Corrugation of a flexible ring under external hydrostatic compression

Dolgikh, D.V.; Kiselev, V. V.

doi:10.1016/j.jappmathmech.2010.05.011

Cited by 3 publications

(6 citation statements)

References 10 publications

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“…The lower the pressure the fewer number of the bulges in the cross section of the shell is possible. The nonlinearity of the problem is that the ranges of the pressure, each corresponding to its own number of bulges, can overlap each other [13,14].…”

Section: Formulation Of the Modelmentioning

confidence: 99%

“…The Frenet-Serret formulae (8) can be reduced to the equation for the phase The solution of Eq. (21) has the form [13,14]…”

Section: Formulation Of the Modelmentioning

confidence: 99%

“…(6) for the parameter γ 0 , then the threshold value (28) coincides with the critical load for the linear theory [3]. In [13,14] the possible equilibrium states of the shell depending on the value of the external pressure were analytically described. In this paper the influence of the most simple constraints on corrugation of the shell is investigated.…”

Section: Formulation Of the Modelmentioning

confidence: 99%

“…However, the influence of the constraints on localization of bends of a hydrostatically compressed shell in the initial non-linear elastic stage of deformation, the ways of controlling the process of change in the shell shape are not yet studied. The papers [13,14] show analytic solutions for the Cosserat model, describing large non-linear bends of the cross-section of the shell under hydrostatic pressure. It is demonstrated that under certain conditions the shell cross-section can be shaped into regular polygons even in absence of external constraints.…”

Section: Introductionmentioning

confidence: 99%

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Controlling the Change in the Shape of a Cylindrical Shell Subjected to External Hydrostatic Pressure

Kiselev¹,

Dolgikh²

2019

JAAP

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Analytic and numerical analysis for the initial non-linear elastic stage of changing in the shape of a circular shell subjected to a high-pressure liquid is performed, with the shell being under two rigid constraints: an external cylindrical cavity and/or an internal rod. In this stage, the emergence of alternating bulges and depressions is governed by the balance between the nonlinearity and dispersion effects. In the framework of the Cosserat theory, the dependence of the curvature of the shell cross-section on the external pressure is obtained. Knowing the curvature make it possible to restore the form of the cross section with the methods of the differential geometry. It is shown that unwanted wave-like folds and rigid ribs on the deformed shell surface can be eliminated by suitably selecting the constraints. Cost-efficient ways of producing hollow articles from pipe billets with the hydrostatic pressure method are discussed.

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Section: Formulation Of the Modelmentioning

confidence: 99%

“…The Frenet-Serret formulae (8) can be reduced to the equation for the phase The solution of Eq. (21) has the form [13,14]…”

Section: Formulation Of the Modelmentioning

confidence: 99%

Section: Formulation Of the Modelmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Controlling the Change in the Shape of a Cylindrical Shell Subjected to External Hydrostatic Pressure

Kiselev¹,

Dolgikh²

2019

JAAP

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“…FEA in principle makes it possible to calculate any corrugated shell [6][7][8][9][10][11][12][13][14][15], but, for the early stages of design, simple analytic solutions are very useful to engineers. Analytical solutions can be also used as benchmark examples for numerical algorithms.…”

Section: Introductionmentioning

confidence: 99%

Buckling of Corrugated Ring under Uniform External Pressure

Andrianov¹,

Diskovsky²,

Ryzhkov³

2020

Symmetry

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Stability analysis of a corrugated ring subjected to uniform external pressure is under consideration. Two main approaches to solving this problem are analyzed. The equivalent bending stiffness approach is often used in engineering practice. It is based on some plausible assumptions about the behavior of a structure. Its advantage is the simplicity of the obtained relations; the disadvantage is the difficulty in estimating the area of applicability. In this paper, we developed an asymptotic homogenization method for calculating the critical pressure for a corrugated ring, which made it possible to mathematically substantiate and refine the equivalent bending stiffness approach. To evaluate the results obtained using the equivalent stiffness approach and asymptotic homogenization method, the imperfection method is used. The influence of the corrugation parameters on buckling pressure is analyzed.

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Non-linear patterns of bends and solitons on surfaces of loaded shells

Kiselev¹,

Dolgikh²

2013

Shell Structures: Theory and Application

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Corrugation of a flexible ring under external hydrostatic compression

Cited by 3 publications

References 10 publications

Controlling the Change in the Shape of a Cylindrical Shell Subjected to External Hydrostatic Pressure

Controlling the Change in the Shape of a Cylindrical Shell Subjected to External Hydrostatic Pressure

Buckling of Corrugated Ring under Uniform External Pressure

Non-linear patterns of bends and solitons on surfaces of loaded shells

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