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Structures and Safety Reliability

A Method for Analyzing Elastic Large Deflection Behavior of Perfect and Imperfect Plates With Partially Rotation-Restrained Edges

[+] Author and Article Information
Jeom Kee Paik1

Department of Naval Architecture and Ocean Engineering,  Pusan National University, Busan, 609-735, South Korea

Do Kyun Kim

Department of Naval Architecture and Ocean Engineering,  Pusan National University, Busan, 609-735, South Korea

Hoseong Lee, Yong Lae Shim

American Bureau of Shipping (ABS), Corporate Department,  Global Technology & Business Development, 16855 Northchase Drive, Houston, TX 77060

1

Corresponding author, email: jeompaik@pusan.ac.kr.

J. Offshore Mech. Arct. Eng 134(2), 021603 (Dec 05, 2011) (12 pages) doi:10.1115/1.4004632 History: Received June 30, 2010; Revised June 02, 2011; Published December 05, 2011; Online December 05, 2011

The edge condition of the plating in a continuous stiffened-plate structure is neither simply supported nor clamped because the torsional rigidity of the support members at the plate edges is neither zero nor infinite. In a robust ship structural design, it is necessary to accurately take into account the effect of the edge condition in analyses of plate behavior in terms of buckling and post-buckling behavior. The aim of this study is to develop a new method for analyzing the geometric nonlinear behavior (i.e., elastic large deflection or post-buckling behavior) of plates with partially rotation-restrained edges in association with the torsional rigidity of the support members and under biaxial compression. An analytical method was developed to solve this problem using the nonlinear governing differential equations of plates. The validity of the developed method was confirmed by comparison with nonlinear finite element method solutions with varying values for the torsional rigidity of the support members, plate aspect ratio, and biaxial loading ratio. The developed method was found to give reasonably accurate results for practical design purpose in terms of the large deflection analysis of plates with partially rotation-restrained edges, and it will be useful for the robust design of ship structures in association with buckling and ultimate strength of plates surrounded by support members.

Copyright © 2012 by American Society of Mechanical Engineers
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References

Figures

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Figure 1

Plate surrounded by longitudinal stiffeners and transverse frames in a continuous stiffened-plate ship structure

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Figure 2

Welding-induced residual stress distribution inside a plate in the x and y directions

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Figure 3

Nomenclature: Geometrical dimensions of the support members

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Figure 4

(a) Variation of the coefficient C3 as a function of the parameter of rotational restraints for the longitudinal stiffeners with varying the plate aspect ratio; (b) variation of the coefficient C3 as a function of the parameter of rotational restraints for the transverse frames with varying the plate aspect ratio

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Figure 10

(a) Comparison of the results of the developed method and the ansys FEA for a plate with a/b = 5 under longitudinal compression for the longitudinal stiffeners with Case I and the transverse frames with Case B; (b) comparison of the results of the developed method and the ansys FEA for a plate with a/b = 5 under longitudinal compression for the longitudinal stiffeners with Case II and the transverse frames with Case B; (c) comparison of the results of the developed method and the ansys FEA for a plate with a/b = 5 under longitudinal compression for the longitudinal stiffeners with Case III and the transverse frames with Case B

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Figure 11

(a) Comparison of the results of the developed method and the ansys FEA for a plate with a/b = 1 under transverse compression for the longitudinal stiffeners with Case I and the transverse frames with Case A; (b) comparison of the results of the developed method and the ansys FEA for a plate with a/b = 1 under transverse compression for the longitudinal stiffeners with Case II and the transverse frames with Case A; (c) comparison of the results of the developed method and the ansys FEA for a plate with a/b = 1 under transverse compression for the longitudinal stiffeners with Case III and the transverse frames with Case A

