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Research Papers

A New Rotation-Free Shell Formulation Using Exact Corotational Frame for Dynamic Analysis and Applications

[+] Author and Article Information
Jiabei Shi

School of Naval Architecture,
Ocean and Civil Engineering,
Shanghai Jiao Tong University,
Shanghai 200240, China
e-mail: sjbnust@163.com

Zhuyong Liu

School of Naval Architecture,
Ocean and Civil Engineering,
Shanghai Jiao Tong University,
Shanghai 200240, China
e-mail: zhuyongliu@sjtu.edu.cn

Jiazhen Hong

School of Naval Architecture,
Ocean and Civil Engineering,
Shanghai Jiao Tong University,
Shanghai 200240, China

1Corresponding author.

Contributed by the Design Engineering Division of ASME for publication in the JOURNAL OF COMPUTATIONAL AND NONLINEAR DYNAMICS. Manuscript received September 1, 2017; final manuscript received January 12, 2018; published online February 27, 2018. Assoc. Editor: Javier Cuadrado.

J. Comput. Nonlinear Dynam 13(4), 041006 (Feb 27, 2018) (12 pages) Paper No: CND-17-1395; doi: 10.1115/1.4039129 History: Received September 01, 2017; Revised January 12, 2018

Rotation-free shell formulations were proved to be an effective approach to speed up solving large-scaled problems. It reduces systems' degrees-of-freedom (DOF) and avoids shortages of using rotational DOF, such as singular problem and rotational interpolation. The rotation-free element can be extended for solving geometrically nonlinear problems using a corotational (CR) frame. However, its accuracy may be lost if the approach is used directly. Therefore, a new nonlinear rotation-free shell element is formulated to improve the accuracy of the local bending strain energy using a CR frame. The linear strain for bending is obtained by combining two re-derived elements, while the nonlinear part is deduced with the side rotation concept. Furthermore, a local frame is presented to correct the conventional local CR frame. An explicit tangential stiffness matrix is derived based on plane polar decomposition local frame. Simple elemental rotation tests show that the stiffness matrix and the proposed local frame are both correct. Several numerical examples and the application of drape simulations are given to verify the accuracy of nonlinear behavior of the presented element, and some of the results show that the presented method only requires few elements to obtain an accurate solution to the problem studied.

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Figures

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Fig. 1

Deformation of a triangle shell element

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Fig. 2

Plane polar decomposition-based local frame

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Fig. 3

Rotation-free bending element patch

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Fig. 6

Stretch a plate at the middle of the edge: (a) the load condition and (b) the normalized error comparison

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Fig. 4

The simplified “S3” element

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Fig. 10

The effect of the nonlinear core element

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Fig. 11

Short cylinder: (a) the model and (b) the load curve

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Fig. 15

The velocity of point A in z direction

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Fig. 7

Point load at center of plate: (a) the load condition and (b) the normalized error comparison

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Fig. 8

Hemispherical shell: (a) the initial configuration and (b) the final configuration

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Fig. 9

Comparison of radial displacement

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Fig. 12

The displacement of point A

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Fig. 13

The velocity of point A in x direction

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Fig. 14

The velocity of point A in y direction

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Fig. 5

The nonlinear bending deformation

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Fig. 17

The configurations of at specific buckling process: (a) t = 0 ms/initial, (b) t = 60 ms/prebuckling, (c) t = 120 ms/prebuckling, (d) t = 140 ms/buckling, (e) t = 150 ms/buckling, (f) t = 158 ms/buckling, (g) t = 170 ms/post-buckling, and (h) t = 180 ms/post-buckling

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Fig. 18

A square fabric sheet drape over a square pedestal, the free boundary shape compare: (a) the draped shapes compared with experiment and Abaqus and (b) the draped shapes compared with those of references

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Fig. 16

The snap-through of a cylindrical shell: (a) the model and (b) result displacements

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Fig. 19

A square fabric sheet drape over a square pedestal: (a) 28 × 28 top view, (b) 28 × 28 isometric view, (c) 56 × 56 top view, and (d) 56 × 56 isometric view

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Fig. 20

A circular fabric sheet draped over a circular pedestal: (a) free boundary shape compare with experiment and ABAQUS, (b) top view, and (c) isometric view

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