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.
Issue Section:
Technical Papers
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
.Copyright © 2003
by ASME
You do not currently have access to this content.