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On the Contact Problem in Elastostatics

  • J. J. Kalker
Part of the International Centre for Mechanical Sciences book series (CISM, volume 288)

Abstract

Some aspects of the contact between elastic bodies are presented. Starting with the formulation of the contact problem we proceed to give algorithms for contact formation and frictional contact, with emphasis on rolling, which is the most general form of contact with friction. Numerical results are shown, and a comparison with experiments is made.

Keywords

Contact Area Contact Problem Elastic Body Pure Spin Contact Formation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Literature

  1. [1]
    A.E.H. Love, A treatise on the mathematical theory of elasticity, 4th Ed. Cambridge UP (1926).Google Scholar
  2. [2]
    G. Fichera, Problemi elastostatici con vincoli unilaterali: il problema di Signorini con ambigue condizioni al contorno, Mem. Ac. N. Lincei 8, 7 (1964) 116–140.Google Scholar
  3. [3]
    G. Duvaut, J.-L. Lions, Les inéquations en mécanique et en physique, Dunod, Paris, 1972.MATHGoogle Scholar
  4. [4]
    P.D. Panagiotopoulos, A non linear programming approach to the unilateral contact and friction-boundary value problem in the theory of elasticity, Ing. Arch. 44 (1975) 421–432.MATHMathSciNetGoogle Scholar
  5. [5]
    K.L. Johnson, Tangential tractions and microslip in rolling contact, In: Proc. Symp. Rolling Contact Phenomena, Elsevier (1962) 6–28.Google Scholar
  6. [6]
    J.J. Kalker, The computation of three-dimensional rolling contact with dry friction, Int. J. Num. Meth. Eng. 14 (1979) 1293–1307.CrossRefMATHGoogle Scholar
  7. [7]
    V.M. Fridman, V.S. Chernina, Iteration methods applied to the solution of contact peoblems between bodies, Mekh. Tverd. Tela AN SSSR, 1 (1967) 116–120.Google Scholar
  8. [8]
    T.F. Conry, A. Seirig, A mathematical programming method for design of elastic bodies in contact, J. Appl. Mech. 38 (1971) 387–392.ADSCrossRefGoogle Scholar
  9. [9]
    J.J. Kalker, Y. van Randen, A minimum principle for frictionless elastic contact with application to non-Hertzian half-space contact problems, J. Eng. Math. 6 (1972) 192–206.CrossRefGoogle Scholar
  10. [10]
    J.J. Kalker, The contact between wheel and rail, In: Int. Cent. Transp. Stud. Vol.IV Proc. Series, Oct. 25–30/1982, p. 275–312.Google Scholar
  11. [11]
    N. Ahmadi, L.M. Keer, T. Mura, Non-Hertzian stress analysis - normal and sliding contact, Rept. Dept. Civil Engineering, Northwestern University, USA, 1981.Google Scholar
  12. [12]
    J.J. Kalker, Two algorithms for the contact problem in elastostatics, In: Proc.Int.Symp. Contact Mechanics and Wear of Rail/ Wheel systems, ed. Gladwell, (1983).Google Scholar
  13. [13]
    J.J. Kalker, On elastic line contact, J. Appl. Mech. 39 (1972) 1125–1132.ADSCrossRefMATHGoogle Scholar
  14. [14]
    H. Reusner, Druckflächenbelastung and Oberflächenverschiebung im Wälzkontakt von Rotationskörpern. Thesis Karlsruhe, SKF Schweinfurt 1977, ( German).Google Scholar
  15. [15]
    J.J. Kalker, On the rolling contact of two elastic bodies in the presence of dry friction, Thesis Delft 1967.Google Scholar
  16. [16]
    J.J. Kalker, A minimum principle for the law of dry friction with application to elastic cylinders in rolling contact, J.Appl.Mech. 38 (1971) 875–887.ADSCrossRefMATHGoogle Scholar
  17. [17]
    J.J. Kalker, H. Goedings, A program for three-dimensional steady-state rolling, Internal Report (1972), Delft U of T.Google Scholar
  18. [18]
    M. Abramovitz, I.A. Stegun, Handbook of Mathematical Functions, Dover (1965).Google Scholar
  19. [19]
    K.L. Johnson, P.J. Vermeulen, Contact of non-spherical bodies transmitting tangential forces, J.Appl.Mech. (1964), p. 338–340.Google Scholar
  20. [20]
    A.E.H. Hobbs, A survey of creep, Brit. Rail Res..Dept. Dyn 52 (1967)(Derby, U.K.).Google Scholar
  21. [21]
    B.V. Brickle, The steady state forces and moments on a railway wheel set including flange contact conditions. Loughborough Chr. Doct. Thesis (1973).Google Scholar
  22. [22]
    N. Kikuchi, Oral Private Communication, July 1982.Google Scholar

Copyright information

© Springer-Verlag Wien 1985

Authors and Affiliations

  • J. J. Kalker
    • 1
  1. 1.Department of Mathematics and InformaticsDelft University of TechnologyThe Netherlands

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