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Research Papers

Inclusion of Transverse Shear Deformation in a Beam Element Based on the Absolute Nodal Coordinate Formulation

[+] Author and Article Information
Aki Mikkola, Oleg Dmitrochenko, Marko Matikainen

Department of Mechanical Engineering, Lappeenranta University of Technology, Skinnarilankatu 34, 53851 Lappeenranta, Finland

J. Comput. Nonlinear Dynam 4(1), 011004 (Nov 11, 2008) (9 pages) doi:10.1115/1.3007907 History: Received August 02, 2007; Revised March 27, 2008; Published November 11, 2008

In this study, a procedure to account for transverse shear deformation in the absolute nodal coordinate formulation is presented. In the absolute nodal coordinate formulation, shear deformation is usually defined by employing the slope vectors in the element transverse direction. This leads to the description of deformation modes that are, in practical problems, associated with high frequencies. These high frequencies, in turn, complicate the time integration procedure burdening numerical performance. In this study, the description of transverse shear deformation is accounted for in a two-dimensional beam element based on the absolute nodal coordinate formulation without the use of transverse slope vectors. In the introduced shear deformable beam element, slope vectors are replaced by vectors that describe the orientation of the beam cross-section. This procedure represents a simple enhancement that does not decrease the accuracy or numerical performance of elements based on the absolute nodal coordinate formulation. Numerical results are presented in order to demonstrate the accuracy of the introduced element in static and dynamic cases. The numerical results obtained using the introduced element agree with the results obtained using previously proposed shear deformable beam elements.

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Copyright © 2009 by American Society of Mechanical Engineers
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Figures

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Figure 1

Kinematics of the element

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Figure 2

The definition of the cross-section

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Figure 3

Mode shapes of the simply supported beam

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Figure 4

Bending mode shapes of the cantilever beam

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Figure 5

Position of the free end of the pendulum (case 1)

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Figure 6

Position of the free end of the pendulum (case 2)

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Figure 7

Position of the free end of the pendulum (case 3)

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