The stress analysis of dovetail attachments presents some challenges. These challenges stem from the high stress gradients near the edges of contact and from the nonlinearities attending conforming contact with friction. To meet these challenges with a finite element analysis, refined grids are needed with mesh sizes near the edges of contact of the order of one percent of the local radii of curvature there. A submodeling procedure is described which can provide grids of sufficient resolution in return for moderate computational effort. This procedure furnishes peak stresses near contact edges which are converging on a sequence of three submodel grids, and which typically do converge to within about five percent.
1.
Hertz
, H.
, 1882
, “On the Contact of Elastic Solids
,” J. Reine Agnew. Math.
, 92
, pp. 156
–171
(in German: for an account in English, see Johnson, 5, Chapter 4).2.
Steuermann
, E.
, 1939
, “To Hertz’s Theory of Local Deformations in Compressed Elastic Bodies
,” C. R. (Dokl.) Acad. Sci. URSS
, 25
, pp. 359
–361
.3.
Sadowsky
, M. A.
, 1928
, “Two-Dimensional Problems of Elasticity Theory
,” Z. Angew. Math. Mech.
, 8
, pp. 107
–121
(in German).4.
Gladwell, G. M. L., 1980, Contact Problems in the Classical Theory of Elasticity, Sijthoff and Noordhoff International Publishers, Alphen aan den Rijn, The Netherlands.
5.
Johnson, K. L., 1985, Contact Mechanics, Cambridge University Press, Cambridge, UK.
6.
Kalker
, J. J.
, 1977
, “A Survey of the Mechanics of Contact Between Solid Bodies
,” Z. Angew. Math. Mech.
, 57
, pp. T3–T17
T3–T17
.7.
Meda, G., and Sinclair, G. B., 1996, “A Survey of Some Recent Papers in Contact Mechanics,” Report SM 96-7, Department of Mechanical Engineering, Carnegie Mellon University, Pittsburgh, PA.
8.
Boddington
, P. H. B.
, Chen
, K.
, and Ruiz
, C.
, 1985
, “The Numerical Analysis of Dovetail Joints
,” Comput. Struct.
, 20
, pp. 731
–735
.9.
ANSYS personnel, 1995, ANSYS User’s Manual, Revision 5.2, Vol. I, ANSYS Inc., Canonsburg, PA.
10.
Kenny
, B.
, Patterson
, E. A.
, Said
, M.
, and Aradhya
, K. S. S.
, 1991
, “Contact Stress Distributions in a Turbine Disk Dovetail Type Joint—A Comparison of Photoelastic and Finite Element Results
,” Strain
,27
, pp. 21
–24
.11.
Papanikos
, P.
, and Meguid
, S. A.
, 1994
, “Theoretical and Experimental Studies of Fretting-Initiated Fatigue Failure of Aeroengine Compressor Discs
,” Fatigue Fract. Eng. Mater. Struct.
, 17
, pp. 539
–550
.12.
Meguid
, S. A.
, Refaat
, M. H.
, and Papanikos
, P.
, 1996
, “Theoretical and Experimental Studies of Structural Integrity of Dovetail Joints in Aeroengine Discs
,” J. Mater. Process. Technol.
, 56
, pp. 668
–677
.13.
Papanikos
, P.
, Meguid
, S. A.
, and Stjepanovic
, Z.
, 1998
, “Three-Dimensional Nonlinear Finite Element Analysis of Dovetail Joints in Aeroengine Discs
,” Finite Elem. Anal. Design
, 29
, pp. 173
–186
.14.
Williams
, M. L.
, 1952
, “Stress Singularities Resulting from Various Boundary Conditions in Angular Corners of Plates in Extension
,” ASME J. Appl. Mech.
, 19
, pp. 526
–528
.15.
Gregory
, R. D.
, 1979
, “Green’s Functions, Bi-Linear Forms, and Completeness of the Eigenfunctions for the Elastostatic Strip and Wedge
,” J. Elast.
, 9
, pp. 283
–309
.16.
Persson, A., 1964, “On the Stress Distribution of Cylindrical Elastic Bodies in Contact,” Doctoral dissertation, Chalmers University of Technology, Go¨teborg, Sweden.
17.
Mossakovskii
, V. I.
, 1954
, “The Fundamental Mixed Problem of the Theory of Elasticity for a Half-Space With a Circular Line Separating the Boundary Conditions
,” Prikl. Mat. Mekh.
, 18
, pp. 187
–196
(in Russian).18.
Spence
, D. A.
, 1975
, “The Hertz Contact Problem with Finite Friction
,” J. Elast.
, 5
, pp. 297
–319
.19.
Dundurs
, J.
, and Comninou
, M.
, 1979
, “Some Consequences of the Inequality Conditions in Contact and Crack Problems
,” J. Elast.
, 9
, pp. 71
–82
.20.
Gere, J. M., and Timoshenko, S. P., 1991, Mechanics of Materials, 3rd SI ed., Chapman & Hall, London.
21.
Hamdy
, M. M.
, and Waterhouse
, R. B.
, 1981
, “The Fretting Wear of Ti-6A1-4V and Aged Inconel 718 at Elevated Temperatures
,” Wear
, 71
, pp. 237
–248
.22.
Sinclair, G. B., 1998, “Finite Element Analysis of Singular Elasticity Problems,” Proceedings of the Eighth International ANSYS Conference, Vol. 1, ANSYS Inc., Canonsburg, PA, pp. 225–236.
23.
Cormier
, N. G.
, Smallwood
, B. S.
, Sinclair
, G. B.
, and Meda
, G.
, 1999
, “Aggressive Submodelling of Stress Concentrations
,” Int. J. Numer. Methods Eng.
, 46
, pp. 889
–909
.24.
Strang, G., and Fix, G. J., 1973, An Analysis of the Finite Element Method, Prentice-Hall, Englewood Cliffs, NJ.
25.
Sinclair, G. B., 1998, “On the Logarithmic Stress Singularities Induced by the Use of Displacement Interpolants as Boundary Conditions in Submodelling,” Report SM 98-5, Department of Mechanical Engineering, Carnegie Mellon University, Pittsburgh, PA.
26.
Poritsky
, H.
, 1950
, “Stresses and Deflections of Cylindrical Bodies in Contact
,” ASME J. Appl. Mech.
, 17
, pp. 191
–196
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