Abstract

Material stiffness, a significant parameter of a contact interface, is investigated to improve the uniformity of the contact pressure. A contact interface material stiffness optimization design algorithm is developed based on the modified solid isotropic material with the penalization (SIMP) method. The uniformity of the contact pressure field is represented by its variance and is defined as the optimization objective. A node-to-node frictionless elastic contact theory is adopted to perform the contact analysis. The effectiveness of the interface material stiffness design for improving the uniformity of the contact surface is verified based on two contact cases. Because the relationship between the material stiffness and the hard-and-soft degree of a contact interface is always a positive correlation, the results in this paper could be extended so that the design of the contact interfaces’ hard-and-soft degree will improve the distributing uniformity of the contact surface.

References

References
1.
Collins
,
J. A.
,
Busby
,
H. R.
, and
Staab
,
G. H.
,
2009
,
Mechanical Design of Machine Elements and Machines: A Failure Prevention Perspective
,
John Wiley & Sons
,
New York
.
2.
Conry
,
T. F.
, and
Seireg
,
A.
,
1971
, “
A Mathematical Programming Method for Design of Elastic Bodies in Contact
,”
ASME J. Appl. Mech.
,
38
(
2
), pp.
387
392
. 10.1115/1.3408787
3.
Páczelt
,
I.
, and
Szabó
,
T.
,
1994
, “
Optimal Shape Design for Contact Problems
,”
Struct. Optim.
,
7
(
1–2
), pp.
66
75
. 10.1007/BF01742507
4.
Tada
,
Y.
, and
Nishihara
,
S.
,
1993
, “
Optimum Shape Design of Contact Surface With Finite Element Method
,”
Adv. Eng. Software
,
18
(
2
), pp.
75
85
. 10.1016/0965-9978(94)90001-9
5.
Li
,
W.
,
Li
,
Q.
,
Steven
,
G.
, and
Xie
,
Y.
,
2003
, “
An Evolutionary Shape Optimization Procedure for Contact Problems in Mechanical Designs
,”
Proc. Inst. Mech. Eng., Part C: J. Mech. Eng. Sci.
,
217
(
4
), pp.
435
446
. 10.1243/095440603321509711
6.
Li
,
W.
,
Li
,
Q.
,
Steven
,
G. P.
, and
Xie
,
Y.
,
2005
, “
An Evolutionary Shape Optimization for Elastic Contact Problems Subject to Multiple Load Cases
,”
Comput. Methods Appl. Mech. Eng.
,
194
(
30–33
), pp.
3394
3415
. 10.1016/j.cma.2004.12.024
7.
Ou
,
H.
,
Lu
,
B.
,
Cui
,
Z.
, and
Lin
,
C.
,
2013
, “
A Direct Shape Optimization Approach for Contact Problems With Boundary Stress Concentration
,”
J. Mech. Sci. Technol.
,
27
(
9
), pp.
2751
2759
. 10.1007/s12206-013-0721-7
8.
Pedersen
,
N. L.
,
2016
, “
On Optimization of Interference Fit Assembly
,”
Struct. Multidiscipl. Optim.
,
54
(
2
), pp.
349
359
. 10.1007/s00158-016-1419-0
9.
Zhu
,
L.
,
Hou
,
Y.
,
Bouzid
,
A.-H.
, and
Hong
,
J.
,
2018
, “
On the Design of Contact Member Surface Shape of Bolted Joints to Minimize Clamping Load Loss
,”
Paper No. V002T02A027
.
10.
Sigmund
,
O.
, and
Maute
,
K.
,
2013
, “
Topology Optimization Approaches: A Comparative Review
,”
Struct. Multidiscipl. Optim.
,
48
(
6
), pp.
1031
1055
. 10.1007/s00158-013-0978-6
11.
Strömberg
,
N.
, and
Klarbring
,
A.
,
2010
, “
Topology Optimization of Structures in Unilateral Contact
,”
Struct. Multidiscipl. Optim.
,
41
(
1
), pp.
57
64
. 10.1007/s00158-009-0407-z
12.
Myśliński
,
A.
,
2008
, “
Level Set Method for Optimization of Contact Problems
,”
Eng. Anal. Boundary Elem.
,
32
(
11
), pp.
986
994
. 10.1016/j.enganabound.2007.12.008
13.
Myśliński
,
A.
,
2015
, “
Piecewise Constant Level Set Method for Topology Optimization of Unilateral Contact Problems
,”
Adv. Eng. Software
,
80
, pp.
25
32
. 10.1016/j.advengsoft.2014.09.020
14.
Myśliński
,
A.
, and
