Abstract
In this paper, the stress compensation method (SCM) adopting an elastic-perfectly plastic (EPP) material is further extended to account for limited kinematic hardening (KH) material model based on the extended Melan's static shakedown theorem using a two-surface model defined by two hardening parameters, namely, the initial yield strength and the ultimate yield strength. Numerical analysis of a cylindrical pipe is performed to validate the outcomes of the extended SCM. The results agree well with ones from literature. Then the extended SCM is applied to the shakedown and limit analysis of KH piping elbows subjected to internal pressure and cyclic bending moments. Various loading combinations are investigated to generate the shakedown limit and the plastic limit load interaction curves. The effects of material hardening, elbow angle, and loading conditions on the shakedown limit and the plastic limit load interaction curves are presented and analyzed. The present method is incorporated in a commercial finite element simulation software and can be considered as a general computational tool for shakedown analysis of KH engineering structures. The obtained results provide a useful information for the structural design and integrity assessment of piping elbows.
Issue Section:
Design and Analysis
References
1.
Calladine
,
C. R.
, 1974
, “
Limit Analysis of Curved Tubes
,” J. Mech. Eng. Sci.
,
16
(2
), pp. 85
–87
.10.1243/JMES_JOUR_1974_016_016_022.
Chattopadhyay
,
J.
,
Nathani
,
D. K.
,
Dutta
,
B. K.
, and
Kushwaha
,
H. S.
, 2000
, “
Closed-Form Collapse Moment Equations of Elbows Under Combined Internal Pressure and In-Plane Bending Moment
,” ASME J. Pressure Vessel Technol.
,
122
(4
), pp. 431
–436
.10.1115/1.12859883.
Robertson
,
A.
,
Li
,
H. J.
, and
Mackenzie
,
D.
, 2005
, “
Plastic Collapse of Pipe Bends Under Combined Internal Pressure and In-Plane Bending
,” Int. J. Pressure Vessels Piping
,
82
(5
), pp. 407
–416
.10.1016/j.ijpvp.2004.09.0054.
Kim
,
Y. J.
, and
Oh
,
C. S.
, 2007
, “
Effects of Attached Straight Pipes on Finite Element Limit Analysis for Pipe Bends
,” Int. J. Pressure Vessels Piping
,
84
(3
), pp. 177
–184
.10.1016/j.ijpvp.2006.09.0175.
Li
,
S. J.
,
Zhou
,
C. Y.
,
Li
,
J.
,
Pan
,
X. M.
, and
He
,
X. H.
, 2017
, “
Effect of Bend Angle on Plastic Limit Loads of Pipe Bends Under Different Load Conditions
,” Int. J. Mech. Sci.
,
131–132
, pp. 572
–585
.10.1016/j.ijmecsci.2017.08.0196.
Tan
,
Y.
, and
Matzen
,
V.
, 2002
, “
Correlation of In-Plane Bending Test and FEA Results for Thin-Walled Elbows
,” Nucl. Eng. Des.
,
217
(1–2
), pp. 21
–39
.10.1016/S0029-5493(02)00137-17.
Chattopadhyay
,
J.
,
Dutta
,
B. K.
,
Kushwaha
,
H. S.
,
Roos
,
E.
, and
Herter
,
K.-H.
, 2004
, “
Load Bearing Capacity of Flawed Piping Components-Comparison of Experiment with Calculation
,” Int. J. Pressure Vessels Piping
,
81
(7
), pp. 599
–608
.10.1016/j.ijpvp.2004.04.0078.
Abdalla
,
H. F.
,
Younan
,
M. Y. A.
, and
Megahed
,
M. M.
, “
A Simplified Technique for Shakedown Load Determination of a 90 Degree Pipe Bend Subjected to Constant Internal Pressure and Cyclic In-Plane Bending
,” ASME
Paper No. PVP2005-71470.10.1115/PVP2005-714709.
Oh
,
C.-S.
,
Kim
,
Y.-J.
, and
Park
,
C.-Y.
, 2008
, “
Shakedown Limit Loads for Elbows Under Internal Pressure and Cyclic In-Plane Bending
,” Int. J. Pressure Vessels Piping
,
85
(6
), pp. 394
–405
.10.1016/j.ijpvp.2007.11.00910.
Korba
,
A. G.
,
Megahed
,
M. M.
,
Abdalla
,
H. F.
, and
Nassar
,
M. M.
, 2013
, “
Shakedown Analysis of 90-degree Mitred Pipe Bends
,” Eur. J. Mech. A/Solids
,
40
, pp. 158
–165
.10.1016/j.euromechsol.2013.01.00611.
Abdalla
,
H. F.
, 2014
, “
Shakedown Boundary Determination of a 90° Back-to-Back Pipe Bend Subjected to Steady Internal Pressures and Cyclic in-Plane Bending Moments
,” Int. J. Pressure Vessels Piping
,
116
, pp. 1
–9
.10.1016/j.ijpvp.2014.01.00112.
