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Research Papers

Coupled Deformation Modes in the Large Deformation Finite Element Analysis: Generalization

[+] Author and Article Information
Oleg N. Dmitrochenko

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

Bassam A. Hussein, Ahmed A. Shabana

Department of Mechanical Engineering, University of Illinois at Chicago, 842 West Taylor Street, Chicago, IL 60607-7022

J. Comput. Nonlinear Dynam 4(2), 021002 (Mar 06, 2009) (8 pages) doi:10.1115/1.3079682 History: Received June 08, 2007; Revised August 21, 2008; Published March 06, 2009

The effect of the absolute nodal coordinate formulation (ANCF)–coupled deformation modes on the accuracy and efficiency when higher order three-dimensional beam and plate finite elements are used is investigated in this study. It is shown that while computational efficiency can be achieved in some applications by neglecting the effect of some of the ANCF-coupled deformation modes, such modes introduce geometric stiffening/softening effects that can be significant in the case of very flexible structures. As shown in previous publications, for stiff structures, the effect of the ANCF-coupled deformation modes can be neglected. For such stiff structures, the solution does not strongly depend on some of the ANCF-coupled deformation modes, and formulations that include these modes lead to numerical results that are in good agreement with formulations that exclude them. In the case of a very flexible structure, on the other hand, the inclusion of the ANCF-coupled deformation modes becomes necessary in order to obtain an accurate solution. In this case of very flexible structures, the use of the general continuum mechanics approach leads to an efficient solution algorithm and to more accurate numerical results. In order to examine the effect of the elastic force formulation on the efficiency and the coupling between different modes of deformation, three different models are used again to formulate the elastic forces in the absolute nodal coordinate formulation. These three methods are the general continuum mechanics approach, the elastic line (midsurface) approach, and the elastic line (midsurface) approach with the Hellinger–Reissner principle. Three-dimensional absolute nodal coordinate formulation beam and plate elements are used in this study. In the general continuum mechanics approach, the coupling between the cross section deformation and the beam centerline or plate midsurface displacement is considered, while in the approaches based on the elastic line and the Hellinger–Reissner principle, this coupling is neglected. In addition to the fully parametrized beam element used in this study, three different plate elements, two fully parametrized and one reduced order thin plate elements, are used. The numerical results obtained using different finite elements and elastic force formulations are compared in this study.

Copyright © 2009 by American Society of Mechanical Engineers
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Figures

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Figure 1

Motion description in the absolute nodal coordinate formulation

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Figure 2

Three-dimensional beam element

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Figure 3

Thin plate element

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Figure 4

Fully parametrized plate element

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Figure 5

Slider-crank mechanism

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Figure 6

Midpoint transverse deformation

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Figure 7

Midpoint transverse deformation using continuum mechanics approach (—◼—, 4-elements; —●—, 8-elements; —▲—, 20-elements)

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Figure 8

Midpoint transverse deformation using elastic line approach (—◼—, 4-elements; —●—, 8-elements; —▲—, 20-elements)

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Figure 9

Midpoint transverse deformation using the Hellinger–Reissner principle (—◼—, 4-elements; —●—, 8-elements; —▲—, 20-elements)

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Figure 10

Midpoint transverse deformation using the neo-Hookean constitutive model (—◼—, 4-elements; —●—, 8-elements; —▲—, 20-elements)

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Figure 11

Midpoint transverse deformation (—◼—, continuum mechanics; —●—, elastic line; —▲—, Hellinger–Reissner; —▼—, neo-Hookean)

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Figure 12

Flexible plate example

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Figure 13

Point Q vertical position using the plate A model (—◼—, 4-elements; —●—, 9-elements; —▲—, 16-elements)

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Figure 14

Point Q vertical position using the plate B model (—◼—, 4-elements; —●—, 9-elements; —▲—, 16-elements)

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Figure 15

Point Q vertical position using the thin plate model (—◼—, 4-elements; —●—, 9-elements; —▲—, 16-elements)

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Figure 16

Point Q vertical position (—◼—, plate A; —●—, plate B; —▲—, thin plate)

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