The three-dimensional, dynamic, elastic-plastic response of a right-angle bent cantilever pipe, with an initially uniform, circular cross section, subjected to out-of-plane loading is examined using finite element beam and shell models in ABAQUS. The large-deflection behavior involves both bending and torsional elastoplastic deformations of the pipe, phenomena which have not been previously studied in the context of the dynamic problem of pipe whip. Initially, neglecting ovalization and local collapse (kinking), the bent pipe is modeled as a beam, using spatial beam elements in ABAQUS. This enables the basic three-dimensional kinematic behavior of the pipe to be analyzed. A similar, but potentially more accurate, analysis was then performed using shell elements. It is shown that there is no significant difference in the global dynamic plastic response. However the ovalization of the pipe cross section and formation and movement of the plastic zones (hinges) can be captured by using shell elements. This provides data which could form the basis for examining local failures in the pipe run. Previously unpublished experimental results, obtained in an earlier study by some of the present authors, are compared with the simulated results. Good agreement is observed and it is concluded that a nonlinear dynamic model using finite elements provides a rigorous approach for estimating the hazard zone (HZ) and, also, for treating the kinematics of a whipping pipe for this complex three-dimensional situation.

References

References
1.
Baum
,
M. R.
, 1985,
“Experimental Study of Pipe Whip Resulting from Rupture of Gas Pressurised system,”
Proceedings of the Institution of Mechanical Engineering Conference on Pipe-work Design and Operation, paper C5/85.
2.
Baum
,
M. R.
, 1996,
“The Rupture of High Pressure Pipe Work: The Influence of Pipeline Geometry on In-Plane Pipe Whip,”
J. Loss Prevention and Process Industry
,
9
(
2
), pp.
147
159
.
3.
Reid
,
S. R.
,
Yu
,
T. X.
, and
Yang
,
J. L.
, 1998,
“An Elastic-Plastic Hardening-Softening Cantilever Beam Subjected to a Force Pulse at its Tip: A Model for Pipe Whip,”
Proc. Roy. Soc. London, Series A
,
454
, pp.
997
1029
.
4.
Reid
,
S. R.
,
Yu
,
T. X.
,
Yang
,
J. L.
, and
Corbett
,
G. G.
, 1996,
“Dynamic Elastic-Plastic Behaviour of Whipping Pipes: Experiments and Theoretical Model,”
Int. J. Impact Engng
,
18
(
7–8
), pp.
703
733
.
5.
Wang
,
B.
, 1991,
“Response of Two Dimensional Piping System During Pipe Whip,”
Ph.D. thesis,
University of Manchester Institute of Science and Technology
.
6.
Reid
,
S. R.
, and
Yang
,
J. L.
, 1998,
“Pipe Whip: In-Plane Whipping of Bent Cantilever Pipes,”
ASME J. Press. Vess. Techn.
,
120
, pp.
70
178
.
7.
Reid
,
S. R.
, and
Yang
,
J. L.
, 1998,
“Non-linear Dynamic Analysis of Cantilever Whipping Pipe,”
Proc. Institution of Mechanical Engineers, Part E: J. Process Mechanical Engineering
,
212
(
3
), pp.
133
149
.
8.
Baum
,
M. R.
, 1996,
“Pipe Whip with a Torsional Component,”
Internal Report, Nuclear Electric plc. No. ED/GEN/REP/0145/95.
9.
Johnson
,
W.
, 1970,
Impact Strength of Materials
,
Edward Arnold
,
London
.
10.
Hua
,
Y. L.
,
Yu
,
T. X.
, and
Johnson
,
W.
, 1985,
“The Plastic Hinge Position in a Bent Cantilever Struck Normal to its Plane by a Steady Jet Applied at its Tip,”
Int. J. Impact Engng
,
3
(
4
), pp.
233
241
.
11.
Reid
,
S. R.
,
Hua
,
Y. L.
, and
Yang
,
J. L.
, 1990,
“Development of Double Hinge Mechanisms in a Bent Cantilever Beams Subjected to an Out-of Plane Force Pulse,”
Int. J. Impact Engng
,
9
(
4
), pp.
485
502
.
12.
Reid
,
S. R.
,
Wang
,
B.
, and
Yu
,
T. X.
, 1995,
“Yield Mechanisms of a Bent Cantilever Beam Subjected to a Suddenly Applied Constant Out-of Plane Tip Force,”
Int. J. Impact Engng
,
16
(
1
), pp.
49
73
.
13.
Reid
,
S. R.
,
Wang
,
B.
, and
Hua
,
Y. L.
, 1995,
“Triple Plastic Hinge Mechanism for a Bent Cantilever Beam Subjected to an Out-of Plane Tip Force Pulse of Finite Duration,”
Int. J. Impact Engng
,
16
(
1
), pp.
75
93
.
14.
Simo
,
J. C.
, and
Vu-Quoc
,
L.
, 1988,
“On the Dynamics in Space of Rods Undergoing Large Motions—A Geometrically Exact Approach,”
Comp. Methods Appl. Mech. Engng
,
66
(
2
), pp.
125
161
.
15.
Hibbitt
,
Sorenssen
and
Karlson
, 1997, ABAQUS Theory Manual, ABAQUS Inc., Pawtucket, RI.
16.
Reid
,
S. R.
,
Roy
,
D.
, and
Aleyaasin
,
M.
, 2005,
“Pipe Whip—Recent Modelling Developments,”
Proceedings of the 6th International Conference on Shock and Impact Loads on Structures, 7–9 December, Perth, W. Australia, pp.
71
82
.
17.
Reid
,
S. R.
,
Wang
,
B.
, and
Aleyaasin
,
M.
, 2011,
“Structural Modelling and Testing of Failed High Energy Pipe Runs: 2D and 3D Pipe Whip,”
Int. J. Press. Vess. and Piping
,
88
, pp.
189
197
.
18.
Reid
,
S. R.
, and
Wang
,
B.
, 1995,
“Large Deflection Analysis of Whipping Pipes. I: Rigid Perfectly Plastic Model with Elastic Root Spring,”
ASCE Trans., J. Engineering Mechs.
,
121
, pp.
881
887
.
You do not currently have access to this content.