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TECHNICAL PAPERS

Optimal Approximated Unfolding of General Curved Shell Plates Based on Deformation Theory

[+] Author and Article Information
Cheolho Ryu

Research Institute of Engineering Science, Seoul National University, San 56-1, Shillim-dong, Kwanak-gu, Seoul 151-744, Korearyuchh@snu.ac.kr

Jong Gye Shin

Department of Naval Architecture and Ocean Engineering, College of Engineering, Seoul National University, San 56-1, Shillim-dong, Kwanak-gu, Seoul 151-744, Koreajgshin@snu.ac.kr

J. Manuf. Sci. Eng 128(1), 261-269 (May 10, 2005) (9 pages) doi:10.1115/1.2113008 History: Received August 02, 2004; Revised May 10, 2005

Surfaces of many engineering structures, especially those of ships and airplanes, are commonly fabricated as either single- or double-curved surfaces to meet functional requirements. The first step in the fabrication process of a three-dimensional design surface is unfolding or flattening the surface, otherwise known as planar development, so that manufacturers can determine the initial shape of the flat plate. Also a good planar development enables the manufacturer to estimate the strain distribution required to form the design shape. In this paper, an algorithm for optimal approximated development of a general curved surface, including both single- and double-curved surfaces, is established by minimizing the strain energy of deformation from its planar development to the design surface. The unfolding process is formulated into a constrained nonlinear programming problem, based on the deformation theory and finite element. Constraints are subjected to the characteristics of the fabrication method. Some typical surfaces, such as convex-, saddle-, and cylinder-type ones, as well as the surfaces of practical ships are unfolded using the proposed algorithm and the results show the effectiveness of this algorithm.

Copyright © 2006 by American Society of Mechanical Engineers
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References

Figures

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Figure 3

Plate element configuration

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Figure 4

Definition of design variables

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Figure 5

Distortion parameter DPi for four-node plate element

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Figure 6

cylindrical surface

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Figure 7

Planar development in cylindrical surface

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Figure 9

Planar development and principal strain distribution in convex surface

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Figure 11

Planar development and principal strain distribution in saddle surface

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Figure 13

Planar development and principal strain distribution in torus

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Figure 14

Verification Model No. 1 (in bow, fashion plate)

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Figure 15

Unfolding result of verification Model No. 1

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Figure 16

Verification Model No. 2 (in bulbous bow)

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Figure 2

Mapping process to obtain strains

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Figure 1

Kinematics of flat plate for xz plane

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Figure 17

Unfolding result of verification Model No. 2

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Figure 18

Verification Model No. 3 (in stern)

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Figure 19

Unfolding result of verification Model No. 3

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