The creep phenomenon has enormous effect on the stress and displacement distribution in the structures. Redistribution of the stress field is one of these effects which is called stress relaxation. The importance of stress relaxation in the design of structures is increasing due to engineering applications especially in high temperature. However, this phenomenon has remained absent from the structural optimization studies. In the present study, the effect of stress relaxation due to high temperature creep is considered in topology optimization (TO). Internal element connectivity parameterization (I-ECP) method is utilized for performing TO. This method is shown to be effective to overcome numerical instabilities in nonlinear problems. Time-dependent adjoint sensitivity formulation is implemented for I-ECP including creep effect. Several benchmark problems are solved, and the optimum layouts obtained by linear and nonlinear methods are compared to show the efficiency of the proposed method and to show the effect of stress relaxation on the optimum layout.

References

References
1.
Doghri
,
I.
,
2013
,
Mechanics of Deformable Solids: Linear, Nonlinear, Analytical and Computational Aspects
,
Springer Science & Business Media
, Berlin.
2.
Kawamoto
,
A.
,
2009
, “
Stabilization of Geometrically Nonlinear Topology Optimization by the Levenberg–Marquardt Method
,”
Struct. Multidiscip. Optim.
,
37
(
4
), pp.
429
433
.
3.
Bendsøe
,
M. P.
, and
Kikuchi
,
N.
,
1988
, “
Generating Optimal Topologies in Structural Design Using a Homogenization Method
,”
Comput. Methods Appl. Mech. Eng.
,
71
(
2
), pp.
197
224
.
4.
Suzuki
,
K.
, and
Kikuchi
,
N.
,
1991
, “
A Homogenization Method for Shape and Topology Optimization
,”
Comput. Methods Appl. Mech. Eng.
,
93
(
3
), pp.
291
318
.
5.
Swan
,
C. C.
, and
Kosaka
,
I.
,
1997
, “
Voigt–Reuss Topology Optimization for Structures With Linear Elastic Material Behaviours
,”
Int. J. Numer. Methods Eng.
,
40
(
16
), pp.
3033
3057
.
6.
Bendsøe
,
M. P.
,
1989
, “
Optimal Shape Design as a Material Distribution Problem
,”
Struct. Optim.
,
1
(
4
), pp.
193
202
.
7.
Jung
,
D.
, and
Gea
,
H. C.
,
2004
, “
Topology Optimization of Nonlinear Structures
,”
Finite Elem. Anal. Des.
,
40
(
11
), pp.
1417
1427
.
8.
Buhl
,
T.
,
Pedersen
,
C. B.
, and
Sigmund
,
O.
,
2000
, “
Stiffness Design of Geometrically Nonlinear Structures Using Topology Optimization
,”
Struct. Multidiscip. Optim.
,
19
(
2
), pp.
93
104
.
9.
Lee
,
H.-A.
, and
Park
,
G.-J.
,
2012
, “
Topology Optimization for Structures With Nonlinear Behavior Using the Equivalent Static Loads Method
,”
ASME J. Mech. Des.
,
134
(
3
), p.
031004
.
10.
Bruns
,
T. E.
, and
Tortorelli
,
D. A.
,
2003
, “
An Element Removal and Reintroduction Strategy for the Topology Optimization of Structures and Compliant Mechanisms
,”
Int. J. Numer. Methods Eng.
,
57
(
10
), pp.
1413
1430
.
11.
Huang
,
X.
, and
Xie
,
Y.
,
2008
, “
Topology Optimization of Nonlinear Structures Under Displacement Loading
,”
Eng. Struct.
,
30
(
7
), pp.
2057
2068
.
12.
Ahmad
,
Z.
,
Sultan
,
T.
,
Zoppi
,
M.
,
Abid
,
M.
, and
Park
,
G. J.
,
2017
, “
Nonlinear Response Topology Optimization Using Equivalent Static Loads—Case Studies
,”
Eng. Optim.
,
49
(
2
), pp.
252
268
.
13.
