A mathematical model of axisymmetric elastic/plastic perforated circular plate bending and stretching is developed which accounts for through thickness yielding, through thickness variations in perforation geometry, elastic outer edge restraint, and moderately large deflections. Selected numerical solutions of the resulting differential equations are presented graphically and used to illustrate interesting trends.

1.
Osweiller
,
F.
,
1989
, “
Evolution and Synthesis of the Effective Elastic Constants Concept for the Design of Tubesheets
,”
ASME J. Pressure Vessel Technol.
,
111
, pp.
209
217
.
2.
Ukadgaonker
,
V. G.
,
Kale
,
P. A.
,
Agnihotri
,
N. A.
, and
Babu
,
S.
,
1996
, “
Review of Analysis of Tubesheets
,”
Int. J. Pressure Vessels Piping
,
67
, pp.
279
297
.
3.
O’Donnell
,
W. J.
, and
Langer
,
B. F.
,
1962
, “
Design of Perforated Plates
,”
ASME J. Eng. Ind.
,
84
, pp.
307
320
.
4.
O’Donnell
,
W. J.
,
1967
, “
A Study of Perforated Plates with Square Penetration Patterns
,”
Weld. Res. Counc. Bull.
,
124
, pp.
1
13
.
5.
Slot
,
T.
, and
O’Donnell
,
W. J.
,
1971
, “
Effective Elastic Constants for Thick Perforated Plates with Square and Triangular Penetration Patterns
,”
ASME J. Eng. Ind.
,
93
, pp.
935
942
.
6.
O’Donnell
,
W. J.
,
1973
, “
Effective Elastic Constants for the Bending of Thin Perforated Plates with Triangular and Square Penetration Patterns
,”
ASME J. Eng. Ind.
,
95
, pp.
121
128
.
7.
Webb
,
D. C.
,
Kormi
,
K.
, and
Al-Hassani
,
S. T. S.
,
1995
, “
Use of FEM in Performance Assessment of Perforated Plates Subjected to General Loading Conditions
,”
Int. J. Pressure Vessels Piping
,
64
, pp.
137
152
.
8.
Baik
,
S. C.
,
Oh
,
K. H.
, and
Lee
,
D. N.
,
1996
, “
Analysis of the Deformation of a Perforated Sheet Under Uniaxial Tension
,”
J. Mater. Process. Technol.
,
58
, pp.
139
144
.
9.
O’Donnell
,
W. J.
, and
Porowski
,
J.
,
1973
, “
Yield Surfaces for Perforated Materials
,”
ASME J. Appl. Mech.
,
40
, pp.
263
270
.
10.
Porowski
,
J.
, and
O’Donnell
,
W. J.
,
1974
, “
Effective Plastic Constants for Perforated Materials
,”
ASME J. Pressure Vessel Technol.
,
96
, pp.
234
241
.
11.
Slot
,
T.
, and
Branca
,
T. R.
,
1974
, “
On the Determination of Effective Elastic-Plastic Properties for the Equivalent Solid Plate Analysis of Tube Sheets
,”
ASME J. Pressure Vessel Technol.
,
96
, pp.
220
227
.
12.
Porowski
,
J.
, and
O’Donnell
,
W. J.
,
1975
, “
Plastic Strength of Perforated Plates with Square Penetration Patterns
,”
ASME J. Pressure Vessel Technol.
,
97
, pp.
146
154
.
13.
Koing
,
M.
,
1988
, “
Yield Surface for Perforated Plates
,”
Engr. Comp.
,
5
, pp.
224
230
.
14.
Rogalska
,
E.
,
Kakol
,
W.
,
Guerlement
,
G.
, and
Lamblin
,
D. J.
,
1997
, “
Limit Load Analysis of Perforated Disks With Square Penetration Pattern
,”
ASME J. Pressure Vessel Technol.
,
119
, pp.
122
126
.
15.
Baik
,
S. C.
,
Han
,
H. N.
,
Lee
,
S. H.
,
Oh
,
K. H.
, and
Lee
,
D. N.
,
1997
, “
Plastic Behavior of Perforated Sheets Under Biaxial Stress State
,”
Int. J. Mech. Sci.