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Figure 12

(a) Comparison of the results of the developed method and the ansys FEA for a plate with a/b = 3 under transverse compression for the longitudinal stiffeners with Case I and the transverse frames with Case B; (b) comparison of the results of the developed method and the ansys FEA for a plate with a/b = 3 under transverse compression for the longitudinal stiffeners with Case II and the transverse frames with Case B; (c) comparison of the results of the developed method and the ansys FEA for a plate with a/b = 3 under transverse compression for the longitudinal stiffeners with Case III and the transverse frames with Case B

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Figure 13

(a) Comparison of the results of the developed method and the ansys FEA for a plate with a/b = 5 under transverse compression for the longitudinal stiffeners with Case I and the transverse frame with Case B; (b) comparison of the results of the developed method and the ansys FEA for a plate with a/b = 5 under transverse compression for the longitudinal stiffeners with Case II and the transverse frames with Case B; (c) comparison of the results of the developed method and the ansys FEA for a plate with a/b=5 under transverse compression for the longitudinal stiffeners with Case III and the transverse frames with Case B

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Figure 14

(a) Comparison of the results of the developed method and the ansys FEA for a plate with a/b = 1 under biaxial compression for the longitudinal stiffeners with Case II and the transverse frames with Case A, σyav/σxav = 0.5; (b) comparison of the results of the developed method and the ansys FEA for a plate with a/b = 1 under biaxial compression for the longitudinal stiffeners with Case II and the transverse frames with Case A, σyav/σxav = 2.0

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Figure 15

(a) Comparison of the results of the developed method and the ansys FEA for a plate with a/b = 3 under biaxial compression for the longitudinal stiffeners with Case II and the transverse frames with Case B, σyav/σxav = 0.5; (b) Comparison of the results of the developed method and the ansys FEA for a plate with a/b = 3 under biaxial compression for the longitudinal stiffeners with Case II and the transverse frames with Case B, σyav/σxav = 2.0

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Figure 16

(a) Comparison of the results of the developed method and the ANSYS FEA for a plate with a/b = 5 under biaxial compression for the longitudinal stiffeners with Case II and the transverse frames with Case B, σyav/σxav = 0.5; (b) Comparison of the results of the developed method and the ANSYS FEA for a plate with a/b = 5 under biaxial compression for the longitudinal stiffeners with Case II and the transverse frames with Case B, σyav/σxav = 2.0

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Figure 8

(a) Comparison of the results of the developed method and the ansys FEA for a plate with a/b = 1 under longitudinal compression for the longitudinal stiffeners with Case I and the transverse frames with Case A; (b) comparison of the results of the developed method and the ansys FEA for a plate with a/b = 1 under longitudinal compression for the longitudinal stiffeners with Case II and the transverse frames with Case A; (c) Comparison of the results of the developed method and the ansys FEA for a plate with a/b = 1 under longitudinal compression for the longitudinal stiffeners with Case III and the transverse frames with Case A

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Figure 9

(a) Comparison of the results of the developed method and the ansys FEA for a plate with a/b = 3 under longitudinal compression for the longitudinal stiffeners with Case I and the transverse frames with Case B; (b) comparison of the results of the developed method and the ansys FEA for a plate with a/b = 3 under longitudinal compression for the longitudinal stiffeners with Case II and the transverse frames with Case B; (c) Comparison of the results of the developed method and the ansys FEA for a plate with a/b = 3 under longitudinal compression for the longitudinal stiffeners with Case III and the transverse frames with Case B

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Figure 5

Boundary conditions for the ansys finite element model

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Figure 6

(a) Mesh modeling for the ansys finite element analysis; (b) Initial deflection pattern applied for a plate with a/b = 5 under predominantly longitudinal axial compression (plate initial deflection amplified 80 times); (c) Initial deflection pattern applied for a plate with a/b = 5 under predominantly transverse axial compression (plate initial deflection amplified 80 times)

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Figure 7

Three types of loading condition considered in the ansys finite element analysis, including longitudinal compression ( σxav), transverse compression ( σyav), and biaxial compression ( σxavand σyav)

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