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Abstract

Compression of compressible, linearly elastic, annular disks by flat rigid platens is analyzed. Coulomb (Amonton) friction is assumed to act at the interfaces between the disk and the platens. Slip may occur in an outer annular region while the inner annular (bonded, stick) region of the disk does not slip. The critical radius (slip boundary) is of major interest. The governing equilibrium equations in terms of the deflections are satisfied exactly. Approximations are made in some of the boundary conditions and the transition (matching) conditions at the critical radius. Numerical results are presented for nearly incompressible disks. The effects of the radius ratio, aspect ratio, and Poisson's ratio of the disk, and of the coefficient of friction at the platens, on the critical radius, effective compression modulus, stresses, and radial deflection are investigated. Applications include structural (especially bridge) bearings, seismic-isolation devices, mounting blocks and bushings, gaskets, and sealing components.

References

1.
Plaut
,
R. H.
, and
Dillard
,
D. A.
,
2024
, “
Frictional Slippage of Elastomeric Disks Compressed Between Rigid Platens and Subjected to Torsion
,”
Int. J. Solids Struct.
,
295
(
1
), p.
112807
.
2.
Chalhoub
,
M. S.
, and
Kelly
,
J. M.
,
1987
, “
Reduction of the Stiffness of Rubber Bearings due to Compressibility
,” Rep. UCB/SEMM-86/06,
University of California
,
Berkeley, Berkeley, CA
.
3.
Billings
,
L. J.
, and
Shepherd
,
R.
,
1996
, “
The Mechanics of Elastomeric Seismic Isolation Bearings
,”
Eleventh World Conference on Earthquake Engineering
,
Acapulco, Mexico
,
June 23–28
.
4.
Constantinou
,
M. C.
,
Kartoum
,
A.
, and
Kelly
,
J. M.
,
1992
, “
Analysis of Compression of Hollow Circular Elastomeric Bearings
,”
Eng. Struct.
,
14
(
2
), pp.
103
111
.
5.
Kelly
,
J. M.
, and
Konstantinidis
,
D. A.
,
2011
,
Mechanics of Rubber Bearings for Seismic and Vibration Isolation
,
Wiley
,
Chichester, UK
.
6.
Van Engelen
,
N. C.
,
2021
, “
Evaluation of Design Equations for Critical Properties of Reinforced Elastomeric Bearings and Recommended Revisions
,”
J. Struct. Eng.
,
147
(
9
), p.
04021133
.
7.
Van Engelen
,
N. C.
, and
Kelly
,
J. M.
,
2015
, “
Correcting for the Influence of Bulk Compressibility on the Design Properties of Elastomeric Bearings
,”
J. Eng. Mech.
,
141
(
6
), p.
04014170
.
8.
Van Engelen
,
N. C.
,
Tait
,
M. J.
, and
Konstantinidis
,
D.
,
2016
, “
Development of Design Code Oriented Formulas for Elastomeric Bearings Including Bulk Compressibility and Reinforcement Extensibility
,”
J. Eng. Mech.
,
142
(
6
), p.
04016024
.
9.
Ling
,
Y.
,
1997
, “
Closure to “Compression of Bonded Annular Rubber Blocks” by Yun Ling
,”
J. Eng. Mech.
,
123
(
4
), pp.
406
407
.
10.
Horton
,
J. M.
, and
Tupholme
,
G. E.
,
2006
, “
Approximate Radial Stiffness of Rubber Bush Mountings
,”
Mater. Des.
,
27
(
3
), pp.
226
229
.
11.
Gent
,
A. N.
, and
Lindley
,
P. B.
,
1959
, “
The Compression of Bonded Rubber Blocks
,”
Proc. Inst. Mech. Eng.
,
173
(
3
), pp.
111
122
.
12.
Gent
,
A. N.
,
1994
, “
Compression of Rubber Blocks
,”
Rubber Chem. Technol.
,
67
(
3
), pp.
549
558
.
13.
Ling
,
Y.
,
Engel
,
P. A.
, and
Brodsky
,
W. L.
,
1995
, “
Compression of Bonded Annular Rubber Blocks