Nakshatrala
,
P. B.
,
Tortorelli
,
D. A.
, and
Nakshatrala
,
K. B.
,
2013
, “
Nonlinear Structural Design Using Multiscale Topology Optimization—Part I: Static Formulation
,”
Comput. Methods Appl. Mech. Eng.
,
261–262
, pp.
167
176
.
14.
Xia
,
L.
, and
Breitkopf
,
P.
,
2014
, “
A Reduced Multiscale Model for Nonlinear Structural Topology Optimization
,”
Comput. Methods Appl. Mech. Eng.
,
280
, pp.
117
134
.
15.
Xia
,
L.
, and
Breitkopf
,
P.
,
2016
, “
Recent Advances on Topology Optimization of Multiscale Nonlinear Structures
,”
Arch. Comput. Methods Eng.
,
2
(
2
), pp.
227
249
.
16.
Luo
,
Q. T.
, and
Tong
,
L. Y.
,
2016
, “
An Algorithm for Eradicating the Effects of Void Elements on Structural Topology Optimization for Nonlinear Compliance
,”
Struct. Multidiscip. Optim.
,
53
(
4
), pp.
695
714
.
17.
Zhang
,
X.
,
Ramos
,
A. S.
, and
Paulino
,
G. H.
,
2017
, “
Material Nonlinear Topology Optimization Using the Ground Structure Method With a Discrete Filtering Scheme
,”
Struct. Multidiscip. Optim.
,
55
(
6
), pp.
2045
2072
.
18.
Osher
,
S. J.
, and
Santosa
,
F.
,
2001
, “
Level Set Methods for Optimization Problems Involving Geometry and Constraints—I: Frequencies of a Two-Density Inhomogeneous Drum
,”
J. Comput. Phys.
,
171
(
1
), pp.
272
288
.
19.
Allaire
,
G.
,
Jouve
,
F.
, and
Toader
,
A.-M.
,
2002
, “
A Level-Set Method for Shape Optimization
,”
C. R. Math.
,
334
(
12
), pp.
1125
1130
.
20.
Allaire
,
G.
,
Jouve
,
F.
, and
Toader
,
A.-M.
,
2004
, “
Structural Optimization Using Sensitivity Analysis and a Level-Set Method
,”
J. Comput. Phys.
,
194
(
1
), pp.
363
393
.
21.
Ha
,
S.-H.
, and
Cho
,
S.
,
2008
, “
Level Set Based Topological Shape Optimization of Geometrically Nonlinear Structures Using Unstructured Mesh
,”
Comput. Struct.
,
86
(
13–14
), pp.
1447
1455
.
22.
Yoon
,
G. H.
, and
Kim
,
Y. Y.
,
2005
, “
Element Connectivity Parameterization for Topology Optimization of Geometrically Nonlinear Structures
,”
Int. J. Solids Struct.
,
42
(
7
), pp.
1983
2009
.
23.
Yoon
,
G. H.
, and
Kim
,
Y. Y.
,
2007
, “
Topology Optimization of Material‐Nonlinear Continuum Structures by the Element Connectivity Parameterization
,”
Int. J. Numer. Methods Eng.
,
69
(
10
), pp.
2196
2218
.
24.
Yoon
,
G. H.
, and
Kim
,
Y. Y.
,
2005
, “
The Element Connectivity Parameterization Formulation for the Topology Design Optimization of Multiphysics Systems
,”
Int. J. Numer. Methods Eng.
,
64
(
12
), pp.
1649
1677
.
25.
Langelaar, M.
,
Yoon, G.
,
Kim, Y.
, and
Van Keulen, F.
, 2011, “
Topology Optimization of Planar Shape Memory Alloy Thermal Actuators Using Element Connectivity Parameterization
,”
Int. J. Numer. Methods Eng.
,
88
(9), pp. 817–840.
26.
Yoon
,
G. H.
,
Kim
,
Y. Y.
,
Langelaar
,
M.
, and
van Keulen
,
F.
,
2008
, “
Theoretical Aspects of the Internal Element Connectivity Parameterization Approach for Topology Optimization
,”
Int. J. Numer. Methods Eng.
,
76
(
6
), pp.
