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Research Papers: Design and Analysis

Buckling Analysis of Toroidal Shell by Rayleigh-Ritz Method

[+] Author and Article Information
Ivo Senjanović

Faculty of Mechanical Engineering
and Naval Architecture,
University of Zagreb,
Ivana Lucica 5,
Zagreb 10000, Croatia
e-mail: ivo.senjanovic@fsb.hr

Neven Alujević, Ivan Ćatipović, Damjan Čakmak, Nikola Vladimir

Faculty of Mechanical Engineering
and Naval Architecture,
University of Zagreb,
Ivana Lucica 5,
Zagreb 10000, Croatia

Dae-Seung Cho

Department of Naval Architecture
and Ocean Engineering,
Pusan National University,
63 beon-gil 2, Busandaehak-ro,
Geumjeong-gu,
Busan 46239, South Korea

Contributed by the Pressure Vessel and Piping Division of ASME for publication in the JOURNAL OF PRESSURE VESSEL TECHNOLOGY. Manuscript received November 26, 2018; final manuscript received April 11, 2019; published online May 13, 2019. Assoc. Editor: Oreste S. Bursi.

J. Pressure Vessel Technol 141(4), 041204 (May 13, 2019) (14 pages) Paper No: PVT-18-1264; doi: 10.1115/1.4043594 History: Received November 26, 2018; Revised April 11, 2019

The energy approach is used to analyze the buckling stability of toroidal shells. A closed and an open toroidal shell, as well as a shell segment are considered. Linear strain energy and nonlinear strain energy due to a uniform external pressure are formulated. Variations of the in-surface and normal displacement components in the circumferential and meridional directions are assumed in the form of a double Fourier series. The eigenvalue problem for the determination of the critical pressure is formulated by the Rayleigh–Ritz method (RRM). The proposed procedure is evaluated by numerical examples: one for a closed and another one for a simply supported open toroidal shell. The obtained results are validated by a comparison with results obtained by the finite strip method (FSM) and the finite element method (FEM), which shows a very good agreement.

FIGURES IN THIS ARTICLE
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Copyright © 2019 by ASME
Topics: Shells , Buckling , Stiffness
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Figures

Grahic Jump Location
Fig. 1

Closed toroidal shell, main dimensions, and displacement components

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Fig. 2

Simply supported open toroidal shell, main dimensions, and displacement components

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Fig. 3

Simply supported segment of toroidal shell

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Fig. 4

Tension forces of closed toroidal shell due to external pressure p =1 MPa, – · – membrane theory, ––– shell theory

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Fig. 5

Displacement components of buckling modes, closed toroidal shell, RRM, FSM: – · – U, - - - V, ––– W

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Fig. 6

Buckling modes of closed toroidal shell under external pressure (abaqus)

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Fig. 7

Buckling modes of closed toroidal shell in the coordinate planes (abaqus)

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Fig. 8

Tension forces of simply supported open toroidal shell due to external pressure p = 1 MPa, – · – membrane theory, ––– shell theory

Grahic Jump Location
Fig. 9

Displacement components of buckling modes, simply supported open toroidal shell, RRM, FSM: – · – U, - - - V, ––– W

Grahic Jump Location
Fig. 10

Buckling modes of simply supported open toroidal shell under external pressure (abaqus)

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Fig. 11

Buckling modes of simply supported open toroidal shell in the coordinate planes (abaqus)

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