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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

## Abstract

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.

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## Figures

Figure 1

Kinematics of flat plate for xz plane

Figure 2

Mapping process to obtain strains

Figure 3

Plate element configuration

Figure 4

Definition of design variables

Figure 5

Distortion parameter DPi for four-node plate element

Figure 6

cylindrical surface

Figure 7

Planar development in cylindrical surface

Figure 8

Convex surface

Figure 9

Planar development and principal strain distribution in convex surface

Figure 10

Figure 11

Planar development and principal strain distribution in saddle surface

Figure 12

Torus

Figure 13

Planar development and principal strain distribution in torus

Figure 14

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

Figure 15

Unfolding result of verification Model No. 1

Figure 16

Verification Model No. 2 (in bulbous bow)

Figure 17

Unfolding result of verification Model No. 2

Figure 18

Verification Model No. 3 (in stern)

Figure 19

Unfolding result of verification Model No. 3

## Errata

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