Abstract
The present paper examines the elastostatic problem related to the axisymmetric rotation of a rigid circular disc bonded to a non-homogeneous half-space containing a penny-shaped crack. The shear modulus of the half-space is assumed to vary with depth according to the relation μ(z) = μ1(z + c)α, c > 0 and μ1, α are constants. Using Hankel transforms, the solution of the problem is reduced to integral equations and finally to simultaneous Fredholm integral equations of the second kind. By solving numerically the simultaneous Fredholm integral equations, results are obtained which are used to estimate the stress intensity factor at the crack tip and the torque required to rotate the disc through an angle ω0.
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References
E. Reissner, Freie und erzwungene Torsionsschwingungen des elastischen Halbraumes. Ing.-Arch. 8 (1937) 229–245.
E. Reissner and H.F. Sagoci, Forced torsional oscillations of an elastic half-space. I, J. Appl. Phys. 15 (1944) 652–654.
H.F. Sagoci, Forced torsional oscillations of an elastic half-space, II. J. Appl. Phys. 15 (1944) 655–662.
I.N. Sneddon, Note on a boundary value problem of Reissner and Sagoci. J. Appl. Phys. 18 (1947) 130–132.
I.N. Sneddon, The Reissner-Sagoci problem. Proc. Glasgow Math. Assoc. 7 (1966) 136–144.
R.S. Dhaliwal, B.M. Singh, and I.N. Sneddon, A problem of Reissner-Sagoci type for an elastic cylinder embedded in an elastic half-space. Int. J. Engng. Sci. 17 (1979) 139–144, 1306.
B.M. Singh, T.B. Moodie, and J.B. Haddow, Torsion by an annular disk of an infinite cylinder embedded in an elastic half-space. Utilitas Math 18 (1980) 97–113.
M.K. Kassir, The Reissner-Sagoci problem for a non-homogeneous solid. Int. J. Engng. Sci. 8 (1970) 875–885.
M.F. Chuaprasert and M.K. Kassir, Torsion of a non-homogeneous solid. Journal of the Engineering Mechanics Division 99 (1973) 703–713.
R.S. Dhaliwal and B.M. Singh, Torsion by a circular die of a non-homogeneous elastic layer bonded to a non-homogeneous half-space. Int. J. Engng. Sci. 16 (1978) 649–658.
A.P.S. Selvadurai, B.M. Singh and J. Vrbik, A Reissner-Sagoci problem for a non-homogeneous elastic solid. J. Elasticity 16 (1986) 383–391.
G.M.L. Gladwell, Contact Problems in the Classical Theory of Elasticity, Sijthoff & Noordhoff, Alphen aan den Rijn (1980).
E.T. Copson, On certain dual integral equations. Proc. Glasgow Math. Assoc., 5 (1961) 19–24.
G.N. Watson, The treatise on the theory of Bessel functions. Cambridge Univ. Press (1958).
I.N. Sneddon, Mixed Boundary Value Problems in Potential Theory. North-Holland Publishing Company, Amsterdam (1966).
R.D. Low, on the torsion of elastic half-spaces with embedded penny-shaped flaws. Trans. ASME Ser. E. J. Appl. Mech. 39 (1972) 786–790.
M.K. Kassir and G.C. Sih, Three-dimensional crack problems. Mechanics of Fracture. Vol. 2, Noordhoff International Publishing, Leyden (1975).
I.S. Gradshteyn and I.M. Ryzhik, Tables of Integrals, Series and Products. Academic Press, New York, (1980).
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Danyluk, H.T., Singh, B.M. & Vrbik, J. The Reissner-Sagoci problem for a non-homogeneous half-space with a penny-shaped crack. J Eng Math 29, 437–449 (1995). https://doi.org/10.1007/BF00043977
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DOI: https://doi.org/10.1007/BF00043977