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Research Papers

A New ANCF/CRBF Fully Parameterized Plate Finite Element

[+] Author and Article Information
Carmine M. Pappalardo

Department of Industrial Engineering,
University of Salerno,
Fisciano (Salerno), 84084, Italy

Michael Wallin, Ahmed A. Shabana

Department of Mechanical and
Industrial Engineering,
University of Illinois at Chicago,
Chicago, IL 60607

Contributed by the Design Engineering Division of ASME for publication in the JOURNAL OF COMPUTATIONAL AND NONLINEAR DYNAMICS. Manuscript received April 3, 2016; final manuscript received August 6, 2016; published online December 5, 2016. Assoc. Editor: Ahmet S. Yigit.

J. Comput. Nonlinear Dynam 12(3), 031008 (Dec 05, 2016) (13 pages) Paper No: CND-16-1176; doi: 10.1115/1.4034492 History: Received April 03, 2016; Revised August 06, 2016

In this paper, the consistent rotation-based formulation (CRBF) is used to develop a new fully parametrized plate finite element (FE) based on the kinematic description of the absolute nodal coordinate formulation (ANCF). The ANCF/CRBF plate element has a general geometric description which is consistent with the basic principles of continuum mechanics, defines a unique rotation field, ensures the continuity of the rotation and strains at the element nodes, can describe an arbitrarily large displacement, and is consistent with computational geometry methods allowing for correctly describing complex shapes as demonstrated in this paper. The proposed ANCF/CRBF finite element does not suffer from the serious and fundamental problems encountered when using other large rotation vector formulations (LRVF) including the coordinate redundancy and violation of the principle of non-commutativity of the finite rotations which cannot be treated as vectors. The proposed bi-cubic ANCF/CRBF plate element employs, as nodal coordinates, three position coordinates and three finite rotation parameters. This element is obtained from a fully parameterized ANCF plate element by writing the position vector gradients of the ANCF plate element in terms of three finite rotation parameters using a nonlinear velocity transformation that systematically reduces the number of the element coordinates. The resulting element captures stretch, bending, and twist deformation modes and it allows for systematically describing complex curved geometry. Because of the lower dimensionality of the resulting ANCF/CRBF plate element, it does not capture complex deformation modes that can be captured using the more general ANCF finite elements. Furthermore, the ANCF/CRBF element mass matrix is not constant, leading to nonlinear Coriolis and centrifugal inertia forces. The new element is validated by examining its performance using several examples that include pendulum plate, free falling plate, and tire models. The results obtained using this new element are compared with the results obtained using the bi-cubic fully parameterized ANCF plate element, the bi-linear shell element, and the conventional solid element implemented in the commercial software ANSYS.

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References

Figures

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Fig. 1

ANCF fully parametrized plate element

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Fig. 2

ANCF/CRBF fully parametrized plate element

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Fig. 3

Straight rectangular plate pendulum

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Fig. 4

Vertical displacement of the plate pendulum tip (25×25 ANSYS mesh, 30×30 ANSYS mesh, 35×35 ANSYS mesh)

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Fig. 5

Deflection of the plate pendulum center (25×25 ANSYS mesh, 30×30 ANSYS mesh, 35×35 ANSYS mesh)

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Fig. 6

Vertical displacement of the plate pendulum tip (8×8 ANCF mesh, 10×10 ANCF mesh, 12×12 ANCF mesh)

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Fig. 7

Vertical displacement of the plate pendulum tip (9×9 ANCF/CRBF mesh, 11×11 ANCF/CRBF mesh, 13×13 ANCF/CRBF mesh)

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Fig. 8

Vertical displacement of the plate pendulum tip (30×30 FEM mesh, 35×35 FEM mesh, 40×40 FEM mesh)

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Fig. 9

Deflection of the plate pendulum center (8×8 ANCF mesh, 10×10 ANCF mesh, 12×12 ANCF mesh)

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Fig. 10

Deflection of the plate pendulum center (9×9 ANCF/CRBF mesh, 11×11 ANCF/CRBF mesh, 13×13 ANCF/CRBF mesh)

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Fig. 11

Deflection of the plate pendulum center (30×30 FEM mesh, 35×35 FEM mesh, 40×40 FEM mesh)

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Fig. 12

Longitudinal strain at the plate pendulum center (8×8 ANCF mesh, 10×10 ANCF mesh, 12×12 ANCF mesh)

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Fig. 13

Longitudinal strain at the plate pendulum center (9×9 ANCF/CRBF mesh, 11×11 ANCF/CRBF mesh, 13×13 ANCF/CRBF mesh)

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Fig. 14

Longitudinal strain at the plate pendulum center (30×30 FEM mesh, 35×35 FEM mesh, 40×40 FEM mesh)

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Fig. 15

Lateral strain at the plate pendulum center (8×8 ANCF mesh, 10×10 ANCF mesh, 12×12 ANCF mesh)

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Fig. 16

Lateral strain at the plate pendulum center (9×9 ANCF/CRBF mesh, 11×11 ANCF/CRBF mesh, 13×13 ANCF/CRBF mesh)

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Fig. 17

Lateral strain at the plate pendulum center (30×30 FEM mesh, 35×35 FEM mesh, 40×40 FEM mesh)

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Fig. 18

Free falling straight rectangular plate

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Fig. 19

Comparison of the vertical displacement of the corner of the plate in free fall without initial velocity (5×5 ANCF mesh, 5×5 ANCF/CRBF mesh, 5×5 FEM mesh)

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Fig. 20

Comparison of the vertical displacement of the corner of the plate in free fall with initial velocity (5×5 ANCF mesh, 5×5 ANCF/CRBF mesh, 5×5 FEM mesh)

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Fig. 21

ANCF/CRBF tire mesh

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Fig. 22

ANCF/CRBF tire cross section

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Fig. 23

Comparison of the vertical displacement of the tire center of mass (22×5 ANCF mesh, 22×5 ANCF/CRBF mesh)

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Fig. 24

Normal pressure distribution on the contact patch for the 22×5 ANCF mesh

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Fig. 25

Normal pressure distribution on the contact patch for the 22×5 ANCF/CRBF mesh

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Fig. 26

Comparison of the normal pressure distribution on the contact patch along the longitudinal direction (22×5 ANCF mesh, 22×5 ANCF/CRBF mesh)

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Fig. 27

Comparison of the normal pressure distribution on the contact patch along the lateral direction (22×5 ANCF mesh, 22×5 ANCF/CRBF mesh)

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