Differences in the response of thin nonshallow spherical shells resulting from the choice of the adopted shell theory (classical or improved) are addressed analytically and through a series of representative shell problems. The analytical approach utilized to study the variation between the two theoretical models is based on the response resulting from Singular loads. The differences are quantified in a set of problems that reflect on the assumptions used in formulating the analytical description of the two theories in question. The broad scope of this paper is to examine the impact of shear deformability, introduced by the improved theory on the stress field when amplified under specific loading and geometric conditions, when those are of primary concern to the engineers. Such cases associated with stress concentration around cutouts, interaction of shells with nozzles, stress field in the vicinity of concentrated surface loads, etc. The mathematical formulation is based on the derivation of appropriate Green functions and the computational scheme is formed upon a special type of boundary integral equation. Comparison solutions for stress concentration around circular cutouts of twisted and sheared shells, stress amplification in the junction of shell with nozzles, and local stress field induced by concentrated loads are presented for the two theories.

1.
Bijlaard
P. P.
,
1957
, “
Local Stresses in Spherical Shells from Radial or Moment Loadings
,”
Welding Journal
, Vol.
36
(
5
) Research Supplement, pp.
240-s to 243-s
240-s to 243-s
.
2.
Chassapis
C.
,
Philippacopoulos
A. J.
, and
Simos
N.
,
1991
, “
Localized Stresses in Spherical Shell/Attachment Interaction: Boundary Integral-Finite Element Approach Comparisons
,”
ASME PVP
-Vol.
214
, pp.
153
159
.
3.
Kraus, H., 1967, Thin Elastic Shells, Wiley, New York, NY.
4.
Prasad
C.
,
1964
, “
On Vibrations of Spherical Shells
,”
Journal of the Acoustical Society of America
, Vol.
36
, pp.
489
494
.
5.
Reissner
E.
,
1959
, “
On the Determination of Stresses and Displacements for Unsymmetrical Deformations of Shallow Spherical Shells
,”
Journal of Mathematical Physics
, Vol.
38
, pp.
16
35
.
6.
Reissner
E.
,
Wan
F. Y. M.
,
1986
, “
On the Effect of Transverse Shear Deformability on Stress Concentration Factors for Twisted and Sheared Shallow Spherical Shells
,”
ASME Journal of Applied Mechanics
, Vol.
53
, pp.
597
601
.
7.
Sanders
J. L.
,
1970
, “
Cutouts in Shallow Shells
,”
ASME Journal of Applied Mechanics
, Vol.
37
, pp.
374
383
.
8.
Simmonds
G. J.
,
1968
, “
Green’s Functions for Closed Elastic Spherical Shells, Exact and Accurate Asymptotic Solutions
,”
Proceedings of the Koninklijke Nederlands Academie van Wetenschappen, Ser. B
, Vol.
71
, No.
3
, pp.
236
249
.
9.
Simos
N.
, and
Sadegh
A. M.
,
1989
a, “
Self-Equilibrated Singular Solutions of a Complete Spherical Shell. Classical Theory Approach
,”
ASME Journal of Applied Mechanics
, Vol.
56
, pp.
105
112
.
10.
Simos, N., and Sadegh, A. M., 1989b, “A Boundary Integral Equation to Nonshallow Spherical Shell Problems with Arbitrary Boundary Constraints,” ASME Journal of Applied Mechanics, Paper No. 89-WA/APM-29.
11.
Simos
N.
, and
Sadegh
A. M.
,
1989
c, “
The Effect of Transverse Shear onto the Singular Solutions of a Complete Spherical Shell
,”
International Journal of Solids and Structures
, Vol.
25
, No.
12
, pp.
1359
1379
.
12.
Simos
N.
, and
Sadegh
A. M.
,
1991
, “
An Indirect BIM for Static Analysis of Spherical Shells Using Auxiliary Boundaries
,”
International Journal of Numerical Methods in Engineering
, Vol.
32
, No.
2
, pp.
313
325
.
13.
Timoshenko, S., and Woinowsky-Krieger, S., 1959, Theory of Plates and Shells, 2nd Edition, McGraw-Hill, New York, NY.
14.
Tsai
C.-J.
, and
Sanders
J. L.
,
1975
, “
Elliptical Cutouts in Cylindrical Shells
,”
ASME Journal of Applied Mechanics
, Vol.
42
, pp.
326
334
.
15.
Wilkinson, J. P., and Kalnins, A., 1965, “On Nonsymmetric Dynamic Problems of Elastic Spherical Shells,” ASME Journal of Applied Mechanics, Paper No. 65-APM-9.
16.
Wilkinson, J. P., and Kalnins, A., 1966, “Deformation of Open Spherical Shells Under Arbitrarily Located Concentrated Loads,” ASME Journal of Applied Mechanics, Paper No. 65-APM-24, pp. 305–312.
This content is only available via PDF.
You do not currently have access to this content.