A boundary layer theory for buckling and postbuckling of anisotropic laminated thin shells is extended to shear deformable stiffened anisotropic laminated shells. A postbuckling behavior is investigated for a shear deformable anisotropic laminated cylindrical shell with geodesical stiffener of finite length subjected to lateral or hydrostatic pressure. The material of each layer of the shell is assumed to be linearly elastic, anisotropic, and fiber-reinforced. The governing equations are based on a higher-order shear deformation shell theory with von Kármán–Donnell-type of kinematic nonlinearity and including the extension/twist, extension/flexural, and flexural/twist couplings. The nonlinear prebuckling deformations and initial geometric imperfections of the shell are both taken into account. A singular perturbation technique is employed to determine the buckling pressure and postbuckling equilibrium paths. The numerical illustrations concern the postbuckling response of perfect and imperfect, moderately thick, geodesically stiffened shells, axial and ring stiffened shells, and unstiffened shells with different values of shell parameters and stacking sequence. The results confirm that there exists a circumferential stress along with an associate shear stress when the shell is subjected to lateral pressure. The postbuckling equilibrium path is stable for the moderately long shell under external pressure and the shell structure is virtually imperfection-insensitive.

1.
Simitses
,
G. J.
, and
Anastasiadis
,
J. S.
, 1992, “
Shear Deformable Theories for Cylindrical Laminates-Equilibrium and Buckling With Applications
,”
AIAA J.
0001-1452,
30
, pp.
826
834
.
2.
Simitses
,
G. J.
,
Tabiei
,
A.
, and
Anastasiadis
,
J. S.
, 1993, “
Buckling of Moderately Thick Laminated Cylindrical Shells Under Lateral Pressure
,”
Composites Eng.
0961-9526,
3
, pp.
409
417
.
3.
Harursampath
,
D.
, and
Hodges
,
D. H.
, 1999, “
Asymptotic Analysis of the Non-Linear Behavior of Long Anisotropic Tubes
,”
Int. J. Non-Linear Mech.
0020-7462,
34
(
6
), pp.
1003
1018
.
4.
Karamanos
,
S. A.
, 2002, “
Bending Instabilities of Elastic Tubes
,”
Int. J. Solids Struct.
0020-7683,
39
(
8
), pp.
2059
2085
.
5.
Houliara
,
S.
, and
Karamanos
,
S. A.
, 2006, “
Buckling and Post-Buckling of Pressurized Thin-Walled Elastic Tubes
,”
Int. J. Non-Linear Mech.
0020-7462,
41
(
4
), pp.
491
511
.
6.
Houliara
,
S.
, and
Karamanos
,
S. A.
, 2010, “
Stability of Long Transversely-Isotropic Elastic Cylinder Under Bending
,”
Int. J. Solids Struct.
0020-7683,
47
(
1
), pp.
10
24
.
7.
Arciniega
,
R. A.
,
Goncalves
,
P. B.
, and
Reddy
,
J. N.
, 2004, “
Buckling and Postbuckling Analysis of Laminated Cylindrical Shells Using Third-Order Shear Deformable Theory
,”
Int. J. Struct. Stab. Dyn.
0219-4554,
4
, pp.
293
312
.
8.
Reddy
,
J. N.
, and
Savoia
,
M.
, 1992, “
Layer-Wise Shell Theory for Postbuckling of Laminated Circular Cylindrical Shells
,”
AIAA J.
0001-1452,
30
, pp.
2148
2154
.
9.
Gerhard
,
C. S.
,
Gurdal
,
Z.
, and
Kapania
,
R. K.
, 1996, “
Finite Element Analysis of Geodesically Stiffened Cylindrical Composite Shells Using a Layerwise Theory
,”
NASA
CR Report No. 1471.
10.
Kasagi
,
A.
, and
Sridharan
,
S.
, 1993, “
Buckling and Postbuckling Analysis of Thick Composite Cylindrical Shells Under Hydrostatic Pressure
,”
Composites Eng.
0961-9526,
3
, pp.
467
487
.
11.
Kasagi
,
A.
, and
Sridharan
,
S.
, 1995, “
Imperfection Sensitivity of Layered Composite Cylinders
,”
J. Eng. Mech.
0733-9399,
121
, pp.
810
818
.
12.
Patel
,
B. P.
,
Singh
,
S.
, and
Nath
,
Y.
, 2008, “
Postbuckling Characteristics of Angle-Ply Laminated Truncated Circular Conical Shells
,”
Commun. Nonlinear Sci. Numer. Simul.
1007-5704,
13
, pp.
1411
1430
.
13.
Singh
,
S.
,
Patel
,
B. P.
, and
Nath
,
Y.
, 2007, “
Postbuckling Behavior of Angle-Ply Laminated Joined Circular Conical-Cylindrical Shells
,”
AIAA J.
