Summary
Two axi-symmetric bodies are pressed together, so that their axes of symmetry coincide with the contact normal and the normal force is held constant. A small torque about the contact normal or a small tangential force is applied. For bodies of equal material, the normal and tangential stress states are uncoupled, and can solved separately. The surfaces of the bodies are thought as a superposition of infinitesimal rigid flat-ended punches. Consequently, the normal stress distribution can be calculated as a summation of differential flat punch solutions. A formula results, which is identical with the solution of Green and Collins. After application of a torque an annular sliding area forms at the border of the contact area. For reasons of symmetry, the common displacement of the inner stick area must be a rigid body rotation. Similarly to the normal problem, the solution can be thought as a superposition of rigid punch rotations. The tangential solution can be derived analogically, in form of a superposition of rigid punch displacements. The present method also solves the problem of simultanous normal and torsional or tangential loading with complete adhesion. As an example, Steuermann's problem for polynomial surfaces of the formA 2nr2nis solved. The solutions for constant normal forces can be used as basic functions for loading histories with varying normal and tangential forces.
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References
Abramowitz, M.; Stegun, I. A. Handbook of mathematical functions. New York: Dover Publications 1972
Barber, J. R.: Elasticity, Dordrecht: Kluwer Academic Publishers 1992
Barber, J. R.: Some polynomial solutions for the non-axisymmetric Bousinessq problem. Elasticity 14 (1984) 217–221
Boussinesq, J.: Application des potentiels à l'étude de l'équilibre et du mouvement des solides élastiques, Paris: Gauthier-Villars 1885
Cerruti, V.: Mem. fis. mat. Roma: Acc. Lincei 1882
Cattaneo, C.: Sul Contatto di due corpi elastici. Accademia nationale dei Lincei, Rendiconti 27 (1938) 342–348, 434–436, 474–478
Hills, D. A.; Nowell, D.; Sackfield, A.: Mechanics of elastic contacts. Oxford: Butterworth-Heinemann 1993
Iwan, W. D.: Application of nonlinear analyses techniques. In: Iwan, W. D. (ed.) Applied Mechanics in Earthquake Engineering. New York: ASME (1974), pp. 135–161
Jäger, J.: Elastic impact with friction. Thesis, Delft, 1992
Jäger, J.: Torsional loading histories of elastic spheres in contact. In: Aliabadi, M. H.; Brebbia, C. A. (eds.) Contact Mechanics 93, First Int. Conf., pp. 405–412. Southampton: Computational Mechanics Publications 1993
Jäger, J.: Elastic contact of equal spheres under oblique forces. Arch. Appl. Mech. 63 (1993) 402–413
Jäger, J.: Analytical solutions of contact impact. Appl. Mech. Rev. 47 (1994) 35–54
Jäger, J.: Rotational impact of elastic bodies. Arch. Appl. Mech. 64 (1994) 235–248
Jarzębowski, A.; Mróz, Z.: On slip and memory rules in elastic, friction contact problems. Acta Mechanica 102 (1994) 199–216
Johnson, K. L.: Contact mechanics. Cambridge: Cambridge University Press 1985
Kolsch, H.: On the identification of parameters for structural members exhibiting static hysteresis. Mech. Res. Communications 21 (1994) 31–40
Lubkin, J. L.: Torsion of elastic spheres in contact. J. Appl. Mech. 18 (1951) 183–187
Mindlin, R. D.: Compliance of elastic bodies in contact. J. Appl. Mech. 16 (1949) 259–268
Munisamy R. L.; Hills, D. A.; Nowell, D.: Contact of similar and dissimilar elastic spheres under tangential loading. In: Contact Mechanics, Int. Symp., pp. 447–461. Lausanne: Presses polytechniques et universitaires romandes 1992
Popp, K.; Stelter, P.: Stick-slip vibrations and chaos. Phil. Trans. R. Soc. Lond. A 332 (1990) 89–105
Shtaerman, E.: On Hertz theory of local deformation of compressed bodies. Comptes Rendus (Doklady) de l'Académie des Sciences de l'URSS 25 (1939) 359–361
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Jäger, J. Axi-symmetric bodies of equal material in contact under torsion or shift. Arch. Appl. Mech. 65, 478–487 (1995). https://doi.org/10.1007/BF00835661
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DOI: https://doi.org/10.1007/BF00835661