An elasticity solution to the problem of buckling of sandwich long cylindrical shells subjected to external pressure is presented. In this context, the structure is considered a three-dimensional body. All constituent phases of the sandwich structure, i.e., the facings and the core, are assumed to be orthotropic. The loading is a uniform hydrostatic pressure, which means that the loading remains normal to the deflected surface during the buckling process. Results are produced for laminated facings, namely, boron/epoxy, graphite/epoxy and kevlar/epoxy laminates with $0deg$ orientation with respect to the hoop direction, and for alloy-foam core. Shell theory results are generated with and without accounting for the transverse shear effect. Two transverse shear correction approaches are compared, one based only on the core, and the other based on an effective shear modulus that includes the face sheets. The results show that the shell theory predictions without transverse shear can produce highly non-conservative results on the critical pressure, but the shell theory formulas with transverse shear correction produce reasonable results with the shear correction based on the core only being in general conservative (i.e., critical load below the elasticity value). The results are presented for four mean radius over shell thickness ratios, namely 15, 30, 60, and 120 in order to assess the effect of shell thickness (and hence that of transverse shear). For the same thickness, the differences between elasticity and shell theory predictions become larger as the mean radius over thickness ratio is decreased. A comparison is also provided for the same shell with homogeneous composite construction. It is shown that the sandwich construction shows much larger differences between elasticity and shell theory predictions than the homogeneous composite construction. The solution presented herein provides a means of a benchmark for accurately assessing the limitations of shell theories in predicting stability loss in sandwich shells.

1.
Hutchinson
,
J. W.
, 1968, “
Buckling and Initial Postbuckling Behavior of Oval Cylindrical Shells Under Axial Compression
,”
J. Appl. Mech.
0021-8936,
35
, pp.
66
72
.
2.
Budiansky
,
B.
, and
Amazigo
,
J. C.
, 1968, “
Initial Post-Buckling Behavior of Cylindrical Shells Under External Pressure
,”
J. Math. Phys. (Cambridge, Mass.)
0097-1421,
47
(
3
), pp.
223
235
.
3.
Kardomateas
,
G. A.
, 1993a, “
Buckling of Thick Orthotropic Cylindrical Shells Under External Pressure
,”
ASME J. Appl. Mech.
0021-8936,
60
, pp.
195
202
.
4.
Kardomateas
,
G. A.
, and
Chung
,
C. B.
, 1994, “
Buckling of Thick Orthotropic Cylindrical Shells Under External Pressure Based on Non-Planar Equilibrium Modes
,”
Int. J. Solids Struct.
0020-7683,
31
(
16
), pp.
2195
2210
.
5.
Kardomateas
,
G. A.
, 1993b, “
Stability Loss in Thick Transversely Isotropic Cylindrical Shells Under Axial Compression
,”
ASME J. Appl. Mech.
0021-8936,
60
, pp.
506
513
.
6.
Kardomateas
,
G. A.
, 1995, “
Bifurcation of Equilibrium in Thick Orthotropic Cylindrical Shells Under Axial Compression
,”
ASME J. Appl. Mech.
0021-8936,
62
, pp.
43
52
.
7.
Soldatos
,
K. P.
, and
Ye
,
J.-Q.
, 1994, “
Three-Dimensional Static, Dynamic, Thermoelastic, and Buckling Analysis of Homogeneous and Laminated Composite Cylinders
,”
Compos. Struct.
0263-8223,
29
, pp.
131
143
.
8.
Lekhnitskii
,
S. G.
, 1963,
Theory of Elasticity of an Anisotropic Elastic Body
,
Holden Day
, San Francisco, also
Mir
, Moscow, 1981.
9.
Kardomateas
,
G. A.
, 2001, “
Elasticity Solutions for a Sandwich Orthotropic Cylindrical Shell Under External Pressure, Internal Pressure and Axial Force
,”
AIAA J.
0001-1452,
39
(
4
), pp.
713
719
.
10.
Birman
,
V.
, and
Simitses
,
G. J.
, 2000, “
Theory of Cylindrical Sandwich Shells with Dissimilar Facings Subjected to Thermo-mechanical Loads
,”
AIAA J.
0001-1452,
37
(
12
), pp.
362
367
.
11.
Birman
,
V.
,
Simitses
,
G. J.
, and
Shen
,
L.
, 2000, “
Stability of Short Sandwich Cylindrical Shells with Rib-Reinforced Facings
,”
,
J. T.
,
D. E.
Beskos
, and
E. E.
Gdoutos
, eds.,
National Technical University of Athens
, Greece, pp.
11
21
.
12.
Birman
,
V.
, and
Simitses
,
G. J.
, 1999, “
Stability of Long Cylindrical Sandwich Shells with Dissimilar Facings Subjected to Lateral Pressure
,” in
Advances in Aerospace Materials and Structures
,
G.
Newaz
, ed.,
, New York, pp.
41
51
.
13.
Smith
,
C. V.
, Jr.
, and
Simitses
,
G. J.
, 1969, “
Effect of Shear and Load Behavior on Ring Stability
,”
ASCE, J. of EM Division
,
95
(
3
), pp.
559
569
.
14.
Simitses
,
G. J.
, and
Aswani
,
M.
, 1974, “
,”
ASME J. Appl. Mech.
0021-8936,
41
(
3
), pp.
827
829
.
15.
Press
,
W. H.
,
Flannery
,
B. P.
,
Teukolsky
,
S. A.
, and
Vetterling
,
W. T.
, 1989,
Numerical Recipes
,
Cambridge University Press
, Cambridge.
16.
Huang
,
H.
, and
Kardomateas
,
G. A.
, 2002, “
Buckling and Initial Postbuckling Behavior of Sandwich Beams Including Transverse Shear
,”
AIAA J.
0001-1452,
40
(
11
),
2331
2335
.