It is shown that the extended variational theorem of Mura et al. (1965, “Extended Theorems of Limit Analysis,” Q. Appl. Math., 23(2), pp. 171–179) can be applied to structures subjected to more than one load and be used to compute lower bound limit load multipliers. In particular, the multiplier proposed by Simha and Adibi-Asl (2011, “Lower Bound Limit Load Estimation Using a Linear Elastic Analysis,” ASME J. Pressure Vessel Technol., 134(2), p. 021207), which can be computed using an elastic stress field, is shown to be a lower bound. Furthermore, it is demonstrated that lower bound limit load for cracked structures may also be computed using a subvolume selection method. No iterations or elastic modulus adjustment are required. Several analytical and numerical examples that illustrate the procedure are presented.

References

References
1.
American Society of Mechanical Engineers
,
2007
,
Boiler and Pressure Vessel Code, Section III, Rules for Construction of Nuclear Facility Components.
2.
American Petroleum Institute
,
2007
,
ASME—API 579-1/ASME FFS-1 Fitness for Service, Washington, DC
.
3.
Seshadri
,
R.
, and
Fernando
,
C. P. D.
,
1992
, “
Limit Loads of Mechanical Components and Structures Using the Gloss R-Node Method
,”
ASME J. Pressure Vessel Technol.
,
114
(
2
), pp.
201
208
.10.1115/1.2929030
4.
Mackenzie
,
D.
,
Boyle
,
J. T.
, and
Hamilton
,
R.
,
2000
, “
The Elastic Compensation Method for Limit and Shakedown Analysis: A Review
,”
J. Strain Anal. Eng. Des.
,
35
(
3
), pp.
171
188
.10.1243/0309324001514332
5.
Belytschko
,
T.
,
Liu
,
W. K.
,
Moran
,
B.
, and
Elkhodary
,
K.
,
2013
,
Nonlinear Finite Elements for Continua and Structures
,
John Wiley and Sons
,
New York
.
6.
Fraldi
,
M.
,
Nunziante
,
L.
,
Gesualdo
,
A.
, and
Guarracino
,
F.
,
2010
, “
On the Bounding of Limit Load Multipliers for Combined Loading
,”
Proc. R. Soc. A
,
466
(2175), pp.
493
514
.10.1098/rspa.2009.0240
7.
Seshadri
,
R.
, and
Mangalaramanan
,
S. P.
,
1997
, “
Lower Bound Limit Loads Using Variational Concepts: The M(Alpha) Method
,”
Int. J. Pressure Vessels Piping
,
71
(
2
), pp.
93
106
.10.1016/S0308-0161(96)00071-3
8.
Mura
,
T.
,
Rimawi
,
W. H.
, and
Lee
,
S. L.
,
1965
, “
Extended Theorems of Limit Analysis
,”
Q. Appl. Math.
,
23
(
2
), pp.
171
179
.
9.
Reinhardt
,
W. D.
, and
Seshadri
,
R.
,
2003
, “
Limit Load Bounds for the M(Alpha) Multiplier
,”
ASME J. Pressure Vessel Technol.
,
125
(
1
), pp.
11
18
.10.1115/1.1526858
10.
Seshadri
,
R.
, and
Indermohan
,
H.
,
2004
, “
Lower Bound Limit Load Determination: The Mβ-Multiplier Method
,”
ASME J. Pressure Vessel Technol.
,
126
(
2
), pp.
237
240
.10.1115/1.1688780
11.
Seshadri
,
R.
, and
Hossain
,
M. M.
,
2009
, “
Simplified Limit Load Determination Using the Mα-Tangent Method
,”
ASME J. Pressure Vessel Technol.
,
131
(
2
), pp.
287
294
.10.1115/1.3067001
12.
Adibi-Asl
,
R.
, and
Seshadri
,
R.
,
2009
, “
Simplified Limit Load Estimation of Components With Cracks Using the Reference Two-Bar Structure
,”
ASME J. Pressure Vessel Technol.
,
131
(
1
), p.
011204
.10.1115/1.3012294
13.
Simha
,
C. H. M.
, and
Adibi-Asl
,
R.
,
2011
, “
Lower Bound Limit Load Estimation Using a Linear Elastic Analysis
,”
ASME J. Pressure Vessel Technol.
,
134
(
2
), p.
021207
.10.1115/1.4005057
14.
Pan
,
L.
, and
Seshadri
,
R. R.
,
2002
, “
Limit Load Estimation Using Plastic Flow Parameter in Repeated Elastic Finite Analyses
,”
ASME J. Pressure Vessel Technol.
,
124
(
4
), pp.
433
439
.10.1115/1.1499960
15.
Seshadri
,
R.
,
1991
, “
The Generalized Local Stress Strain (Gloss) Analysis—Theory and Applications
,”
ASME J. Pressure Vessel Technol.
,
113
(
2
), pp.
219
227
.10.1115/1.2928749
16.
Larson
,
L. D.
,
Stokey
,
W. F.
, and
Panarell
,
J. E.
,
1974
, “
Limit Analysis of a Thin-Walled Tube Under Internal-Pressure, Bending Moment, Axial Force, and Torsion
,”
ASME J. Appl. Mech.
,
41
(
3
), pp.
831
832
.10.1115/1.3423410
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