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Axially symmetric deformation of thin shells of revolution made of a non-linearly elastic material. / Tovstik, PY.

In: Journal of Applied Mathematics and Mechanics, Vol. 61, No. 4, 1997, p. 639-651.

Research output: Contribution to journal › Article › peer-review

Harvard

Tovstik, PY 1997, 'Axially symmetric deformation of thin shells of revolution made of a non-linearly elastic material', Journal of Applied Mathematics and Mechanics, vol. 61, no. 4, pp. 639-651.

APA

Tovstik, PY. (1997). Axially symmetric deformation of thin shells of revolution made of a non-linearly elastic material. Journal of Applied Mathematics and Mechanics, 61(4), 639-651.

Vancouver

Tovstik PY. Axially symmetric deformation of thin shells of revolution made of a non-linearly elastic material. Journal of Applied Mathematics and Mechanics. 1997;61(4):639-651.

Author

Tovstik, PY. / Axially symmetric deformation of thin shells of revolution made of a non-linearly elastic material. In: Journal of Applied Mathematics and Mechanics. 1997 ; Vol. 61, No. 4. pp. 639-651.

BibTeX

@article{561db4cfa6884a1e904d93be396d35c1,
title = "Axially symmetric deformation of thin shells of revolution made of a non-linearly elastic material",
abstract = "Approximate elasticity relations are derived for the axially symmetric deformation of a thin shell of revolution made of a non-linearly elastic material using the three-dimensional equations of the theory of elasticity. The deformations are assumed to be of the order of a small parameter which is proportional to the square root of the dimensionless thickness of the shell. Terms of the second order of smallness with respect to the deformations are retained in the elasticity relations, as a result of which the equations obtained have an error of the order of the dimensionless thickness of the shell, which is customary in the linear theory of shells. The Kirchhoff-Love hypotheses are satisfied only in the first approximation. The axial compression of a shell, assuming that one of the extreme parallels can freely slide along a plane of support, which is perpendicular to the axis of revolution, is considered as an example. A formula is obtained for the limiting load, which physically and geometrically takes account of non-linear effects in the first approximation.",
author = "PY Tovstik",
year = "1997",
language = "English",
volume = "61",
pages = "639--651",
journal = "Journal of Applied Mathematics and Mechanics",
issn = "0021-8928",
publisher = "Elsevier",
number = "4",

}

RIS

TY - JOUR

T1 - Axially symmetric deformation of thin shells of revolution made of a non-linearly elastic material

AU - Tovstik, PY

PY - 1997

Y1 - 1997

N2 - Approximate elasticity relations are derived for the axially symmetric deformation of a thin shell of revolution made of a non-linearly elastic material using the three-dimensional equations of the theory of elasticity. The deformations are assumed to be of the order of a small parameter which is proportional to the square root of the dimensionless thickness of the shell. Terms of the second order of smallness with respect to the deformations are retained in the elasticity relations, as a result of which the equations obtained have an error of the order of the dimensionless thickness of the shell, which is customary in the linear theory of shells. The Kirchhoff-Love hypotheses are satisfied only in the first approximation. The axial compression of a shell, assuming that one of the extreme parallels can freely slide along a plane of support, which is perpendicular to the axis of revolution, is considered as an example. A formula is obtained for the limiting load, which physically and geometrically takes account of non-linear effects in the first approximation.

AB - Approximate elasticity relations are derived for the axially symmetric deformation of a thin shell of revolution made of a non-linearly elastic material using the three-dimensional equations of the theory of elasticity. The deformations are assumed to be of the order of a small parameter which is proportional to the square root of the dimensionless thickness of the shell. Terms of the second order of smallness with respect to the deformations are retained in the elasticity relations, as a result of which the equations obtained have an error of the order of the dimensionless thickness of the shell, which is customary in the linear theory of shells. The Kirchhoff-Love hypotheses are satisfied only in the first approximation. The axial compression of a shell, assuming that one of the extreme parallels can freely slide along a plane of support, which is perpendicular to the axis of revolution, is considered as an example. A formula is obtained for the limiting load, which physically and geometrically takes account of non-linear effects in the first approximation.

UR - http://www.scopus.com/inward/record.url?scp=0031284060&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:0031284060

VL - 61

SP - 639

EP - 651

JO - Journal of Applied Mathematics and Mechanics

JF - Journal of Applied Mathematics and Mechanics

SN - 0021-8928

IS - 4

ER -

ID: 9286650