Wróblewski
,
M.
,
2017
, “
Structural Optimization of Contact Problems Using Cahn–Hilliard Model
,”
Comput. Struct.
,
180
, pp.
52
59
. 10.1016/j.compstruc.2016.03.013
15.
Lawry
,
M.
, and
Maute
,
K.
,
2015
, “
Level Set Topology Optimization of Problems With Sliding Contact Interfaces
,”
Struct. Multidiscipl. Optim.
,
52
(
6
), pp.
1107
1119
. 10.1007/s00158-015-1301-5
16.
Zhang
,
W.
, and
Niu
,
C.
,
2018
, “
A Linear Relaxation Model for Shape Optimization of Constrained Contact Force Problem
,”
Comput. Struct.
,
200
, pp.
53
67
. 10.1016/j.compstruc.2018.02.005
17.
Niu
,
C.
,
Zhang
,
W.
, and
Gao
,
T.
,
2019
, “
Topology Optimization of Continuum Structures for the Uniformity of Contact Pressures
,”
Struct. Multidiscipl. Optim.
,
60
(
1
), pp.
185
210
. 10.1007/s00158-019-02208-8
18.
Xiang
,
Y.
,
Yu
,
D.
,
Cao
,
X.
,
Liu
,
Y.
, and
Yao
,
J.
,
2017
, “
Effects of Thermal Plasma Surface Hardening on Wear and Damage Properties of Rail Steel
,”
Proc. Inst. Mech. Eng., Part J: J. Eng. Tribol.
,
232
(
7
), pp.
787
796
. 10.1177/1350650117729073
19.
Athukorala
,
A. C.
,
De Pellegrin
,
D. V.
, and
Kourousis
,
K. I.
,
2017
, “
A Unified Material Model to Predict Ratcheting Response in Head-Hardened Rail Steel Due to Non-Uniform Hardness Distributions
,”
Tribol. Int.
,
111
, pp.
26
38
. 10.1016/j.triboint.2017.02.018
20.
Mukhtar
,
F.
,
Qayyum
,
F.
,
Anjum
,
Z.
, and
Shah
,
M.
,
2019
, “
Effect of Chrome Plating and Varying Hardness on the Fretting Fatigue Life of AISI D2 Components
,”
Wear
,
418–419
, pp.
215
225
. 10.1016/j.wear.2018.12.001
21.
Rahemi
,
R.
, and
Li
,
D.
,
2015
, “
Variation in Electron Work Function With Temperature and Its Effect on the Young’s Modulus of Metals
,”
Scr. Mater.
,
99
, pp.
41
44
. 10.1016/j.scriptamat.2014.11.022
22.
Wang
,
X.
,
Wang
,
J.
,
Wu
,
P.
, and
Zhang
,
H.
,
2004
, “
The Investigation of Internal Friction and Elastic Modulus in Surface Nanostructured Materials
,”
Mater. Sci. Eng. A
,
370
(
1–2
), pp.
158
162
. 10.1016/j.msea.2003.02.002
23.
Hofmann
,
F.
,
Nguyen-Manh
,
D.
,
Gilbert
,
M.
,
Beck
,
C.
,
Eliason
,
J.
,
Maznev
,
A.
,
Liu
,
W.
,
Armstrong
,
D.
,
Nelson
,
K.
, and
Dudarev
,
S.
,
2015
, “
Lattice Swelling and Modulus Change in a Helium-Implanted Tungsten Alloy: X-Ray Micro-Diffraction, Surface Acoustic Wave Measurements, and Multiscale Modelling
,”
Acta Mater.
,
89
, pp.
352
363
. 10.1016/j.actamat.2015.01.055
24.
Tromas
,
C.
,
Stinville
,
J.
,
Templier
,
C.
, and
Villechaise
,
P.
,
2012
, “
Hardness and Elastic Modulus Gradients in Plasma-Nitrided 316l Polycrystalline Stainless Steel Investigated by Nanoindentation Tomography
,”
Acta Mater.
,
60
(
5
), pp.
1965
1973
. 10.1016/j.actamat.2011.12.012
25.
Li
,
Q.
,
Hua
,
G.
,
Lu
,
H.
,
Yu
,
B.
, and
Li
,
D.
,
2018
, “
Understanding the Effect of Plastic Deformation on Elastic Modulus of Metals Based on a Percolation Model With Electron Work Function
,”
JOM
,
70
(
7
), pp.
1130
1135
. 10.1007/s11837-018-2891-3
26.
Sigmund
,
O.
,
2001
, “
A 99 Line Topology Optimization Code Written in Matlab
,”
Struct. Multidiscipl. Optim.
,
21
(
2
), pp.
120
127
. 10.1007/s001580050176
27.
Svanberg
,
K.
,
1987
, “
The Method of Moving Asymptotes—A New Method for Structural Optimization
,”
Int. J. Numer. Methods Eng.
,
24
(
2
), pp.
359
373
. 10.1002/nme.1620240207
28.
Stupkiewicz
,
S.
,
2001
, “
Extension of the Node-to-Segment Contact Element for Surface-Expansion-Dependent Contact Laws
,”
Int. J. Numer. Methods Eng.
,
50
(
3
), pp.
739
759
. 10.1002/1097-0207(20010130)50:3<739::AID-NME49>3.0.CO;2-G
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