The paper reports on recent progress in numerical shakedown and limit analysis based on Melan's lower bound shakedown theorem. After explaining the theoretical foundations of their approach, the authors describe in detail the numerical scheme, in particular the underlying optimization via interior point methods. Numerous examples mostly related to pressure vessel technology are presented, illustrating the potential of the method.

References

1.
Melan
,
E.
,
1938
, “
Zur Plastizität des räumlichen Kontinuums
,”
Ing. Arch.
,
9
(
2
), pp.
116
126
.10.1007/BF02084409
2.
Weichert
,
D.
,
Hachemi
,
A.
, and
Schwabe
,
F.
,
1999
, “
Shakedown Analysis of Composites
,”
Mech. Res. Commun.
,
26
(
3
), pp.
309
318
.10.1016/S0093-6413(99)00029-4
3.
Weichert
,
D.
, and
Hachemi
,
A.
,
2010
, “
Progress in the Application of Lower Bound Direct Methods in Structural Design
,”
ASME Int. J. Appl. Mech.
,
2
(
1
), pp.
145
160
.10.1142/S175882511000041X
4.
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)90040-9
5.
Halphen
,
B.
, and
Quoc Son
,
N.
,
1975
, “
Sur les matériaux Standards généralisés
,”
J. Méc.
,
14
(
1
), pp.
39
63
.
6.
Chen
,
M.
,
Hachemi
,
A.
, and
Weichert
,
D.
,
2013
, “
Shakedown and Optimization Analysis of Periodic Composite
,”
Limit State of Materials and Structures: Direct Methods
, Vol.
2
,
G.
de Saxcé
,
A.
Oueslati
,
E.
Charkaluk
, and
J.-B.
Tritsh
, eds.,
Springer
,
New York
, pp.
45
69
.10.1007/978-94-007-5425-6_3
7.
Akoa
,
F.
,
Hachemi
,
A.
,
An
,
L. T. H.
,
Mouhtamid
,
S.
, and
Tao
,
P. D.
,
2007
, “
Application of Lower Bound Direct Method to Engineering Structures
,”
J. Global Optim.
,
37
(
4
), pp.
609
630
.10.1007/s10898-006-9069-1
8.
Simon
,
J.-W.
, and
Weichert
,
D.
,
2011
, “
Numerical Lower Bound Shakedown Analysis of Engineering Structures
,”
Comput. Methods Appl. Mech. Eng.
,
200
(
41–44
), pp.
2828
2839
.10.1016/j.cma.2011.05.006
9.
Simon
,
J.-W.
,
Kreimeier
,
M.
, and
Weichert
,
D.
,
2013
, “
A Selective Strategy for Shakedown Analysis of Engineering Structures
,”
Int. J. Numer. Methods Eng.
,
94
(
11
), pp.
985
1014
.10.1002/nme.4476
10.
Simon
,
J.-W.
, and
Weichert
,
D.
,
2013
, “
Interior-Point Method for Lower Bound Shakedown Analysis of von Mises-Type Materials
,”
Limit States of Materials and Structures—Direct Methods
, Vol.
2
,
G.
de Saxce
,
E.
Charkaluk
,
A.
Oueslati
, and
J.-B.
Tritsch
, eds.,
Springer
,
New York
, pp.
103
128
.10.1007/978-94-007-5425-6_6
11.
Simon
,
J.-W.
, and
Weichert
,
D.
,
2012
, “
Shakedown Analysis of Engineering Structures With Limited Kinematical Hardening
,”
Int. J. Solids Struct.
,
49
(
4
), pp.
2177
2186
.10.1016/j.ijsolstr.2012.04.039
12.
Simon
,
J.-W.
,
2013
, “
Direct Evaluation of the Limit States of Engineering Structures exhibiting Limited, Nonlinear Kinematical Hardening
,”
Int. J. Plast.
,
42
, pp.
141
167
.10.1016/j.ijplas.2012.10.008
13.
Simon
,
J.-W.
,
2014
, “
Shakedown Analysis of Kinematically Hardening Structures in n-Dimensional Loading Spaces
,”
Direct Methods for Limit States in Structures and Materials
,
K. V.
Spiliopoulos
and
D.
Weichert
, eds.,
Springer
,
New York
, pp.
57
77
.10.1007/978-94-007-6827-7_3
14.
Wagner
,
W.
,
1991
,
Festigkeitsberechnungen im Apparate- und Rohrleitungsbau
,
Vogel Buchverlag
,
Würzburg, Germany
.
15.
Cloud
,
R. L.
, and
Rodabaugh
,
E. C.
,
1968
, “
Approximate Analysis of the Plastic Limit Pressures of Nozzles in Cylindrical Shells
,”
J. Eng. Power
,
90
(
2
), pp.
171
176
.
16.
Mouhtamid
,
S.
,
2007
, “
Anwendung Direkter Methoden zur industriellen Berechnung von Grenzlasten Mechanischer Komponenten
,” Ph.D. thesis, RWTH Aachen University, Aachen, Germany.
17.
Fuschi
,
P.
, and
Polizzotto
,
C.
,
1995
, “
The Shakedown Load Boundary of an Elastic Perfectly Plastic Structure
,”
Meccanica
,
30
(
2
), pp.
155
174
.10.1007/BF00990454
18.
Schwabe
,
F.
,
2000
, “
Einspieluntersuchungen von Verbundwerkstoffen mit periodischer Mikrostruktur
,” Ph.D. thesis, RWTH Aachen University, Aachen, Germany.
19.
Simon
,
J.-W.
,
Chen
,
G.
, and
Weichert
,
D.
,
2014
, “
Shakedown Analysis of Nozzles in the Knuckle Region of Torispherical Heads Under Multiple Thermo-Mechanical Loadings
,”
Int. J. Pressure Vessels Piping
,
116
, pp.
47
55
.10.1016/j.ijpvp.2014.01.004
You do not currently have access to this content.