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Research Papers

Gradient Deficient Curved Beam Element Using the Absolute Nodal Coordinate Formulation

[+] Author and Article Information
Hiroyuki Sugiyama

Department of Mechanical Engineering, Tokyo University of Science, Tokyo 102-0073, Japanhsugiy1@rs.kagu.tus.ac.jp

Hirohisa Koyama, Hiroki Yamashita

Department of Mechanical Engineering, Tokyo University of Science, Tokyo 102-0073, Japan

J. Comput. Nonlinear Dynam 5(2), 021001 (Feb 09, 2010) (8 pages) doi:10.1115/1.4000793 History: Received January 27, 2009; Revised August 18, 2009; Published February 09, 2010; Online February 09, 2010

In this investigation, a gradient deficient beam element of the absolute nodal coordinate formulation is generalized to a curved beam for the analysis of multibody systems, and the performance of the proposed element is discussed by comparing with the fully parametrized curved beam element and the classical large displacement beam element with incremental solution procedures. Strain components are defined with respect to the initially curved configuration and described by the arc-length coordinate. The Green strain is used for the longitudinal stretch, while the material measure of curvature is used for bending. It is shown that strains of the curved beam can be expressed with respect to those defined in the element coordinate system using the gradient transformation, and the effect of strains at the initially curved configuration is eliminated using one-dimensional Almansi strain. This property can be effectively used with a nonincremental solution procedure employed for the absolute nodal coordinate formulation. Several numerical examples are presented in order to demonstrate the performance of the gradient deficient curved beam element developed in this investigation. It is shown that the use of the proposed element leads to better element convergence as compared with the fully parametrized element and the classical large displacement beam element with incremental solution procedures.

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Copyright © 2010 by American Society of Mechanical Engineers
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Figures

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Figure 1

Absolute nodal coordinates of the curved beam

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Figure 2

Rolling-up problem of the straight beam (ten elements)

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Figure 3

Convergence to the exact solution (straight beam rolling-up)

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Figure 4

Rolling-up problem of the curved beam (ten elements)

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Figure 5

Convergence to the exact solution (curved beam rolling-up)

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Figure 6

Curved beam pendulum

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Figure 7

Tip displacements (Model I)

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Figure 8

Deformed shapes of the curved beam pendulum (Model I)

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Figure 9

Energy balance (Model I)

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Figure 10

Tip displacements (Model II)

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Figure 11

Deformed shapes of the curved beam pendulum (Model II)

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Figure 12

Energy balance (Model II)

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