0001-1452,
45
, pp.
942
949
.
14.
Teng
,
J. G.
, and
Hong
,
T.
, 2006, “
Postbuckling Analysis Of Elastic Shells of Revolution Considering Mode Switching and Interaction
,”
Int. J. Solids Struct.
0020-7683,
43
, pp.
551
568
.
15.
Han
,
B.
, and
Simitses
,
G. J.
, 1991, “
Analysis of Anisotropic Laminated Cylindrical Shells Subjected to Destabilizing Loads, part II: Numerical Results
,”
Compos. Struct.
0263-8223,
19
(
2
), pp.
183
205
.
16.
Hur
,
S. H.
,
Son
,
H. J.
,
Kweon
,
J. H.
, and
Choi
,
J. H.
, 2008, “
Postbuckling of Composite Cylinders Under External Hydrostatic Pressure
,”
Compos. Struct.
0263-8223,
86
, pp.
114
124
.
17.
Baruch
,
M.
, and
Singer
,
J.
, 1963, “
Effect of Eccentricity of Stiffeners on the General Instability of Stiffened Cylindrical Shells Under Hydrostatic Pressure
,”
J. Mech. Eng. Sci.
0022-2542,
5
, pp.
23
27
.
18.
Reddy
,
J. N.
, and
Starnes
,
J. H.
, 1993, “
General Buckling of Stiffened Circular Cylindrical Shells According to a Layerwise Theory
,”
Comput. Struct.
0045-7949,
49
, pp.
605
616
.
19.
Weaver
,
P. M.
,
Driesen
,
J. R.
, and
Roberts
,
P.
, 2002, “
Anisotropic Effects in the Compression Buckling of Laminated Composite Cylindrical Shells
,”
Compos. Sci. Technol.
0266-3538,
62
, pp.
91
105
.
20.
Shen
,
H. S.
, 2008, “
Boundary Layer Theory for the Buckling and Postbuckling of an Anisotropic Laminated Cylindrical Shell, Part II: Prediction Under External Pressure
,”
Compos. Struct.
0263-8223,
82
, pp.
362
370
.
21.
Reddy
,
J. N.
, and
Liu
,
C. F.
, 1985, “
A Higher-Order Shear Deformation Theory of Laminated Elastic Shells
,”
Int. J. Eng. Sci.
0020-7225,
23
, pp.
319
330
.
22.
Khdeir
,
A. A.
,
Reddy
,
J. N.
, and
Frederick
,
D.
, 1989, “
Study of Bending, Vibration and Buckling of Cross-Ply Circular Cylindrical Shells With Various Shell Theories
,”
Int. J. Eng. Sci.
0020-7225,
27
, pp.
1337
1351
.
23.
Reddy
,
J. N.
, 2004,
Mechanics of Laminated Plates and Shells
,
2nd ed.
,
CRC
,
Boca Raton, FL
.
24.
Shen
,
H. S.
, 2006, “
Thermal Buckling and Postbuckling of Laminated Plates
,”
Analysis and Design of Plated Structures. Stability
,
N. E.
Shanmugam
and
C. M.
Wang
, eds.,
Woodhead
,
Cambridge
, Vol.
1
. pp.
170
213
.
25.
Shen
,
H. S.
, 2001, “
Postbuckling of Shear Deformable Cross-Ply Laminated Cylindrical Shells Under Combined External Pressure and Axial Compression
,”
Int. J. Mech. Sci.
0020-7403,
43
, pp.
2493
2523
.
26.
Li
,
Z. M.
, and
Shen
,
H. S.
, 2008, “
Postbuckling of Shear-Deformable Anisotropic Laminated Cylindrical Shell Under Axial Compression
,”
Int. J. Struct. Stab. Dyn.
0219-4554,
8
, pp.
389
414
.
27.
Batdorf
,
S. B.
, 1947, “
A Simplified Method of Elastic-Stability Analysis for Thin Cylindrical Shells
,”
NACA
Technical Report No. 874.
28.
Budiansky
,
B.
, and
Amazigo
,
J. C.
, 1968, “
Initial Post-Buckling Behavior of Cylindrical Shells Under External Pressure
,”
J. Math. Phys.
0022-2488,
47
, pp.
223
235
.
29.
Amazigo
,
J. C.
, 1974, “
Asymptotic Analysis of the Buckling of Externally Pressurized Cylinders With Random Imperfections
,”
Q. Appl. Math.
0033-569X,
31
, pp.
429
442
.
30.
Yuan
,
F. G.
, and
Hsieh
,
C. C.
, 1998, “
Three-Dimensional Wave Propagation in Composite Cylindrical Shells
,”
Compos. Struct.
0263-8223,
42
, pp.
153
167
.
You do not currently have access to this content.