Hydrostatic buckling of shells with various boundary conditions

Pinna, Rodney; Ronalds, Beverley

doi:10.1016/s0143-974x(99)00104-2

Cited by 31 publications

(15 citation statements)

References 4 publications

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“…Cylinders under hydrostatic or axial and lateral pressure loading with various boundary conditions have been analysed by Pinna and Ronalds [79,123,124] both for elastic bifurcation and nonlinear collapse. Miller [125] made an investigation of welded cylindrical pressure vessels with imperfections based on theory and experimental data.…”

Section: External Pressurementioning

confidence: 99%

Buckling of metallic shells: Buckling and postbuckling behaviour of isotropic shells, especially cylinders

Edlund

2007

Struct. Control Health Monit.

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The large discrepancies between observed buckling loads for thin shells and the predictions of the classical theory have been a great challenge to many researchers since the 1920s. In this paper, the basic behaviour and characteristics are described and recent research, mainly from the last 10 years, is reviewed. The focus is on cylindrical shells and on the influence of initial imperfections on the buckling behaviour.Examples of recent surveys in the field, each with a certain bias, are [1][2][3][4]. The first and the last both deal with imperfections in real structures and numerical buckling analysis and simulation. The second one, by Rotter, focuses on cylindrical steel shell structures like silos and tanks with relationship to the Eurocode. The third one, by Schmidt, gives an outline of several problems for steel shells, especially on approaches to a numerically based stability design. The fourth relates to applications in aerospace structures, including composite shells and reliability-based design. For a specialized review on stochastic buckling or 'uncertain buckling', see [5]. For an outline of buckling phenomena, including shell types not covered by the present paper see [6].Books: The now classic books by Bushnell [7] on computerized shell buckling and by Yamaki [8] on buckling of elastic cylinders are recommended reading. The shell stability handbook [9] treats various important shell buckling problems of practical interest. The German compilation of stability problems for civil engineering shells of revolution [10] is in handbook style and mainly deals with cylindrical, conical and spherical shells. Volume 2 of the monumental work on experimental buckling of thin-walled structures by Singer et al. [11] contains two chapters devoted to shell buckling experiments and five chapters partly dealing with that subject. A recent book by 16 authors on the stability of thin metal shells [12] is certainly essential reading. It has a focus on cylindrical shells and covers several different aspects of buckling behaviour and applications to real civil engineering shell structures. The first chapter [13], by Teng and Rotter, is a comprehensive overview on the buckling of thin shells with almost 400 references.Eurocodes: As an example of codes, the Eurocode will be briefly discussed. The most recent editions of the European design code for metal shell structures are the Draft Eurocode 3, Part 1.6 (European Prestandard ENV) published in 1999 [2,3] and the thoroughly revised EN 1993-1-6, Eurocode 3, Part 1.6 issued in 2005 [14,15]. Rotter [2] also refers to older codes and standards both of the generic type, i.e. intended for a whole class of structures of a common form, and of the application type, i.e. intended for a certain structural type, such as tanks or silos. The new EN of 2005 [14] permits all forms of analysis and should be fully general for all kinds of thinwalled metal shells. The Eurocode defines two reference strengths: the 'elastic critical resistance' R cr , computed by a linear bifurcation analysis (...

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Section: External Pressurementioning

confidence: 99%

Buckling of metallic shells: Buckling and postbuckling behaviour of isotropic shells, especially cylinders

Edlund

2007

Struct. Control Health Monit.

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“…Analytical discrepancies is approximatively three times to twice as small as numerical ones for the considered depths of immersion. Analytical discrepancies remain small, inferior to 1.6% for immersion depths up to 350m, which is quite closed to the critical immersion of the cylinder, equal to 487 m according to formulations from Pinna [10]. In conclusion, this simplified mechanical model shows that axial forces may be neglected when estimating the response of an immersed cylinder to an underwater explosion.…”

Section: Cylindrical Shell Mechanical Behaviourmentioning

confidence: 72%

“…Where p choc is the pressure obtained from eqn (8). using the simplified expression of the field of water added mass given by eqn (10), and assuming a plane stress state and the love-kirchhoff hypothesis for the shell deformation, eqn (14) becomes:…”

Section: Cylindrical Shell Mechanical Behaviourmentioning

confidence: 99%

A simplified method to assess the damage of a deeply immersed cylinder subjected to underwater explosion

Brochard¹,

Sourne²,

Barras³

2019

Int. J. SAFE

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The presented work is focused on the development of a simplified analytical method to study the structural response of a deeply immersed cylinder submitted to the primary shock wave of an underwater explosion. It relies on a methodology developed by hoo Fatt and Wierzbicki where the two dimensional boundary value problem for a cylindrical shell is converted to an equivalent one-dimensional problem of a plastic string on a non-linear plastic foundation. unstiffened cylinders immersed in shallow water have already been investigated by the authors, taking into account fluid structure interaction effects. The aim of the proposed work is to adapt the formulations to a deep immersed cylinder. The analytical developments will be presented for unstiffened cylinders. The resulting plastic dents are compared to experimental and numerical results. Although some limitations are pointed out, it is shown that this method is promising and may be advantageously used to assess rapidly the damage of a deep immersed cylinder submitted to an underwater explosions.

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“…Therefore, the investigation of the free vibration of cylindrical shell under hydrostatic pressure is meaningful when the hydrostatic pressure is below the critical pressure cr q . The critical pressure cr q of an infinite long cylindrical shell can be obtained from the formula (Pinna and Ronalds, 2000) as…”

Section: Cylindrical Shell Immersed In Watermentioning

confidence: 99%

The effect of hydrostatic pressure fields on the dispersion characteristics of fluid-shell coupled system

Liu

Zhu

et al. 2010

J. Marine. Sci. Appl.

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The effect of hydrostatic pressure on the vibration dispersion characteristics of fluid-shell coupled structures was studied. Both fluid-loaded cylindrical shells and fluid-filled cylindrical shells were considered. Numerical analysis was applied to solve the dispersion equations for shells filled with or loaded with fluid at various hydrostatic pressures. The results for external pressure showed that non-dimensional axial wave numbers are nearly independent when the pressure is below the critical level. The influence of internal pressure on wave numbers was found significant for the real branch s=1 and the complex branches of dispersion curves. The presence of internal pressure increased the cut on frequencies for the branch s=1 for high order wave modes.

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Hydrostatic buckling of shells with various boundary conditions

Cited by 31 publications

References 4 publications

Buckling of metallic shells: Buckling and postbuckling behaviour of isotropic shells, especially cylinders

Buckling of metallic shells: Buckling and postbuckling behaviour of isotropic shells, especially cylinders

A simplified method to assess the damage of a deeply immersed cylinder subjected to underwater explosion

The effect of hydrostatic pressure fields on the dispersion characteristics of fluid-shell coupled system

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