Elastic spherical shells loaded under uniform pressure are subject to equal and opposite compressive probing forces at their poles to trigger and explore buckling. When the shells support external pressure, buckling is usually axisymmetric; the maximum probing force and the energy barrier the probe must overcome are determined. Applications of the probing forces under two different loading conditions, constant pressure or constant volume, are qualitatively different from one another and fully characterized. The effects of probe forces on both perfect shells and shells with axisymmetric dimple imperfections are studied. When the shells are subject to internal pressure, buckling occurs as a nonaxisymmetric bifurcation from the axisymmetric state in the shape of a mode with multiple circumferential waves concentrated in the vicinity of the probe. Exciting new experiments by others are briefly described.

References

References
1.
Thompson
,
J. M. T.
,
2015
, “
Advances in Shell Buckling: Theory and Experiments
,”
Int. J. Bifurcation Chaos
,
25
(
1
), p.
1530001
.
2.
Thompson
,
J. M. T.
, and
Sieber
,
J.
,
2016
, “
Shock-Sensitivity in Shell-Like Structures: With Simulations of Spherical Shell Buckling
,”
Int. J. Bifurcation Chaos
,
26
(
2
), p.
1630003
.
3.
Taffetani
,
M.
, and
Vella
,
D.
,
2017
, “
Regimes of Wrinkling in Pressurized Elastic Shells
,”
Philos. Trans. R. Soc. A
,
A375
, p.
20160330
.
4.
Hutchinson
,
J. W.
,
2016
, “
Buckling of Spherical Shells Revisited
,”
Proc. R. Soc. A
,
472
(
2195
), p.
20160577
.
5.
Hutchinson
,
J. W.
, and
Thompson
,
J. M. T.
,
2017
, “
Nonlinear Buckling Behavior of Spherical Shells: Barriers and Symmetry Breaking Dimples
,”
Philos. Trans. R. Soc. A
,
A375
, p.
20160154
.
6.
Sanders
,
J. L.
,
1963
, “
Nonlinear Shell Theories for Thin Shells
,”
Q. Appl. Math.
,
21
(
1
), pp.
21
36
.
7.
Koiter
,
W. T.
,
1966
, “
On the Nonlinear Theory of Thin Elastic Shells
,”
Proc. Kon. Ned. Ak. Wet.
,
B69
, pp.
1
54
.
8.
Koiter
,
W. T.
,
1967
, “
General Equations of Elastic Stability for Thin Shells
,”
Proceedings: Symposium on the Theory of Shells to Honor Lloyd Hamilton Donnell
,
D.
Muster
, ed.,
University of Houston
,
Houston, TX
, pp.
187
227
.
9.
Fitch
,
J. R.
,
1968
, “
The Buckling and Post-Buckling Behavior of Spherical Caps Under Concentrated Load
,”
Int. J. Solids Struct.
,
4
(
4
), pp.
421
446
.
10.
Evkin
,
A.
,
Kolesnikov
,
M.
, and
Prikazchikov
,
D. A.
,
2016
, “
Buckling of a Spherical Shell Under External Pressure and Inward Concentrated Load: Asymptotic Solution
,”
Math. Mech. Solids
,
1
, pp.
1
13
.
11.
Lee
,
A.
,
Marthelot
,
J.
,
Jimenez
,
F. L.
,
Hutchinson
,
J. W.
, and
Reis
,
P. M.
,
2016
, “
The Geometric Role of Precisely Engineered Imperfections on the Critical Buckling Load of Spherical Elastic Shells
,”
ASME J. Appl. Mech.
,
83
(
11
), p.
111005
.
12.
Jimenez
,
F. L.
,
Marthelot
,
J.
,
Lee
,
A.
,
Hutchinson
,
J. W.
, and
Reis
,
P. M.
,
2017
, “
Technical Brief: Knockdown Factor for the Buckling of Spherical Shells Containing Large-Amplitude Geometric Defects
,”
ASME J. Appl. Mech.
,
84
(
3
), p.
034501
.
13.
Vaziri
,
A.
, and
Mahadevan
,
L.
,
2008
, “
Localized and Extended Deformations of Elastic Shells
,”
Proc. Natl. Acad. Sci. U.S.A.
,
105
(
23
), pp.
7913
7918
.
14.
Vaziri
,
A.
,
2009
, “
Mechanics of Highly Deformed Elastic Shells
,”
Thin-Walled Struct.
,
47
(
6–7
), pp.
692
700
.
15.
Vella
,
D.
,
Ajdari
,
A.
,
Vaziri
,
A.
, and
Boudadoud
,
A.
,
2012
, “
The Indentation of Pressurized Elastic Shells: From Polymeric Capsules to Yeast Cells
,”
J. R. Soc. Interface
,
9
(
68
), pp.
448
455
.
16.
Nasto
,
A.
,
Ajdari
,
A.
,
Lazarus
,
A.
,
Vaziri
,
A.
, and
Reif
,
P. M.
,
2013
, “
Localization of Deformation in Thin Shells Under Indentation
,”
Soft Matter
,
9
(
29
), pp.
6796
6803
.
17.
Nasto
,
A.
, and
Reis
,
P. M.
,
2014
, “
Localized Structures in Indented Shells: A Numerical Investigation
,”
ASME J. Appl. Mech.
,
81
(
12
), p.
121008
.
18.
Vella
,
D.
,
Ebrahimi
,
H.
,
Vaziri
,
A.
, and
Davidovitch
,
B.
,
2015
, “
Wrinkling Reveals a New Isometry of Pressurized Elastic Shells
,”
Eur. Phys. Lett.
,
112
(
2
), p.
24007
.
19.
Thompson
,
J. M. T.
,
1979
, “
Stability Predictions Through a Succession of Folds
,”
Philos. Trans. R. Soc. London A
,
292
(
1386
), pp.
1
23
.
20.
Rubinstein
,
S. M.
, 2017, “
SMRLab
,” Harvard University, Cambridge, MA, accessed Apr. 4, 2017, http://projects.iq.harvard.edu/smrlab/
You do not currently have access to this content.