Mixed functionals in the theory of nonlinearly elastic shells

2004 ◽  
Vol 40 (11) ◽  
pp. 1226-1262 ◽  
Author(s):  
V. A. Maksimyuk ◽  
I. S. Chernyshenko
Keyword(s):  
Elastic Shells ◽  
Nonlinearly Elastic

Asymptotic shapes of inflated spheroidal nonlinearly elastic shells

1985 ◽  
Vol 97 (3) ◽  
pp. 541-549 ◽  
Author(s):  
Stuart S. Antman ◽  
M. Carme Calderer
Keyword(s):  
Hydrostatic Pressure ◽  
Asymptotic Behaviour ◽  
Large Volume ◽  
Large Parameter ◽  
Spherical Shells ◽  
Elastic Shells ◽  
Nonlinearly Elastic

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.

Free vibrations of nonlinearly elastic shells

1971 ◽  
Vol 7 (3) ◽  
pp. 246-249
Author(s):  
V. N. Pastushikhin
Keyword(s):  
Free Vibrations ◽  
Elastic Shells ◽  
Nonlinearly Elastic

scholarly journals Corrigenda

1987 ◽  
Vol 101 (2) ◽  
pp. 383-383
Author(s):  
Stuart S. Antman ◽  
M. Carme Calderer
Keyword(s):  
Higher Order ◽  
Elastic Shells ◽  
Right Hand ◽  
Higher Order Terms ◽  
Image Position ◽  
The Right ◽  
Nonlinearly Elastic

‘Asymptotic shapes of inflated noncircular elastic rings’‘Asymptotic shapes of inflated spheroidal nonlinearly elastic shells’Formulae (2·12) of both papers, giving an expression for the curvature, k̅, are wrong. To correct them, let ο(s) be the angle between r̅′ = ν̅a+ηb and i. Thenwhence formulae (3·2) of both papers imply thatFormula (C) corrects the erroneous expression for k by adding the second term on the right-hand side of (C). Since this term is of order ∈, the analysis in the remainder of both papers is unaffected by this correction. (The analyses of higher-order terms do not include a study of corrections to the curvature.)

Asymptotic analysis of nonlinearly elastic shells “mixed approach”

2012 ◽  
Vol 80 (3-4) ◽  
pp. 323-346
Author(s):  
Djamal Ahmed Chacha ◽  
Madjda Miloudi
Keyword(s):  
Asymptotic Analysis ◽  
Elastic Shells ◽  
Mixed Approach ◽  
Nonlinearly Elastic

A Simplified Displacement-Rotation Form for the Equations of Motion of Nonlinearly Elastic Shells of Revolution Undergoing Combined Bending and Torsion

1996 ◽  
Vol 63 (2) ◽  
pp. 539-542 ◽  
Author(s):  
J. G. Simmonds
Keyword(s):  
Equations Of Motion ◽  
Shell Of Revolution ◽  
Shells Of Revolution ◽  
Elastic Shells ◽  
Axisymmetric Bending ◽  
Nonlinearly Elastic

By appropriately defining two displacements and a rotation, it is shown that the equations of motion of a shell of revolution undergoing combined axisymmetric bending and torsion, in which the extensional strains and the rotations may be arbitrarily large, can be given a form in which there are three effective extensional strains and two effective bending strains, each of which is only linear or quadratic in the displacements and rotation.

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