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Research Papers

A Large Deformation Planar Finite Element for Pipes Conveying Fluid Based on the Absolute Nodal Coordinate Formulation

[+] Author and Article Information
Michael Stangl

Institute of Technical Mechanics, Johannes Kepler University of Linz, Altenberger Strasse 69, A-4040 Linz, Austriamichael.stangl@jku.at

Johannes Gerstmayr

 Linz Center of Mechatronics GmbH, Altenberger Strasse 69, A-4040 Linz, Austriajohannes.gerstmayr@lcm.at

Hans Irschik

Institute of Technical Mechanics, Johannes Kepler University of Linz, Altenberger Strasse 69, A-4040 Linz, Austriahans.irschik@jku.at

J. Comput. Nonlinear Dynam 4(3), 031009 (Jun 09, 2009) (8 pages) doi:10.1115/1.3124091 History: Received April 10, 2008; Revised September 17, 2008; Published June 09, 2009

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.

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Copyright © 2009 by American Society of Mechanical Engineers
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Figures

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Figure 3

Cantilevered pipe conveying fluid

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Figure 4

Transverse outlet deflection of the cantilevered pipe

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Figure 5

Normalized maximum amplitude of the limit cycle for 4s<t<6s

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Figure 6

(a) Loosely constrained cantilevered pipe; (b) constrained cantilevered pipe

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Figure 7

(a) Transverse outlet deflection for U=12.5 m/s; (b) transverse outlet deflection for U=17 m/s

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Figure 8

Normalized maximum amplitude of the limit cycle for 4s<t<6s

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Figure 9

Initially curved pipe

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Figure 10

Angular velocity at the hinge

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Figure 11

Stationary angular velocity for varying flexural rigidity EI

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Figure 12

Curved pipe simulation for EI=10 Nm2

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Figure 1

The ANCF element in the (a) original and the (b) current configuration

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Figure 2

Surface vectors for two attached pipe elements

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