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.
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August 2019
Research-Article
Buckling Analysis of Toroidal Shell by Rayleigh-Ritz Method
Ivo Senjanović,
Ivo Senjanović
Faculty of Mechanical Engineering
and Naval Architecture,
University of Zagreb,
Ivana Lucica 5,
Zagreb 10000, Croatia
e-mail: ivo.senjanovic@fsb.hr
and Naval Architecture,
University of Zagreb,
Ivana Lucica 5,
Zagreb 10000, Croatia
e-mail: ivo.senjanovic@fsb.hr
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Neven Alujević,
Neven Alujević
Faculty of Mechanical Engineering
and Naval Architecture,
University of Zagreb,
Ivana Lucica 5,
Zagreb 10000, Croatia
and Naval Architecture,
University of Zagreb,
Ivana Lucica 5,
Zagreb 10000, Croatia
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Ivan Ćatipović,
Ivan Ćatipović
Faculty of Mechanical Engineering
and Naval Architecture,
University of Zagreb,
Ivana Lucica 5,
Zagreb 10000, Croatia
and Naval Architecture,
University of Zagreb,
Ivana Lucica 5,
Zagreb 10000, Croatia
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Damjan Čakmak,
Damjan Čakmak
Faculty of Mechanical Engineering
and Naval Architecture,
University of Zagreb,
Ivana Lucica 5,
Zagreb 10000, Croatia
and Naval Architecture,
University of Zagreb,
Ivana Lucica 5,
Zagreb 10000, Croatia
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Nikola Vladimir,
Nikola Vladimir
Faculty of Mechanical Engineering
and Naval Architecture,
University of Zagreb,
Ivana Lucica 5,
Zagreb 10000, Croatia
and Naval Architecture,
University of Zagreb,
Ivana Lucica 5,
Zagreb 10000, Croatia
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Dae-Seung Cho
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
and Ocean Engineering,
Pusan National University,
63 beon-gil 2, Busandaehak-ro,
Geumjeong-gu,
Busan 46239, South Korea
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Ivo Senjanović
Faculty of Mechanical Engineering
and Naval Architecture,
University of Zagreb,
Ivana Lucica 5,
Zagreb 10000, Croatia
e-mail: ivo.senjanovic@fsb.hr
and Naval Architecture,
University of Zagreb,
Ivana Lucica 5,
Zagreb 10000, Croatia
e-mail: ivo.senjanovic@fsb.hr
Neven Alujević
Faculty of Mechanical Engineering
and Naval Architecture,
University of Zagreb,
Ivana Lucica 5,
Zagreb 10000, Croatia
and Naval Architecture,
University of Zagreb,
Ivana Lucica 5,
Zagreb 10000, Croatia
Ivan Ćatipović
Faculty of Mechanical Engineering
and Naval Architecture,
University of Zagreb,
Ivana Lucica 5,
Zagreb 10000, Croatia
and Naval Architecture,
University of Zagreb,
Ivana Lucica 5,
Zagreb 10000, Croatia
Damjan Čakmak
Faculty of Mechanical Engineering
and Naval Architecture,
University of Zagreb,
Ivana Lucica 5,
Zagreb 10000, Croatia
and Naval Architecture,
University of Zagreb,
Ivana Lucica 5,
Zagreb 10000, Croatia
Nikola Vladimir
Faculty of Mechanical Engineering
and Naval Architecture,
University of Zagreb,
Ivana Lucica 5,
Zagreb 10000, Croatia
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
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. Aug 2019, 141(4): 041204 (14 pages)
Published Online: May 13, 2019
Article history
Received:
November 26, 2018
Revised:
April 11, 2019
Citation
Senjanović, I., Alujević, N., Ćatipović, I., Čakmak, D., Vladimir, N., and Cho, D. (May 13, 2019). "Buckling Analysis of Toroidal Shell by Rayleigh-Ritz Method." ASME. J. Pressure Vessel Technol. August 2019; 141(4): 041204. https://doi.org/10.1115/1.4043594
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