The time-dependent progressive evolution of transverse displacements of an axially impacted, slender, geometrically imperfect, column is studied here. The analysis is concerned with evaluating the time-history associated with the evolution of the buckling response as a function of the initial geometric imperfection amplitude. The exact solution of the axial stress wave propagation is employed to study the physics of the buckling response with the nonuniform axial strain distribution varying in time and space. The responses of axially impacted columns are examined in light of past experimental results and associated numerical solutions. Results in the present paper are limited to elastic column behavior.

References

References
1.
Koning
,
C.
, and
Taub
,
J.
,
1934
, “
Impact Buckling of Thin Bars in the Elastic Range Hinged at Both Ends
,”
National Advisory Committee for Aeronautics—Technical Memorandums
.
2.
Taub
,
J.
,
1934
, “
Impact Buckling of Thin Bars in Elastic Range for Any End Condition
,”
National Advisory Committee for Aeronautics—Technical Memorandums, Report Review 749
.
3.
Meier
,
J.
,
1945
, “
On the Dynamics of Elastic Buckling
,”
J. Aeronaut. Sci.
,
12
(
4
),
pp.
433
440
.
4.
Hoff
,
N. J.
,
1951
, “
Dynamics of Buckling of Elastic Columns
,”
ASME J. Appl. Mech.
,
18
(
1
),
pp.
68
74
.
5.
Davidson
,
J. F.
,
1953
, “
Buckling of Struts Under Dynamic Loading
,”
J. Mech. Phys. Solids
,
2
(
1
),
pp.
54
66
.10.1016/0022-5096(53)90027-1
6.
Sevin
,
E.
,
1960
, “
On Elastic Bending of Columns Due to Dynamic Axial Forces Including Effects of Axial Inertia
,”
ASME J. Appl. Mech.
,
27
(
1
),
pp.
125
131
.10.1115/1.3643886
7.
Budiansky
,
B.
, and
Roth
,
R.S.
,
1962
, “
Axisymmetric Dynamic Buckling of Clamped Shallow Spherical Shells
,”
Collected Papers on Instability of Shell Structures
,
Technical Report NASA TN D-1510
.
8.
Hutchinson
,
J. W.
, and
Budiansky
,
B.
,
1966
, “
Dynamic Buckling Estimates
,”
AIAA J.
,
4
(
3
),
pp.
525
530
.10.2514/3.3468
9.
Hsu
,
C. S.
,
1967
, “
The Effects of Various Parameters on the Dynamic Stability of a Shallow Arch
.
ASME J. Appl. Mech.
,
34
(
2
),
pp.
349
356
.10.1115/1.3607689
10.
Bolotin
,
V. V.
,
1964
,
The Dynamic Stability of Elastic Systems
,
Holden-Day
,
London
.
11.
Ari-Gur
,
J.
,
Weller
,
T.
, and
Singer
,
J.
,
1982
, “
Experimental and Theoretical Studies of Columns Under Axial Impact
,”
Int. J. Solids Struct.
,
18
(
7
),
pp.
619
641
.10.1016/0020-7683(82)90044-0
12.
Simitses
,
G. J.
,
1989
,
Dynamic Stability of Suddenly Loaded Structures
Springer-Verlag
,
New York
.
13.
Kenny
,
S.
,
Taheri
,
F.
, and
Pegg
,
N.
,
2000
, “
Dynamic Elastic Buckling of a Slender Beam With Geometric Imperfections Subject to an Axial Impulse
,”
Finite Elem. Anal. Des.
,
35
(
3
)
pp.
,
227
246
.10.1016/S0168-874X(99)00067-0
14.
Wang
,
A.
, and
Tian
,
W.
,
2002
, “
Twin-Characteristic-Parameter Solution for Dynamic Buckling of Columns Under Elastic Compression Wave
,”
Int. J. Solids Struct.
,
39
(
4
)
pp.
861
877
.10.1016/S0020-7683(01)00245-1
15.
Gladden
,
J. R.
,
Handzy
,
N. Z.
,
Belmonte
,
A.
, and
Villermaux
,
E.
2005
, “
Dynamic Buckling and Fragmentation in Brittle Rods
,”
Phys. Rev. Lett.
,
94
(
3
), p.
035503
.10.1103/PhysRevLett.94.035503
16.
Vaughn
,
D. G.
, and
Hutchinson
,
J. W.
,
2006
, “
Bucklewaves
,”
Eur., J. Mech.-A Solids.
,
25
(
1
),
pp.
1
12
.10.1016/j.euromechsol.2005.09.003
17.
Ji
,
W.
, and
Waas
,
A. M.
,
2010
, “
Fragmentation of an Axially Impacted Slender Rod
,”
Europhys. Lett.
,
89
(
4
), p.
46003
.10.1209/0295-5075/89/46003
18.
Ji
,
W.
, and
Waas
,
A. M.
,
2008
, “
Dynamic Bifurcation Buckling of an Impacted Column
,”
Int. J. Eng. Sci.
,
46
(
10
)
pp.
958
967
.10.1016/j.ijengsci.2008.04.003
You do not currently have access to this content.