordinates ◽  
The Absolute

The objective of this study is to investigate the accuracy of elastic force models that can be used in the absolute nodal coordinate finite element formulation for the analysis of threedimensional beams. The elastic forces of the absolute nodal coordinate formulation can be derived using a continuum mechanics approach. This study investigates the accuracy and usability of such an approach for the three-dimensional absolute nodal coordinate beam element. This study also presents an improvement proposal for the use of a continuum mechanics approach in deriving the expression of the elastic forces of the beam element. The improvement proposal is verified using several numerical examples. Numerical examples show that the proposed elastic force model of the beam element agrees with analytical results as well as with solutions obtained using existing finite element formulation. The results also imply that the beam element does not suffer from the phenomenon called shear locking. In the beam element under investigation, global displacements and slopes are used as the nodal coordinates, which resulted in a large number of nodal degrees of freedom. This study provides a physical interpretation of the nodal coordinates used in the absolute nodal coordinate beam element. It is shown that the beam element based on the absolute nodal coordinate formulation relaxes the assumption of the rigid cross-section and is capable of representing a distortional deformation of the cross-section.

Measurements of the neutron capture cross section of 243Am around 23.5 keV

2021 ◽  
pp. 1-6
Author(s):  
Yu Kodama ◽  
Tatsuya Katabuchi ◽  
Gerard Rovira ◽  
Atsushi Kimura ◽  
Shoji Nakamura ◽  
...  
Keyword(s):  
Cross Section ◽  
Neutron Capture ◽  
Capture Cross Section ◽  
Capture Cross ◽  
Neutron Capture Cross Section
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