Abstract
The paper deals with the plane elastostatic contact problem for an infinite elastic wedge of arbitrary angle. The medium is loaded through a frictionless rigid wedge of a given symmetric profile. Using the Mellin transform formulation the mixed boundary value problem is reduced to a singular integral equation with the contact stress as the unknown function. With the application of the results to the fracture of the medium in mind, the main emphasis in the study has been on the investigation of the singular nature of the stress state around the apex of the wedge and on the determination of the contact pressure.
Résumé
Dans cet essai le problème plan élastostatique de contact pour un coin élastique d'angle arbitraire est étudié. Le milieu est chargé à travers un coin rigide de profil symétrique sans friction. En utilisant la transformation de Mellin le problème de valeurs limites mixtes, est réduit à une équation intégrale singulière où l'effort de contact est la fonction inconnue. Avec l'application des résultats de la rupture du milieu, l'étude est concentrée principalement sur l'investigation de la nature singulière de l'état d'effort autour du sommet du coin et sur la détermination de la pression de contact.
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References
Neuber, H.,Theory of Notch Stresses, J. W. Edwards, Ann Arbor, Michigan 1946
Tranter, C. J., “The use of Mellin transform in finding the stress distribution in an infinite wedge”,Quart. J. of Mech. and Appl. Math., 1 (1948) p. 125
Karp, S. N. and Karal, F. C., “The elastic field behavior in the neighborhood of a crack of arbitrary angle”,Comm. on Pure and Appl. Math., 15 (1962) p. 413.
Williams, M. L., “Stress singularities resulting from various boundary conditions in angular corners of plates in extension”,Trans. ASME, 74 (1952) p. 625
Godfrey, D. E. R., “Ggneralized plane stress in an elastic wedge under isolated loads”,Quart. J. of Mech. and Appl. Math., 8 (1955) p. 226
Piechocki, W. and Zorski, H., “Thermoelastic problem for a wedge”,Bull. Acad. Pol. Sci. Ser. Sci. Tech. 7 (1959) p. 10
Piechocki, W., “The stresses in an infinite wedge due to a heat source”,Archwn. Mech. stosow 11 (1959) p. 93
Brahtz, J. H. A., “Stress distribution in wedges with arbitrary boundary forces”,Physics, Vol. 4 (1933) p. 56
Sternberg, E. and Koiter, W. T., “The wedge under concentrated couple: a paradox in the two-dimensional theory of elasticity“,J. Appl. Mech., Vol. 25, Trans. ASME (1958) p. 575
Lucas, R. A. and Erdogan, F., “Quasi-static transient thermal stresses in an infinite wedge”,Int. J. Solids Structures, 2 (1966) p. 205
Hein, V. L. and Erdogan, F., “Stress singularities in a two-material wedge”,Int. J. Fracture Mechanics, 7 (1971) p. 317.
Erdogan, F., “The interaction between inclusions and cracks”, inFracture Mechanies of Ceramics, Bradt, R. C. Hasselman, D. P. H. and Lange, F. F. ed. Vol. 1, p. 245, Plenum Press, New York 1973
Galin, L. A.,Contact Problems in the Theory of Elasticity, North Carolina State College, Raleigh, N.C. 1961
Muskhelishvili, N. I.,Singular Integral Equations, Wolters-Noordhoff, Groningen 1972
Erdogan, F. and Gupta, G. D., “On the numerical solution of singular integral equations”,Quart. Appl. Math., Vol. 30 (1972) p. 525
Erdogan, F., Gupta, G. D., and Cook, T. S., “Numerican solution of singular integral equations”, Chapter 7 inMethods of Analysis and Solutions of Crack Problems, G. C. Sih ed. Noordhoff International Publishing, Leyden 1973
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This work was supported by NSF under the Grant GK 42771X and by NASA under the Grant NGR 39-007-011.
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Erdogan, F., Arin, K. Fracture and contact problems for and elastic wedge. J Elasticity 6, 57–71 (1976). https://doi.org/10.1007/BF00135176
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DOI: https://doi.org/10.1007/BF00135176