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.

Issue Section:
Technical Papers
Topics:
Displacement, Equations of motion, Rotation, Shells, Torsion
1.
Budiansky
B.
,
1968
, “
Notes on Nonlinear Shell Theory
,”
ASME JOURNAL OF APPLIED MECHANICS
, Vol.
35
, pp.
393
–
401
.
2.
England
R.
, and
Simmonds
J. G.
,
1991
, “
Simplifications under the Kirchhoff Hypothesis of Taber’s Nonlinear Theory for the Axisymmetric Bending and Torsion of Elastic Shells of Revolution
,”
Int. J. Solids Structures
, Vol.
28
, pp.
507
–
515
.
3.
Libai, A., and Simmonds, J. G., 1983, “Nonlinear Elastic Shell Theory,” Advances in Applied Mechanics, Vol. 23, J. W. Hutchinson and T. Y. Wu, eds. Academic Press, New York, pp. 271–371.
4.
Schieck
B.
,
Pietraszkiewicz
W.
, and
Stumpf
H.
,
1992
, “
Theory and Numerical Analysis of Shells undergoing Large Elastic Strains
,”
Int. J. Solids Structures
, Vol.
29
, pp.
689
–
709
.
5.
Simmonds
J. G.
, and
Danielson
D. A.
,
1972
, “
Nonlinear Shell Theory with Finite Rotation and Stress-Function Vectors
,”
ASME JOURNAL OF APPLIED MECHANICS
, Vol.
39
, pp.
1085
–
1090
.
6.
Simmonds, J. G., 1979, “Special Cases of the Nonlinear Shell Equations,” Trends in Solid Mechanics 1979 (the Koiter 65th Birthday Volume), J. F. Besseling and van der Heijden, eds., Delft University Press, Delft, pp. 211–223.
7.
Simmonds
J. G.
,
1985
, “
A New Displacement Form for the Nonlinear Equations of Motion of Shells of Revolution
,”
ASME JOURNAL OF APPLIED MECHANICS
, Vol.
52
, pp.
507
–
509
.
8.
Taber
L. A.
,
1988
, “
On a Theory for Large Elastic Deformation of Shells of Revolution including Torsion and Thick Shell Effects
,”
Int. J. Solids Structures
, Vol.
24
, pp.
973
–
985
.
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