Simplified theoretical solution of circular toroidal shell with ribs under uniform external pressure

Du, Qikui; Zou, Guang Ping; Zhang, Bowen; Wan, Zhinian

doi:10.1016/j.tws.2015.07.019

Cited by 18 publications

(5 citation statements)

References 16 publications

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“…R 0 [37] Major radius [8,37] Shell crown radius [42] Meridian radius [44] Bend/bending radius [35,36,38,39] Toroidal radius [45] Ring radius [46,47] r [mm] Cross-sectional radius a [8,31,32,41,42,48,49] x, y [44] r 0 [37] R 1 , R 2 [45] r 1 [50] R [43] Minor radius [37] Shell meridian radius [42] Toroid internal radius [42] Tube radius [35,36,38] Toroid tube radius [33,51,52] Toroidal shell radius [32] Meridian circle radius [48,49]…”

Section: Toroidal Pressure Vessel Parametersmentioning

confidence: 99%

“…Relative bending radius [35][36][37] Aspect ratio [50] a [43,50] λ [33] ϕ [°] Hoop angle ss [41] u [37] θ [39] x 1 [46,47] Material coordinate [42] Parallel angular coordinate [36] Meridional angle [8,31,[35][36][37][38][39][40]50] Meridional coordinate [33,46,47,52] Co-latitude [51] Tangential angle [48,49]…”

Section: R/r [-]mentioning

confidence: 99%

“…Axial angle θθ [41] v [37] ϕ [39] x 2 [46,47] Material coordinate [42] Parallel angle [35][36][37][38] Circumferential angle [8,31,39,40] Circumferential coordinate [46,47] Meridian rotational angle [48,49]…”

Section: R/r [-]mentioning

confidence: 99%

“…No information was given regarding possible manufacturing methods or vessel-strut joining techniques which are important to avoid local failure locations. The addition of stiffened ribs to the outside of toroidal shells to increase external buckling performance has also been addressed [48,49] however this sort of technique is not suitable for toroidal CPVs for on-board gaseous fuel storage applications.…”

Section: Hoop Stress Variation and Design Optimisation Of Toroidal Pressure Vesselsmentioning

confidence: 99%

See 3 more Smart Citations

A review of toroidal composite pressure vessel optimisation and damage tolerant design for high pressure gaseous fuel storage

Fowler

Orifici

Wang

2016

International Journal of Hydrogen Energy

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On-board high-pressure storage of hydrogen gas and compressed natural gas is critical to the widespread adoption of alternative gaseous fuel to reduce CO 2 emissions in transportation. Cylindrical pressure vessels are the traditional option for on-board gaseous fuel storage; however they possess domed heads that are prone to over-design and a source of manufacturing difficulties. Toroidal composite pressure vessels (CPV) have been recognised as a volumetrically efficient solution that could address these problems, thus reducing vessel mass, while improving storage efficiencies. Currently, there exist many gaps in toroidal CPV research which must be addressed to fully realise the potential of this technology. Herein we present a comprehensive and critical review of the design and optimisation of toroidal CPVs, focusing on damage tolerant design as a key requirement to meet safety standards and optimisation of toroidal cross-sectional profiles (shape, thickness variation and fibre winding pattern) to reduce or eliminate stress non-uniformity. An original analysis of toroidal radius ratio (R/r) influence on the thickness profiles of naturally-thickened and isotensoid circular toroidal CPVs is conducted. It is concluded that a focus on smaller radius ratios (1.25 < R/r < 3) is required to maximise the potential spacesaving and volumetric efficiencies of the torus. Leading international CPV standards are analysed in order to adapt three important design qualification requirements from cylindrical to toroidal structures. Building block approaches are also presented to aid the damage tolerant design of toroidal CPVs for the relevant design qualification tests.

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Section: Toroidal Pressure Vessel Parametersmentioning

confidence: 99%

Section: R/r [-]mentioning

confidence: 99%

Section: R/r [-]mentioning

confidence: 99%

Section: Hoop Stress Variation and Design Optimisation Of Toroidal Pressure Vesselsmentioning

confidence: 99%

See 2 more Smart Citations

A review of toroidal composite pressure vessel optimisation and damage tolerant design for high pressure gaseous fuel storage

Fowler

Orifici

Wang

2016

International Journal of Hydrogen Energy

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show abstract

“…He obtained the eigenvalues of part of the toroidal vessel by using the Galerkin's scheme to calculate stability equations [8]. Studies proposed analytical algorithms for examining the strength of ribbed toroid shells and performed a nonlinear analysis to analyze the buckling of such shells [1,9,10]. Civalek used the discrete singular convolution method to analyze the buckling of CNT-reinforced laminated nonrectangular plates [11].…”

Section: Introductionmentioning

confidence: 99%

Numerical and Experimental Buckling and Post-Buckling Analyses of Sphere-Segmented Toroidal Shell Subject to External Pressure

Zhang

Wang

2022

Metals

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This study determined the buckling characteristics of sphere-segmented toroidal shells subjected to external pressure. The proposed toroidal vessel comprises six spheres and six rings. Two laboratory models with the same nominal dimensions were manufactured, measured, tested, and evaluated. To investigate whether sphere-segmented toroidal shells are imperfection-sensitive structures with closely spaced eigenvalues, the subspace algorithm was applied to evaluate the first 50 eigenmodes, and the modified Riks algorithm was used to obtain post-buckling characteristics. The results indicated that the deviation between the results of the experimental and numerical analyses was within a reasonable range. The proposed sphere-segmented toroidal shells were highly imperfection-sensitive structures with closely spaced eigenvalues. Subsequently, imperfection sensitivity analysis confirmed this conclusion. In numerical analyses, the first eigenmode could be considered as the worst eigenmode of sphere-segmented toroidal shells. The trend of the equilibrium path of sphere-segmented toroidal shells was consistent with spherical shells, revealing instability. In addition, ellipticity and completeness exerted a negligible effect on the buckling load of sphere-segmented toroidal shells.

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Collapse behavior of corrugated stiffened pressure shells under external hydrostatic pressure considering actual fabrication imperfections: A reverse modeling technique

Zhang,

Sun,

Shan

et al. 2024

Applied Ocean Research

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Simplified theoretical solution of circular toroidal shell with ribs under uniform external pressure

Cited by 18 publications

References 16 publications

A review of toroidal composite pressure vessel optimisation and damage tolerant design for high pressure gaseous fuel storage

A review of toroidal composite pressure vessel optimisation and damage tolerant design for high pressure gaseous fuel storage

Numerical and Experimental Buckling and Post-Buckling Analyses of Sphere-Segmented Toroidal Shell Subject to External Pressure

Collapse behavior of corrugated stiffened pressure shells under external hydrostatic pressure considering actual fabrication imperfections: A reverse modeling technique

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