,”
J. Eng. Mech.
,
121
(
6
), pp.
661
666
.
14.
Ling
,
Y.
,
1996
, “
An Approximate Solution for the Compression of a Bonded Thin Annular Disk
,”
ASME J. Appl. Mech.
,
63
(
3
), pp.
780
787
.
15.
Constantinou
,
M. C.
,
1997
, “Discussion of “
Compression of Bonded Annular Rubber Blocks
”,”
J. Eng. Mech.
,
123
(
4
), pp.
405
406
.
16.
Yeoh
,
O. H.
,
Pinter
,
G. A.
, and
Banks
,
H. T.
,
2002
, “
Compression of Bonded Rubber Blocks
,”
Rubber Chem. Technol.
,
75
(
3
), pp.
549
562
.
17.
Pinarbasi
,
S.
,
Mengi
,
Y.
, and
Akyuz
,
U.
,
2008
, “
Compression of Solid and Annular Circular Discs Bonded to Rigid Surfaces
,”
Int. J. Solids Struct.
,
45
(
16
), pp.
4543
4561
.
18.
Tsai
,
H.-C.
,
2012
, “
Compression Behavior of Annular Elastic Layers Bonded Between Rigid Plates
,”
J. Mech.
,
28
(
4
), pp.
657
663
.
19.
Pinarbasi
,
S.
, and
Okay
,
F.
,
2011
, “
Compression of Hollow-Circular Fiber-Reinforced Rubber Bearings
,”
Struct. Eng. Mech.
,
38
(
3
), pp.
361
384
.
20.
Pinarbasi
,
S.
, and
Okay
,
F.
,
2016
, “Effects of a Central Hole on Compressive Behavior of Circular Fiber-Reinforced Rubber Bearings,”
Interaction Between Theory and Practice in Civil Engineering and Construction
,
R.
Komurly
,
A. P.
Gurgun
,
A.
Singh
, and
S.
Yazdani
, eds.,
ISEC Press
,
Fargo, ND
, pp.
223
228
.
21.
Horton
,
J. M.
,
Tupholme
,
G. E.
, and
Gover
,
M. J. C.
,
2003
, “
Axial Loading of Annular Bonded Rubber Blocks
,”
Rubber Chem. Technol.
,
76
(
5
), pp.
1194
1211
.
22.
Robert
,
M.
, and
Keer
,
L. M.
,
1987
, “
An Elastic Circular Cylinder with Displacement Prescribed at the Ends – Axially Symmetric Case
,”
Q. J. Mech. Appl. Math.
,
40
(
3
), pp.
339
363
.
23.
Schapery
,
R. A.
,
2018
, “
Elastomeric Bearing Sizing Analysis, Part 2: Flat and Cylindrical Bearings
,”
Int. J. Solids Struct.
,
152
(
1
), pp.
140
150
.
24.
Timoshenko
,
S.
, and
Goodier
,
J. N.
,
1951
,
Theory of Elasticity
, 2nd ed.,
McGraw-Hill
,
New York
.
25.
Qiao
,
S.
, and
Lu
,
N.
,
2015
, “
Analytical Solutions for Bonded Elastically Compressible Layers
,”
Int. J. Solids Struct.
,
58
(
1
), pp.
353
565
.
26.
Hattori
,
T.
,
Nakamura
,
M.
, and
Watanabe
,
T.
,
2003
, “
Simulation of Fretting-Fatigue Life by Using Stress-Singularity Parameters and Fracture Mechanics
,”
Tribol. Int.
,
36
(
2
), pp.
87
97
.
27.
Solecki
,
J. S.
, and
Swedlow
,
J. L.
,
1980
, “
Elastic Stress Analysis of Constrained Cylinders by a Special Finite Element Method
,”
Int. J. Solids Struct.
,
16
(
11
), pp.
959
968
.
28.
Ling
,
Y.
,
Engel
,
P. A.
, and
Geer
,
J. A.
,
1994
, “
The End Problem of Incompressible Elastic Cylinders
,”
ASME J. Appl. Mech.
,
61
(
1
), pp.
30
37
.
29.
Gent
,
A. N.
,
Discenzo
,
F. M.
, and
Suh
,
J. B.
,
2009
, “
Compression of Rubber Disks Between Frictional Surfaces
,”
Rubber Chem. Technol.
,
82
(
1
), pp.
1
17
.
30.
Movchan
,
A. B.
,
Rebrov
,
K. R.
, and
Rodin
,
G. J.
,
2021
, “
Axisymmetric Deformation of Compressible, Nearly Incompressible, and Incompressible Thin Layers Between Two Rigid Surfaces
,”
Int. J. Solids Struct.
,
214–215
(
1
), pp.
61
73
.
31.
Alzaidi
,
A. S. M.
,
Kaplunov
,
J.
,
Nikonov
,
A.
, and
Zupančič
,
B.
,
2024
, “
Transverse Compression of a Thin Elastic Disc
,”
Z. Angew. Math. Phys.
,
75
(
3
), p.
116
.
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