With the aid of the static-geometric duality of Goldenveizer (1961), Cartesian tensor notation, and nondimensionalization, it is shown that the equations of linear shell theory of Sanders (1959) and Koiter (1959), when specialized to a circular cylindrical shell with stress-strain relations exhibiting full anisotropy (21 elastic-geometric constants), can be reduced, with no essential loss of accuracy, to two coupled fourth-order partial differential equations for a stress function F and a curvature function G. Auxiliary formulas for the midsurface displacement components are also given. For isotropic shells with uncoupled stress-strain relations, the equations reduce to a form given by Danielson and Simmonds (1969). The reduction is achieved by adding certain negligibly small terms to the given stress-strain relations. For orthotropic shells of mean radius R and thickness h with uncoupled stress-strain relations, it is shown that the very short decay length of O($hR$) and the very long decay length of O(R$R/h$) (associated with separable solutions of the form e−Rz sin nθ) depend, respectively, to within a relative error of O(h/R), only on the products of different pairs of the eight possible elastic constants.

1.
Cheng
S.
, and
He
F. B.
,
1984
, “
Theory of Orthotropic and Composite Cylindrical Shells, Accurate and Simple Fourth-Order Governing Equations
,”
ASME JOURNAL OF APPLIED MECHANICS
, Vol.
51
, pp.
736
744
.
2.
Danielson
D. A.
, and
Simmonds
J. G.
,
1969
, “
Accurate Buckling Equations for Arbitrary and Cylindrical Elastic Shells
,”
Int. J. Engr. Sci
, Vol.
7
, pp.
459
468
.
3.
Flu¨gge, W., 1967, Stresses in Shells, Springer-Verlag, Berlin.
4.
Goldenveizer, A. L., 1961, Theory of Thin Elastic Shells, Pergamon, New York.
5.
Koiter, W. T., 1959, “A Consistent First Approximation in the General Theory of Thin Elastic Shells,” The Theory of Thin Elastic Shells, Proc. IUTAM Sympos. Delft, W. T. Koiter, ed., North-Holland, Amsterdam, pp. 12–33.
6.
Koiter
W. T.
, and
Cle´ment
Ph.
,
1979
, “
On the So-Called Comparison Theorem in the Linear Theory of Elasticity
,”
Z.A.M.P.
, Vol.
30
, pp.
534
536
.
7.
Niordson, F., 1985, Shell Theory, North-Holland, Amsterdam.
8.
Sanders, J. L., Jr., 1959, “An Improved First-Approximation Theory for Thin Shells,” NASA Report No. 24.
9.
Sanders
J. L.
,
1983
, “
Analysis of Circular Cylindrical Shells
,”
ASME JOURNAL OF APPLIED MECHANICS
, Vol.
50
, pp.
1165
1170
.
10.
Simmonds
J. G.
,
1966
, “
A Set of Simple Accurate Equations for Circular Cylindrical Elastic Shells
,”
Int. J. Solids Struct.
, Vol.
2
, pp.
524
541
.
11.
Simmonds
J. G.
,
1970
, “
Simplification and Reduction of the Sanders-Koiter Linear Shell Equations for Various Midsurface Geometries
,”
Q. Appl. Math.
, Vol.
28
, pp.
259
275
.
12.
Simmonds
J. G.
,
1971
, “
Extension of Koiter’s L2-Error Estimate to Approximate Shell Solutions With No Strain Energy Functional
,”
Z.A.M.P.
, Vol.
22
, pp.
339
345
.
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