775
797
.
27.
Yoon
,
G. H.
,
Joung
,
Y. S.
, and
Kim
,
Y. Y.
,
2007
, “
Optimal Layout Design of Three-Dimensional Geometrically Non-Linear Structures Using the Element Connectivity Parameterization Method
,”
Int. J. Numer. Methods Eng.
,
69
(
6
), pp.
1278
1304
.
28.
Yoon
,
G. H.
,
2010
, “
Maximizing the Fundamental Eigenfrequency of Geometrically Nonlinear Structures by Topology Optimization Based on Element Connectivity Parameterization
,”
Comput. Struct.
,
88
(
1–2
), pp.
120
133
.
29.
van Dijk
,
N. P.
,
Yoon
,
G. H.
,
van Keulen
,
F.
, and
Langelaar
,
M.
,
2010
, “
A Level-Set Based Topology Optimization Using the Element Connectivity Parameterization Method
,”
Struct. Multidiscip. Optim.
,
42
(
2
), pp.
269
282
.
30.
Moon
,
S. J.
, and
Yoon
,
G. H.
,
2013
, “
A Newly Developed qp-Relaxation Method for Element Connectivity Parameterization to Achieve Stress-Based Topology Optimization for Geometrically Nonlinear Structures
,”
Comput. Methods Appl. Mech. Eng.
,
265
, pp.
226
241
.
31.
Richard, B. H.
, and
Eslami, M. R.
,
2008
,
Thermal Stresses: Advanced Theory and Applications
,
Springer
, Dordrecht, The Netherlands.
32.
Betten
,
J.
,
2008
,
Creep Mechanics
,
Springer Science & Business Media
, Berlin.
33.
Chen
,
W. J.
, and
Liu
,
S. T.
,
2014
, “
Topology Optimization of Microstructures of Viscoelastic Damping Materials for a Prescribed Shear Modulus
,”
Struct. Multidiscip. Optim.
,
50
(
2
), pp.
287
296
.
34.
Amir
,
O.
, and
Sigmund
,
O.
,
2013
, “
Reinforcement Layout Design for Concrete Structures Based on Continuum Damage and Truss Topology Optimization
,”
Struct. Multidiscip. Optim.
,
47
(
2
), pp.
157
174
.
35.
James
,
K. A.
, and
Waisman
,
H.
,
2014
, “
Failure Mitigation in Optimal Topology Design Using a Coupled Nonlinear Continuum Damage Model
,”
Comput. Methods Appl. Mech. Eng.
,
268
, pp.
614
631
.
36.
James
,
K. A.
, and
Waisman
,
H.
,
2015
, “
Topology Optimization of Viscoelastic Structures Using a Time-Dependent Adjoint Method
,”
Comput. Methods Appl. Mech. Eng.
,
285
, pp.
166
187
.
37.
Weertman
,
J.
,
1955
, “
Theory of Steady‐State Creep Based on Dislocation Climb
,”
J. Appl. Phys.
,
26
(
10
), pp.
1213
1217
.
38.
Penny
,
R. K.
, and
Marriott
,
D. L.
,
2012
,
Design for Creep
, Chapman & Hall, Boca Raton, FL.
39.
Tegart
,
W. M.
, and
Sherby
,
O. D.
,
1958
, “
Activation Energies for High Temperature Creep of Polycrystalline Zinc
,”
Philos. Mag.
,
3
(
35
), pp.
1287
1296
.
40.
Hayhurst
,
D.
,
1972
, “
Creep Rupture Under Multi-Axial States of Stress
,”
J. Mech. Phys. Solids
,
20
(
6
), pp.
381
382
.
41.
Bruggi
,
M.
,
2008
, “
On an Alternative Approach to Stress Constraints Relaxation in Topology Optimization
,”
Struct. Multidiscip. Optim.
,
36
(
2
), pp.
125
141
.
42.
Sigmund
,
O.
,
2001
, “
A 99 Line Topology Optimization Code Written in Matlab
,”
Struct. Multidiscip. Optim.
,
21
(
2
), pp.
120
127
.
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