Abstract
The present paper examines the elastostatic problem related to the axisymmetric rotation of a rigid circular punch which is bonded to the surface of a non-homogeneous isotropic elastic halfspace. The non-homogeneity corresponds to an axial variation of the linear elastic shear modulus according to the exponential form % MathType!MTEF!2!1!+-% feaafiart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaam4raiaacI% cacaWG6bGaaiykaiabg2da9iaadEeadaWgaaWcbaGaaGymaaqabaGc% cqGHRaWkcaWGhbWaaSbaaSqaaiaaikdaaeqaaOGaaeiiaiaabwgada% ahaaWcbeqaaiaab2cacqaH+oaEcaqG6baaaaaa!439C!\[G(z) = G_1 + G_2 {\text{ e}}^{{\text{ - }}\xi {\text{z}}} \]. A Hankel transform development of the governing equations yields a set of dual integral equations which in turn can be reduced to a Fredholm integral equation of the second kind. A numerical evaluation of this integral equation yields results which can be used to estimate the torque-twist relationship for the circular punch.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
E. Reissner and H. Sagoci, Forced torsional oscillations of an elastic halfspace, J. Appl. Phys., 15, 652–654 (1944).
I.N. Sneddon, A note on a boundary value problem of Reissner and Sagoci, J. Appl. Phys., 18, 130–132 (1947).
I.N. Sneddon, The Reissner-Sagoci problem, Proc. Glas. Math. Assoc., 7, 136–144 (1966).
N.A. Rostovtsev, On the problem of torsion of an elastic halfspace, Prikl. Math. Mekh., 19, 55–60 (1955).
Ia.S. Uflyand, Torsion of an elastic layer, Dokl. Akad. Nauk. S.S.S.R., 129, 997–999 (1959).
W.D. Collins, The forced torsional oscillations of an elastic-halfspace and an elastic stratum, Proc. Lond. Math. Soc., 12, 226–244 (1962).
I.N. Sneddon, R.P. Srivastav and S.C. Mathur, The Reissner-Sagoci problem for a long cylinder of finite radius, Q.J. Mech. Appl. Math., 19, 123–129 (1966).
R.S. Dhaliwal, B.M. Singh and I.N. Sneddon, A problem of Reissner-Sagoci type for an elastic cylinder embedded in an elastic halfspace, Int. J. Engng. Sci., 17, 139–144 (1979).
A.P.S. Selvadurai, The Reissner-Sagoci problem for a finitely deformed incompressible elastic solid, Proc. 16th Midwestern Mechanics Conf., 2, 12–13 (1979).
A.E. Green, R.S. Rivlin and R.T. Shield, General theory of small elastic deformations superposed on finite elastic deformations, Proc. Roy. Soc., A 211, 128–155 (1952).
A.P.S. Selvadurai, The statical Reissner-Sagoci problem for an internally loaded transversely isotropic elastic halfspace, Lett. Appl. Engng. Sci., 20, 1365–1372 (1982).
N.J. Freeman and L.M. Keer, Torsion of a cylindrical rod welded to an elastic halfspace, J. Appl. Mech., 34, 687–692 (1967).
J.E. Luco, Torsion of a rigid cylinder embedded in an elastic halfspace, J. Appl. Mech., 43, 419–423 (1976).
A.P.S. Selvadurai, On the estimation of the deformability characteristics of an isotropic elastic soil medium by means of a vane test. Int. J. Numer. Anal. Methods Geomech., 3, 231–243 (1979).
P. Karasudhi, R.K.N.D. Rajapakse and B.Y. Hwang, Torsion of a long cylindrical elastic bar partially embedded in a layered elastic halfspace, Int. J. Solids Struct., 20, 1–11 (1984).
R.K.N.D. Rajapakse and A.P.S. Selvadurai, Torsional stiffness of non-uniform and hollow rigid piers embedded in isotropic elastic media, Int. J. Num. Anal. Meth. Geomech. (in press).
A.P.S. Selvadurai and R.K.N.D. Rajapakse, A variational scheme for the analysis of torsion of non-uniform elastic bars embedded in elastic media (to be published).
V.S. Protsenko, Torsion of an elastic halfspace with the modulus of elasticity varying according to the power law, Prikl. Mekh., 3, 127–130 (1967).
V.S. Protsenko, Torsion of a generalized elastic halfspace, Prikl. Mekh., 4, 93–97 (1968).
M.K. Kassir, The Reissner-Sagoci problem for a non-homogeneous solid, Int. J. Engng. Sci., 8, 875–885 (1970).
Iu.D. Kolybikhin, The contact problem of the torsion of a halfspace due to an elastic disc, Prikl. Mekh., 12, 25–31 (1971).
B.M. Singh, A note on Reissner-Sagoci problem for a non-homogeneous solid, Zeit. Angew. Math. Mech., 53, 419–420 (1973).
M.F. Chuapresert and M.K. Kassir, Torsion of a non-homogeneous solid, J. Eng. Mech. Div. Proc. A.S.C.E., 99, 703–714 (1973).
V.S. Protsenko, Torsion of a non-homogeneous elastic layer, Prikl. Mekh., 4, 139–141 (1968).
Dhaliwal and B.M. Singh, On the theory of elasticity of a non-homogeneous medium, J. Elasticity, 8, 211–219 (1978).
R.S. Dhaliwal and B.M. Singh, Torsion of a circular die on a non-homogeneous halfspace, Int. J. Engng. Sci., 16, 649–658 (1978).
H.A.Z. Hassan, Reissner-Sagoci problem for a non-homogeneous large thick plate, J. Mecanique, 18, 197–206 (1979).
G.M.L. Gladwell and S. Coen, An inverse problem in elastostatics, IMA J. Appl. Math., 27, 407–421 (1981).
G.M.L. Gladwell, Contact Problems in the Classical Theory of Elasticity, Sijthoff and Noordhoff, The Netherlands (1980).
E. Kamke, Differentialgleichungen Losungsmethoden und Losungen, Akademische Verlagsgesellschaft, Geest und Protig, K.G. (1951).
I.N. Sneddon, The Special Functions of Mathematical Physics and Chemistry, Interscience, New York (1961).
I.N. Sneddon, The Use of Integral Transforms, McGraw Hill, New York (1972).
K. Atkinson, A Survey of Numerical Methods for the Solution of Fredholm Integral Equations of the Second Kind, Society for Industrial and Applied Mathematics, Philadelphia (1976).
C.T.H. Baker, The Numerical Treatment of Integral Equations, Clarendon Press, Oxford (1977).
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Selvadurai, A.P.S., Singh, B.M. & Vrbik, J. A Reissner-Sagoci problem for a non-homogeneous elastic solid. J Elasticity 16, 383–391 (1986). https://doi.org/10.1007/BF00041763
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF00041763