Asymptotic shapes of inflated spheroidal nonlinearly elastic shells

In this paper we study the asymptotic behaviour of large axisymmetric deformations of closed axisymmetric nonlinearly elastic shells under internal hydrostatic pressure. These shells can suffer flexure, extension, and shear. Since there are spherical shells that can enclose an arbitrarily large volume at a finite pressure (cf. [1]), we take the volume rather than the pressure as the large parameter.

Download Full-text

Numerical Treatment of the Buckling of Nonlinearly Elastic Shells under Hydrostatic Pressure

Civil Engineering in the Oceans VI ◽

10.1061/40775(182)24 ◽

2005 ◽

Author(s):

Irina Peckel ◽

Leonid S. Srubshchik

Keyword(s):

Hydrostatic Pressure ◽

Numerical Treatment ◽

Elastic Shells ◽

Nonlinearly Elastic

Download Full-text

Asymptotic shapes of inflated noncircular elastic rings

Mathematical Proceedings of the Cambridge Philosophical Society ◽

10.1017/s0305004100062903 ◽

1985 ◽

Vol 97 (2) ◽

pp. 357-379 ◽

Cited By ~ 5

Author(s):

Stuart S. Antman ◽

M. Carme Calderer

Keyword(s):

Hydrostatic Pressure ◽

Asymptotic Behaviour ◽

Large Deformations ◽

Cylindrical Shells ◽

Governing Equations ◽

Nonlinearly Elastic

In this paper we study the asymptotic behaviour of large deformations of nonlinearly elastic, noncircular rings under internal hydrostatic pressure. These rings can undergo flexure, extension, and shear. Their governing equations are the same as those for the inflation of cylindrical shells.

Download Full-text

Qualitative and Quantitative Behaviour of Nonlinearly Elastic Rings under Hydrostatic Pressure

Bifurcation and Chaos: Analysis, Algorithms, Applications ◽

10.1007/978-3-0348-7004-7_31 ◽

1991 ◽

pp. 243-247

Author(s):

Franz Karl Labisch

Keyword(s):

Hydrostatic Pressure ◽

Qualitative And Quantitative ◽

Nonlinearly Elastic

Download Full-text

Mixed functionals in the theory of nonlinearly elastic shells

International Applied Mechanics ◽

10.1007/s10778-005-0032-5 ◽

2004 ◽

Vol 40 (11) ◽

pp. 1226-1262 ◽

Cited By ~ 18

Author(s):

V. A. Maksimyuk ◽

I. S. Chernyshenko

Keyword(s):

Elastic Shells ◽

Nonlinearly Elastic

Download Full-text

Buckling of a Pressurized Hemispherical Shell Subjected to a Probing Force

Journal of Applied Mechanics ◽

10.1115/1.4038063 ◽

2017 ◽

Vol 84 (12) ◽

Cited By ~ 29

Author(s):

Joel Marthelot ◽

Francisco López Jiménez ◽

Anna Lee ◽

John W. Hutchinson ◽

Pedro M. Reis

Keyword(s):

Mechanical Response ◽

Nondestructive Method ◽

Pressure Loading ◽

Spherical Shells ◽

Nondestructive Technique ◽

Nonlinear Load ◽

Elastic Shells ◽

Geometric Imperfection ◽

Hemispherical Shell ◽

The Stability

We study the buckling of hemispherical elastic shells subjected to the combined effect of pressure loading and a probing force. We perform an experimental investigation using thin shells of nearly uniform thickness that are fabricated with a well-controlled geometric imperfection. By systematically varying the indentation displacement and the geometry of the probe, we study the effect that the probe-induced deflections have on the buckling strength of our spherical shells. The experimental results are then compared to finite element simulations, as well as to recent theoretical predictions from the literature. Inspired by a nondestructive technique that was recently proposed to evaluate the stability of elastic shells, we characterize the nonlinear load-deflection mechanical response of the probe for different values of the pressure loading. We demonstrate that this nondestructive method is a successful local way to assess the stability of spherical shells.

Download Full-text

Asymptotic behaviour of integrals with a large parameter in the argument of a bessel function

USSR Computational Mathematics and Mathematical Physics ◽

10.1016/0041-5553(73)90079-7 ◽

1973 ◽

Vol 13 (4) ◽

pp. 250-258

Author(s):

V.D. Larichev

Keyword(s):

Asymptotic Behaviour ◽

Bessel Function ◽

Large Parameter

Download Full-text

Taking account of hydrostatic pressure in the modeling of corrosion of thick spherical shells

2015 International Conference on Mechanics - Seventh Polyakhov's Reading ◽

10.1109/polyakhov.2015.7106771 ◽

2015 ◽

Cited By ~ 4

Author(s):

Olga S. Sedova ◽

Yulia G. Pronina

Keyword(s):

Hydrostatic Pressure ◽

Spherical Shells

Download Full-text

Analysis of Two Colliding Thin Spherical Shells

International Journal of Energy ◽

10.46300/91010.2020.14.5 ◽

2020 ◽

Vol 14 ◽

Keyword(s):

Shock Waves ◽

Wave Theory ◽

Contact Theory ◽

Hertz Contact ◽

Wave Fronts ◽

Spherical Shells ◽

Elastic Shells ◽

Hertz Contact Theory ◽

The Moment ◽

Contact Domain

In the present paper, the collision of two elastic spherical shells is investigated using the wave theory of impact. The model developed here suggests that after the moment of impact quasi-longitudinal and quasi-transverse shock waves are generated, which then propagate along the spherical shells. The solution behind the wave fronts is constructed with the help of the theory of discontinuities. Since the local bearing of the materials of the colliding elastic shells is taken into account, then the solution in the contact domain is found via the Hertz contact theory.

Download Full-text