,
39
, pp.
781
793
.
16.
Reinhardt
,
W. D.
, and
Mangalaramanan
,
S. P.
,
2001
, “
Efficient Tubesheet Design Using Repeated Elastic Limit Analysis Technique
,”
ASME J. Pressure Vessel Technol.
,
123
, pp.
197
202
.
17.
Tekinalp, B., 1955, “Elastic, Plastic Bending of a Simply Supported Circular Plate Under a Uniformly Distributed Load,” Brown University DAM Report CH-6.
18.
Tekinalp
,
B.
,
1956
, “
Elastic-Plastic Bending of a Built-in Circular Plate Under a Uniformly Distributed Load
,”
J. Mech. Phys. Solids
,
5
, pp.
135
142
.
19.
Hodge, P. G., 1958, The Mathematical Theory of Plasticity, Wiley, New York.
20.
Haythornthwaite
,
R. M.
,
1954
, “
The Deflection of Plates in the Elastic-Plastic Range
,”
Proc. U.S. Nat. Congress Appl. Mech.
,
2
, pp.
521
526
.
21.
French
,
F. W.
,
1964
, “
Elastic-Plastic Analysis of Centrally Clamped Annular Plates Under Uniform Loads
,”
J. Franklin Inst.
,
277
, pp.
575
592
.
22.
Brady, E. F., 1963, “The Elastic-Plastic Bending of an Elastically-Restrained Circular Plate Under a Uniformly Distributed Load,” Ph.D. dissertation, University of Pittsburgh, Pittsburgh, PA.
23.
Srivastava
,
N. K.
, and
Sherbourne
,
A. N.
,
1971
, “
Elastic Plastic Bending of Circular Plates
,”
ASCE J. Eng. Mech. Div.
,
97
, pp.
13
31
.
24.
Popov
,
E.
,
Bakht
,
M.
, and
Yaghmai
,
S.
,
1967
, “
Bending of Circular Plates of Hardening Material
,”
Int. J. Solids Struct.
,
3
, pp.
975
988
.
25.
Ohashi
,
Y.
, and
Murakami
,
S.
,
1964
, “
On the Elasto-Plastic Bending of a Clamped Circular Plate Under a Partial Circular Uniform Load
,”
Bull. JSME
,
7
, pp.
491
498
.
26.
Ohashi
,
Y.
, and
Murakami
,
S.
,
1966
, “
The Elasto-Plastic Bending of a Clamped Thin Circular Plate
,”
Proc. Int. Cong. Appl. Mech.
,
11
, pp.
212
223
.
27.
Turvey
,
G. J.
, and
Salehi
,
M.
,
1991
, “
Computer Generated Elasto-Plastic Design Data for Pressure Loaded Circular Plates
,”
Comput. Struct.
,
41
, pp.
1329
1340
.
28.
Timoshenko, S., and Woinowsky-Krieger, S., 1959, Theory of Plates and Shells, McGraw-Hill, New York.
29.
Budiansky
,
B.
,
1959
, “
A Reassessment of Deformation Theories of Plasticity
,”
ASME J. Appl. Mech.
,
26
, pp.
259
264
.
30.
Goldberg
,
J. E.
, and
Richard
,
R. M.
,
1963
, “
Analysis of Nonlinear Structures
,”
J. Struct. Div. ASCE
89
, pp.
333
351
.
31.
Richard
,
R. M.
, and
Abbott
,
B. J.
,
1975
, “
Versatile Elastic-Plastic Stress-Strain Formula
,”
ASCE J. Eng. Mech. Div.
,
101
, pp.
511
515
.
32.
Blottner
,
F. J.
,
1970
, “
Finite Difference Methods of Solution of the Boundary Layer Equations
,”
AIAA J.
,
8
, pp.
193
205
.
33.
Wu
,
D.
,
Peddieson
,
J.
, and
Buchanan
,
G. R.
,
2002
, “
Elastic Compensation Using Deformation Plasticity Models
,”
Dev. Theor. Appl. Mech.
,
21
, pp.
1
9
.
You do not currently have access to this content.