Pure bending of a pressurized curved tube

Kolesnikov, A. A.; Popov, Alexander V.

doi:10.1201/b15684-26

Cited by 4 publications

(11 citation statements)

References 1 publication

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“…The second solution corresponds to points on the descending part of this curve and it is unstable . Similar behavior can be observed in the pure bending problems of inflated cylindrical membranes and in bending – inflation of curved tubes . Here we have presented the solution associated with ascending branch of the pressure.…”

Section: Discussionsupporting

confidence: 66%

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Bending of inflated curved hyperelastic tubes

2019

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We discuss large flexure of an inflated curved thin‐walled tube within the framework of the nonlinear theory of elastic membranes. Wrinkling of the membrane is taken into account by using a relaxed strain energy density derived from a strain energy function of incompressible hyperelastic material. We consider curved tubes with elliptical cross‐section and analyze the influence of a cross‐section shape and initial curvature of the tube at its deformation. Dependence of the bending moment on the tube curvature is obtained and discussed. In particular, the comparison with the pure bending of a cylindrical tube same material is made. We study the fact that the curving of the curved tube under in‐plane bending might be realized in two directions. Depending on the flexure direction the behavior of a curved tube can be similar or significantly different from the behavior of a cylindrical tube.

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Section: Discussionsupporting

confidence: 66%

“…[14,16] Similar behavior can be observed in the pure bending problems of inflated cylindrical membranes [14,15] and in bending -inflation of curved tubes. [18][19][20] Here we have presented the solution associated with ascending branch of the pressure.…”

Section: Discussionmentioning

confidence: 99%

Bending of inflated curved hyperelastic tubes

2019

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“…The statistical equilibrium equations are obtained from the equations (7) under the assumption that the inertial terms in the first two equations equal to zero:…”

Section: The Static Solutionmentioning

confidence: 99%

“…For materials with nonlinear mechanical properties in view of the experimental data [4] the methods of accounting for the large deformations were developed [5,6]. That allowed solving the specific tasks of static stretching of rubber membranes [7,8]. In the last years the theory of shells found its development in the works of M. Amabili [9], H. Parisch [10], L. Zubov [11].…”

Section: Introductionmentioning

confidence: 99%

Non-linear vibrations of rubber membrane

Kolpak¹,

Maltseva²,

Ivanov³

et al. 2016

ams

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“…Zubov and Kolesnikov derived a system of differential equations governing nonlinear bending of inflated cylindrical tubes made of incompressible Mooney‐Rivlin material and studied the effect of pressure preload and material properties on the maximum bending moment that the membrane can carry. Recently, Kolesnikov and Popov have reported results on finite pure bending of inflated curved tubes of circular and elliptic cross sections.…”

Section: Introductionmentioning

confidence: 99%

The effect of inflating pressure on the finite pure bending of hyperelastic tubes

Levyakov

2016

Z. Angew. Math. Mech.

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The problem of nonlinear bending of a curved tube made of incompressible rubber-like material is considered. The tube shaped like a portion of a thin-walled toroidal shell between two radial planes is inflated by pressure and then subjected to in-plane bending moments. To investigate nonlinear response and stability of the tube under these loading conditions, a finite-element approach is proposed. A special shell finite element is formulated under the assumption of uniform deformation along the tube length. The effect of wrinkling on nonlinear response of the tube is described using the tension-field theory. A change in the inflating pressure resulting from deformation of the tube due to bending is taken into account in the formulation of the governing equations. The effect of pressure on the bending stiffness, stability, and deformations of a curved tube is examined and discussed.

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Pure bending of a pressurized curved tube

Cited by 4 publications

References 1 publication

Bending of inflated curved hyperelastic tubes

Bending of inflated curved hyperelastic tubes

Non-linear vibrations of rubber membrane

The effect of inflating pressure on the finite pure bending of hyperelastic tubes

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