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Asymptotic models of contact interaction among elliptic punches on a semiclassical foundation

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Consideration is given to the contact without friction among an arbitrary number of elliptic punches or punches in the form of an elliptic paraboloid and an elastic half-space with Young's modulus as a power-law function of the distance from the edge. Asymptotic models of contact interaction are designed assuming that the distance between punches is large compared with their dimensions

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References

  1. V. M. Aleksandrov and A. A. Shmatkova, “Indentation of a parabolic punch into an elastic layer and of two parabolic punches into an elastic half-space,” Izv. RAN, Mekh. Tverd. Tela, No. 4, 149–155 (1998).

  2. A. E. Andreikiv and V. V. Panasyuk, “Pressure of a system of circular punches on an elastic half-space,” Dop. AN URSR, Ser. A, No. 6, 535–536 (1971).

  3. I. I. Argatov, “Capacity characteristics of a punch with smooth flat base,” Izv. VUZov, Stroit., No. 4, 26–32 (2000).

  4. I. I. Argatov, “Asymptotic modeling of the contact interaction of a system of rigidly connected punches with an elastic foundation,” Sib. Zh. Industr. Mat., 3, No. 2, 10–22 (2000).

    MATH  MathSciNet  Google Scholar 

  5. I. I. Argatov, “Stability of a rigid column on an elastic foundation,” in: Studies on the Mechanics of Engineering Structures and Materials [in Russian], Izd. SPbGASU, St.-Petersburg (2000), pp. 56–65.

    Google Scholar 

  6. I. I. Argatov, “Interaction of punches on an elastic half-space,” Uspekhi Mekh., 1, No. 4, 8–40 (2002).

    MathSciNet  Google Scholar 

  7. I. I. Argatov, “Interaction of several punches on an elastic half-space,” Int. Appl. Mech., 39, No. 9, 1054–1059 (2003).

    Article  MATH  Google Scholar 

  8. I. I. Argatov and N. N. Dmitriev, Fundamentals of the Theory of Elastic Discrete Contact [in Russian], Politekhnika, St.-Petersburg (2003).

    Google Scholar 

  9. Ya. P. Buz'ko and V. S. Protsenko, “Pressure of a system of circular punches on an elastic half-space with elastic modulus E = E 0 z ν (0 ≤ ν < 1),” Dop. AN URSR, Ser. A, No. 3, 246–249 (1974).

  10. L. A. Galin, Contact Problems in the Theory of Elasticity and Viscoelasticity [in Russian], Nauka, Moscow (1980).

    MATH  Google Scholar 

  11. I. S. Gradshtein and I. M. Ryzhik, Tables of Integrals, Sums, Series, and Products [in Russian], Nauka, Moscow (1971).

    Google Scholar 

  12. K. L. Johnson, Contact Mechanics, Cambridge Univ. Press (1985).

  13. V. I. Dovnorovich, Spatial Contact Problems in the Theory of Elasticity [in Russian], Izd. Byeloruss. Gos. Univ., Minsk (1959).

    Google Scholar 

  14. A. I. Lurie, Spatial Problems of Elasticity [in Russian], Gostekhizdat, Moscow (1955).

    Google Scholar 

  15. V. I. Mossakovskii, “A note on displacement evaluation in spatial contact problems,” Prikl. Mat. Mech., 15, No. 5, 635–636 (1951).

    MATH  MathSciNet  Google Scholar 

  16. V. I. Mossakovskii and L. R. Mossakovskaya, “Influence of a load acting outside a circular punch on the contact pressure under its base,” Prikl. Mekh., 1, No. 3, 132–133 (1965).

    Google Scholar 

  17. N. P. Pavlyuk, “Stability of rigid walls and columns,” in: Trans. Leningrad Institute of Municipal Building, 2, ONTI, Leningrad (1935), pp. 3–21.

    Google Scholar 

  18. Ya. G. Panovko and I. I. Gubanova, Stability and Vibrations of Elastic Systems [in Russian], Nauka, Moscow (1987).

    Google Scholar 

  19. G. Ya. Popov, “On one method of solving an axisymmetric contact problem in the theory of elasticity,” Prikl. Mat. Mech., 25, No. 1, 76–85 (1961).

    MATH  Google Scholar 

  20. G. Ya. Popov, Elastic Stress Concentration around Punches, Cuts, Thin Inclusions, and Reinforcements [in Russian], Nauka, Moscow (1982).

    Google Scholar 

  21. A. Kh. Rakov and V. L. Rvachov, “A contact problem of elasticity for a half-space with elastic modulus as a power function of depth,” Dop. AN URSR, No. 3, 286–290 (1961).

  22. N. A. Rostovtsev, “On one integral equation appearing in the problem of a rigid foundation on an inhomogeneous ground,” Prikl. Mat. Mech., 25, No. 1, 164–168 (1961).

    MATH  Google Scholar 

  23. N. A. Rostovtsev, “On some solutions to the integral equation of the theory of linearly elastic foundations,” Prikl. Mat. Mech., 28, No. 1, 111–127 (1964).

    MATH  MathSciNet  Google Scholar 

  24. S. Yu. Babich, A. N. Guz, and V. B. Rudnitskii, “Contact problems for prestressed elastic bodies and rigid and elastic punches,” Int. Appl. Mech., 40, No. 7, 744–765 (2004).

    Article  Google Scholar 

  25. V. I. Fabrikant and L. M. Keer, “The interaction between a system of circular punches on a non homogeneous elastic half space,” Int. J. Mech. Sci., 25, No. 7, 513–518 (1983).

    Article  MATH  Google Scholar 

  26. G. M. L. Gladwell and V. I. Fabrikant, “The interaction between a system of circular punches on an elastic half-space,” Trans. ASME, J. Appl. Mech., 49, No. 2, 341–344 (1982).

    Article  MATH  Google Scholar 

  27. P. P. Krasnyuk, “Contact interaction of a rigid heat-conducting punch with an elastic layer involving nonstationary frictional heating,” Int. Appl. Mech., 41, No. 12, 1357–1367 (2005).

    Article  MathSciNet  Google Scholar 

  28. R. Shailt, “Lamé polynomial solutions to some elliptic crack and punch problems,” Int. J. Eng. Sci., 16, 551–563 (1978).

    Article  Google Scholar 

  29. B. G. Shelestovskii and G. V. Gabrusev, “Thermoelastic state of a transversely isotropic layer between two annular punches,” Int. Appl. Mech., 40, No. 4, 417–425 (2004).

    Article  Google Scholar 

  30. A. T. Vasilenko, E. I. Bespalova, and G. P. Urusova, “Contact interaction between a laminated shell of revolution and a rigid or elastic foundation,” Int. Appl. Mech., 41, No. 5, 520–525 (2005).

    Article  Google Scholar 

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Translated from Prikladnaya Mekhanika, Vol. 42, No. 1, pp. 78–96, January 2006.

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Argatov, I.I. Asymptotic models of contact interaction among elliptic punches on a semiclassical foundation. Int Appl Mech 42, 67–83 (2006). https://doi.org/10.1007/s10778-006-0060-9

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