Abdalla
,
H. F.
,
Younan
,
M. Y. A.
, and
Megahed
,
M. M.
, 2011
, “
Shakedown Limit Load Determination for a Kinematically Hardening 90 eg Pipe Bend Subjected to Steady Internal Pressures and Cyclic Bending Moments
,” ASME J. Pressure Vessel Technol.
,
133
(5
), p. 051212. 10.1115/1.400347413.
Simon
,
J. W.
, 2013
, “
Direct Evaluation of the Limit States of Engineering Structures Exhibiting Limited, Nonlinear Kinematical Hardening
,” Int. J. Plasticity
,
42
, pp. 141
–167
.10.1016/j.ijplas.2012.10.00814.
Mackenzie
,
D.
,
Boyle
,
J. T.
, and
Hamilton
,
R.
, 2000
, “
Elastic Compensation Method for Limit and Shakedown Analysis: A Review
,” J. Strain Anal
,
35
(3
), pp. 171
–188
.10.1243/030932400151433215.
Chen
,
H. F.
, and
Ponter
,
A. R. S.
, 2001
, “
Shakedown and Limit Analyses for 3-D Structures Using the Linear Matching Method
,” Int. J. Pressure Vessels Piping
,
78
(6
), pp. 443
–451
.10.1016/S0308-0161(01)00052-716.
Peng
,
H.
,
Liu
,
Y.
, and
Chen
,
H.
, 2019
, “
A Numerical Formulation And algorithm for Limit and Shakedown Analysis of Large-Scale Elastoplastic Structures
,” Comput. Mech.
,
63
(1
), pp. 1
–22
.10.1007/s00466-018-1581-x17.
Peng
,
H.
,
Liu
,
Y.
,
Chen
,
H.
, and
Shen
,
J.
, 2018
, “
Shakedown Analysis of Engineering Structures Under Multiple Variable Mechanical and Thermal Loads Using the Stress Compensation Method
,” Int. J. Mech. Sci.
,
140
, pp. 361
–375
.10.1016/j.ijmecsci.2018.03.02018.
Peng
,
H.
,
Shen
,
J.
,
Liu
,
Y.
, and
Chen
,
H.
, 2020
, “
Limit and Shakedown Analysis of 45-Degree Piping Elbows Under Internal Pressure and in-Plane Bending
,” ASME J. Pressure Vessel Technol.
,
142
(2
), p. 021302. 10.1115/1.404572619.
Chen
,
H. F.
,
Ure
,
J.
,
Li
,
T. B.
,
Chen
,
W. H.
, and
Mackenzie
,
D.
, 2011
, “
Shakedown and Limit Analysis of 90 Degree Pipe Bends under Internal Pressure, Cyclic In-Plane Bending and Cyclic Thermal Loading
,” Int. J. Pressure Vessels Piping
,
88
(5–7
), pp. 213
–222
.10.1016/j.ijpvp.2011.05.00320.
Peng
,
H.
, and
Liu
,
Y.
, “
Shakedown and Limit Analysis of 45-Degree Piping Elbows Under Internal Pressure and Cyclic In-Plane Bending
,” ASME
Paper No. PVP2019-93263.10.1115/PVP2019-9326321.
Weichert
,
D.
, and
Gross-Weege
,
J.
, 1988
, “
The Numerical Assessment of Elastic-Plastic Sheets Under Variable Mechanical and Thermal Loads Using a Simplified Two-Surface Yield Condition
,” Int. J. Mech. Sci.
,
30
(10
), pp. 757
–767
.10.1016/0020-7403(88)90040-922.
Heitzer
,
M.
,
Pop
,
G.
, and
Staat
,
M.
, 2000
, “
Basis Reduction for the Shakedown Problem for Bounded Kinematic Hardening Material
,” J. Global Optim.
,
17
(1/4
), pp. 185
–200
.10.1023/A:100832102606323.
Pham
,
D. C.
, 2017
, “
Consistent Limited Kinematic Hardening Plasticity Theory and Path-Independent Shakedown Theorems
,” Int. J. Mech. Sci.
,
130
(Suppl. C
), pp. 11
–18
.10.1016/j.ijmecsci.2017.06.00524.
Ma
,
Z.
,
Chen
,
H.
,
Liu
,
Y.
, and
Xuan
,
F.-Z.
, 2020
, “
A Direct Approach to the Evaluation of Structural Shakedown Limit Considering Limited Kinematic Hardening and Non-Isothermal Effect
,” Eur. J. Mech. A/Solids
,
79
, p. 103877
.10.1016/j.euromechsol.2019.10387725.
Gokhfeld
,
D. A.
, and
Charniavsky
,
O. F.
, 1980
, Limit analysis of structures at thermal cycling
,
Alphen aan den Rijn
,
The Netherlands.
26.
Abaqus
, 2014
, “Dassault Systèms, Version 6.14,” Dassault Systèms, Vélizy-Villacoublay, France.Copyright © 2022 by ASME
You do not currently have access to this content.
