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Research Papers

Continuum Mechanics Based Bilinear Shear Deformable Shell Element Using Absolute Nodal Coordinate Formulation

[+] Author and Article Information
Hiroki Yamashita

Department of Mechanical and
Industrial Engineering,
The University of Iowa,
2312 Seamans Center,
Iowa City, IA 52242

Antti I. Valkeapää

Department of Mechanical Engineering,
Lappeenranta University of Technology,
Skinnarilankatu 34,
Lappeenranta 53850, Finland

Paramsothy Jayakumar

US Army RDECOM TARDEC,
6501 E. 11 Mile Road,
Warren, MI 48397-5000

Hiroyuki Sugiyama

Department of Mechanical
and Industrial Engineering,
The University of Iowa,
2416C Seamans Center,
Iowa City, IA 52242
e-mail: hiroyuki-sugiyama@uiowa.edu

Contributed by the Design Engineering Division of ASME for publication in the JOURNAL OF COMPUTATIONAL AND NONLINEAR DYNAMICS. Manuscript received March 12, 2014; final manuscript received September 22, 2014; published online April 6, 2015. Assoc. Editor: Dan Negrut. This material is declared a work of the US Government and is not subject to copyright protection in the United States. Approved for public release; distribution is unlimited.

J. Comput. Nonlinear Dynam 10(5), 051012 (Sep 01, 2015) (9 pages) Paper No: CND-14-1072; doi: 10.1115/1.4028657 History: Received March 12, 2014; Revised September 22, 2014; Online April 06, 2015

In this investigation, a continuum mechanics based bilinear shear deformable shell element is developed using the absolute nodal coordinate formulation (ANCF) for the large deformation analysis of multibody shell structures. The element consists of four nodes, each of which has the global position coordinates and the transverse gradient coordinates along the thickness introduced for describing the orientation and deformation of the cross section of the shell element. The global position field on the middle surface and the position vector gradient at a material point in the element are interpolated by bilinear polynomials. The continuum mechanics approach is used to formulate the generalized elastic forces, allowing for the consideration of nonlinear constitutive models in a straightforward manner. The element lockings exhibited in the element are eliminated using the assumed natural strain (ANS) and enhanced assumed strain (EAS) approaches. In particular, the combined ANS and EAS approach is introduced to alleviate the thickness locking arising from the erroneous transverse normal strain distribution. Several numerical examples are presented in order to demonstrate the accuracy and the rate of convergence of numerical solutions obtained by the continuum mechanics based bilinear shear deformable ANCF shell element proposed in this investigation.

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Figures

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Fig. 1

Kinematics of bilinear ANCF element

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Fig. 2

Sampling points for ANS

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Fig. 3

Deformed shape of a cantilevered plate subjected to a large transverse tip load

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Fig. 4

Numerical convergence with large deformation (initially flat)

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Fig. 5

Deformed shape of a cantilevered plate subjected to a large transverse tip load

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Fig. 6

Numerical convergence with large deformation (initially curved)

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Fig. 7

Deformed shape of pinched semicylindrical shell

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Fig. 8

Load–deflection curve of pinched semicylindrical shell

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Fig. 9

Deformed shape of slit annular plate subjected to lifting force

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Fig. 10

Load–deflection curve of slit annular plate at points A and B subjected to lifting force

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Fig. 11

Deformed shapes of quarter-cylindrical shell pendulum

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Fig. 12

Global X-position at point A

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Fig. 13

Global Y-position at point A

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Fig. 14

Global Z-position at point A

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