The Reissner - Sagoci Problem for Layered Orthotropic Elastic Media
The problem of the torsional displacements of an elastic medium consisting of orthotropic layers, produced by a rigid circular disc attached to the surface is considered. The mixed boundary value problem is reduced to the Fredholm integral equation. The latter is solved by an iterative method, the solution being proved to converge to a unique continuous function.
References
E.REISSNER, H.SAGOCI, Forced torsional oscillations of elastic half-space, J.Appl. Phys., 15, 9, 652-654, 1944.
I.N.SNEDDON, A note on a boundary value problem of Reissner and Sagoci, J. Appl. Phys., 18, 1, 130-132, 1947.
W.D.COLLINS, The forced torsional oscillations of an elastic half-space and an elastic stratum, Proc. London, Math. Soc., 12, 3, 226-244, 1962.
G.M.L.GLADWELL, The forced torsional vibration of an elastic stratum, Int. J. Engng, Sci., 7, 1011-1024, 1969.
B.ROGOWSKI, Mixed boundary value problems of a transversely isotropic layer under torsion and various boundary conditions, Rozpr. Inżyn., 31, 3 , 293-315, 1983.
R.C.TANG, Torsion of an anisotropic layer, Fiber Sci. Technol., 12, 187-200, 1979.
M.K.KASSIR, The Reissner - Sagoci problem for non-homogeneous solid, Int. J. Engng, Sci., 8, 875-885, 1970.
A.Z.H. HASSAN, Reissner - Sagoci problem for a nonhomogeneous large thick plate, J. Mecanique, 18, 1, 197-209, 1980.
A.P.S.SELVADURAI, B.M.SINGH and J.VRBIK, A Reissner -Sagoci problem for a nonhomogeneous elastic solid, J.Elasticity, 16, 383-391, 1986.
B.NOBLE, Dual Bessel function integral equations, Proc. Camb. Phil. Soc., Math. Phys., 59, 351, 1963.
E.ERDELYI, Higher transcendental functions, Vol., 1, pp.27-35, Mc Graw-Hill, 1953.
B.ROGOWSKI, Indentation of a transversely isotropic layer by a truncated conical punch, Mech. Teoret. i Stos., 27, 2, 303-320, 1989.