Abstract
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
Similar content being viewed by others
References
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).
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).
I. I. Argatov, “Capacity characteristics of a punch with smooth flat base,” Izv. VUZov, Stroit., No. 4, 26–32 (2000).
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).
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.
I. I. Argatov, “Interaction of punches on an elastic half-space,” Uspekhi Mekh., 1, No. 4, 8–40 (2002).
I. I. Argatov, “Interaction of several punches on an elastic half-space,” Int. Appl. Mech., 39, No. 9, 1054–1059 (2003).
I. I. Argatov and N. N. Dmitriev, Fundamentals of the Theory of Elastic Discrete Contact [in Russian], Politekhnika, St.-Petersburg (2003).
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).
L. A. Galin, Contact Problems in the Theory of Elasticity and Viscoelasticity [in Russian], Nauka, Moscow (1980).
I. S. Gradshtein and I. M. Ryzhik, Tables of Integrals, Sums, Series, and Products [in Russian], Nauka, Moscow (1971).
K. L. Johnson, Contact Mechanics, Cambridge Univ. Press (1985).
V. I. Dovnorovich, Spatial Contact Problems in the Theory of Elasticity [in Russian], Izd. Byeloruss. Gos. Univ., Minsk (1959).
A. I. Lurie, Spatial Problems of Elasticity [in Russian], Gostekhizdat, Moscow (1955).
V. I. Mossakovskii, “A note on displacement evaluation in spatial contact problems,” Prikl. Mat. Mech., 15, No. 5, 635–636 (1951).
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).
N. P. Pavlyuk, “Stability of rigid walls and columns,” in: Trans. Leningrad Institute of Municipal Building, 2, ONTI, Leningrad (1935), pp. 3–21.
Ya. G. Panovko and I. I. Gubanova, Stability and Vibrations of Elastic Systems [in Russian], Nauka, Moscow (1987).
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).
G. Ya. Popov, Elastic Stress Concentration around Punches, Cuts, Thin Inclusions, and Reinforcements [in Russian], Nauka, Moscow (1982).
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).
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).
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).
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).
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).
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).
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).
R. Shailt, “Lamé polynomial solutions to some elliptic crack and punch problems,” Int. J. Eng. Sci., 16, 551–563 (1978).
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).
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).
Author information
Authors and Affiliations
Additional information
__________
Translated from Prikladnaya Mekhanika, Vol. 42, No. 1, pp. 78–96, January 2006.
Rights and permissions
About this article
Cite this article
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
Received:
Issue Date:
DOI: https://doi.org/10.1007/s10778-006-0060-9