A comparative analysis of rubber-like shells of revolution which undergo arbitrarily large rotations and strains is presented. The comparison is made between two alternative definitions of the deformed reference surface: (i) The deformed reference surface is composed of the same particles as the undeformed reference surface. (ii) The deformed reference is taken as the surface of mass of the shell (the dynamic consistency condition) according to which (i) is not necessarily valid. The results obtained from the buckling analysis of circular neo-Hookean plates under radial loads using various approaches strengthen the latter definition relative to the former one.

1.
Green, A. E., and Adkins, J. E., 1960, Large Elastic Deformations and Non-Linear Continuum Mechanics, Clarendon Press, Oxford, U.K., p. 26.
2.
Guo
Z. H.
,
1962
, “
Vibration and Stability of a Cylinder Subject to Finite Deformation
,”
Archives of Mechanics
, Vol.
14
, pp.
757
768
.
3.
Makowski
J.
, and
Stumpf
H.
,
1989
, “
Finite Axisymmetric Deformation of Shells of Revolution with Application to Flexural Buckling of Circular Plates
,”
Ingenieur—Archiv
, Vol.
59
, pp.
456
472
.
4.
Simmonds
J. G.
,
1986
, “
The Strain-Energy Density of Rubber-Like Shells of Revolution Undergoing Torsionless, Axisymmetric Deformation (Axishells)
,”
ASME JOURNAL OF APPLIED MECHANICS
, Vol.
53
, pp.
593
596
.
5.
Taber
L. A.
,
1987
, “
Large Elastic Deformation of Shear Deformable Shells of Revolution: Theory and Analysis
,”
ASME JOURNAL OF APPLIED MECHANICS
, Vol.
54
, pp.
578
584
.
6.
Treloar, L. R. G., 1975, The Physics of Rubber Elasticity, 3rd ed., Clarendon Press, Oxford, U.K., pp. 214–218.
This content is only available via PDF.
You do not currently have access to this content.