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Research Papers

Three-Dimensional Fully Parameterized Triangular Plate Element Based on the Absolute Nodal Coordinate Formulation

[+] Author and Article Information
Abdel-Nasser A. Mohamed

MotionSolve Group,
Altair Engineering, Inc.,
38 Executive Park,
Irvine, CA 92614-6729
e-mail: amohamed@altair.com

Contributed by the Design Engineering Division of ASME for publication in the Journal of Computational and Nonlinear Dynamics. Manuscript received July 13, 2012; final manuscript received May 13, 2013; published online June 20, 2013. Assoc. Editor: Aki Mikkola.

J. Comput. Nonlinear Dynam 8(4), 041016 (Jul 20, 2013) (7 pages) Paper No: CND-12-1107; doi: 10.1115/1.4024729 History: Received July 13, 2012; Revised May 13, 2013

In this work, a new three-dimensional fully parameterized triangular plate element based on the absolute nodal coordinate formulation (ANCF) is introduced. This plate element has 12 coordinates per node; therefore, it can be used in thick plate applications. The proposed 12 shape functions are obtained by adding three shape functions to the nine shape functions that were previously used with the ANCF thin triangular plate element. Unlike the existing ANCF thin triangular plate element, which allows only the use of classical Kirchoff's plate theory, the fully parameterized ANCF triangular plate element proposed in this work allows for the use of a general continuum mechanics approach and also allows for a straight forward implementation of general nonlinear constitutive equations. Moreover, all deformation modes including thickness deformation can be captured using the fully parameterized ANCF triangular plate element proposed in this paper. The numerical results obtained in this investigation show that in case of negligible deformation, the fully parameterized ANCF triangular plate element behaves like a rigid body. Moreover, it is found that there is a good agreement between the solutions obtained using the proposed fully parameterized ANCF triangular plate element and the theoretical model in the case of small deformations. Furthermore, it is shown that the results of the proposed element agree well with the results obtained using the existing fully parameterized ANCF rectangular plate element when large deformation conditions are applied. The twist behavior of the proposed element is verified by comparison with the results obtained using a conventional nonlinear rectangular plate element.

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Figures

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Fig. 1

Triangular and Cartisian coordinates

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Fig. 2

Fully parameterized ANCF triangular plate element

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Fig. 3

Stiff pendulum example

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Fig. 4

Triangular cantilever plate example

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Fig. 5

Rectangular cantilever plate model

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Fig. 6

Vertical position of the pendulum tip. (–•– Rigid pendulum, –▴– stiff pendulum).

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Fig. 7

Vertical position of the triangular cantilever plate tip (–▪– one element, –•– 2 elements, –▴– 3 elements, –▾– 5 elements, –♦– 19 elements)

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Fig. 8

The end point vertical position of the rectangular cantilever plate model (–▴– triangular element, –▪– rectangular element)

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Fig. 9

The total CPU time of the rectangular cantilever plate model (–▴– triangular element, –▪– rectangular element)

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Fig. 10

End point vertical deflection error of the rectangular cantilever plate against the number of elements (–▴– triangular element, –▪– rectangular element)

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Fig. 11

Rectangular cantilever plate subjected to twist load

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Fig. 12

Vertical deflection of the rectangular cantilever plate subjected to twist load when modeled using (a) the fully parameterized ANCF triangular element model and (b) RADIOSS nonlinear rectangular plate element model

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