An acceptable variant of the Koiter–Morley equations for an elastically isotropic circular cylindrical shell is replaced by a constant coefficient fourth-order partial differential equation for a complex-valued displacement-stress function. An approximate formal solution for the associated “free-space” Green’s function (i.e., the Green’s function for a closed, infinite shell) is derived using an inner and outer expansion. The point wise error in this solution is shown rigorously to be of relative order $(h∕a)(1+h∕a∣x∣)$, where $h$ is the constant thickness of the shell, $a$ is the radius of the mid surface, and $ax$ is distance along a generator of the mid surface.

1.
Sanders
,
J. L.
, Jr.
, 1959, “
An Improved First-Approximation Theory for Thin Shells
,” NASA Report No. 24.
2.
Koiter
,
W. T.
, 1959, “
A Consistent First Approximation in the Theory of Elastic Shells
,”
Proceedings of the Symposium on the Theory of Thin Elastic Shells
,
W. T.
Koiter
ed.,
North–Holland
, Amsterdam, pp.
12
33
.
3.
Simmonds
,
J. G.
, 1966, “
A Set of Simple, Accurate Equations for Circular Cylindrical Elastic Shells
,”
Int. J. Solids Struct.
0020-7683,
2
, pp.
525
541
.
4.
Sanders
,
J. L.
, Jr.
, and
Simmonds
,
J. G.
, 1970, “
Concentrated Forces on Shallow Cylindrical Shells
,”
ASME J. Appl. Mech.
0021-8936,
37
, pp.
367
373
.
5.
Buchwald
,
V. T.
, 1967, “
Some Problems of Thin Circular Cylindrical Shells, I
,”
J. Math. Phys.
0022-2488,
46
, pp.
237
252
.
6.
Morley
,
L. S. D.
, 1959, “
An Improvement on Donnell’s Approximation for Thin-Walled Circular Cylinders
,”
Q. J. Mech. Appl. Math.
0033-5614,
12
, pp.
89
99
.
7.
Morley
,
L. S. D.
, 1960, “
,”
Q. J. Mech. Appl. Math.
0033-5614,
13
, pp.
24
37
.
8.
Lighthill
,
J.
, 1960,
Fourier Analysis and Generalized Functions
,
Cambridge University Press
, Cambridge.
9.
Jolley
,
L. B. W.
, 1961,
Summation of Series
, 2nd revised ed.,
Dover
, New York.
10.
Abramowitz
,
M.
, and
Stegun
,
I.
, eds., 1965,
Handbook of Mathematical Functions
,
National Bureau of Standards
.