We consider the contact interaction of a stamp with rectilinear base and an elastic wedge. One of the wedge faces is fixed, and the stamp edge touches the wedge vertex. Using the Wiener–Hopf method, we have obtained an exact solution of this problem. We have also determined the stress distributions in the contact region and on the wedge fixed face as well as the displacements of its free boundary.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
V. M. Aleksandrov, “On contact problems for an elastic wedge with one restrained face,” Izv. Akad. Nauk Arm. SSR, Mekh., 21, No. 2, 17–27 (1968).
V. M. Aleksandrov, “Contact problems for an elastic wedge,” Izv. Akad. Nauk SSSR, Mekh. Tverd. Tela, No. 2, 120–131 (1967).
V. M. Aleksandrov, “Contact problems for an elastic plane wedge,” in: Contact Problems and Their Engineering Applications [in Russian], NIIMash, Moscow (1969).
V. M. Aleksandrov, “On one contact problem for an elastic wedge,” Izv. Akad. Nauk Arm. SSR, Mekhanika, 20, No. 1, 3–13 (1967).
V. M. Aleksandrov and V. V. Kopasenko, “Contact problem for an elastic wedge with a rigidly restrained face,” Prikl. Mekh., 4, No. 7, 75–82 (1968).
M. I. Bronshtein, “Solution of contact problem for a stamp on a wedge-shaped base,” Osnov., Fundam., Mekh. Gruntov, No. 4, 2–4 (1968).
S. A. Lutchenko, “On the indentation of stamps into the lateral surface of an elastic wedge-shaped base,” Prikl. Mekh., 2, No. 12, 61–66 (1966).
S. A. Lutchenko and G. Ya Popov, “On some plane contact problems of the theory of elasticity for a wedge,” Prikl. Mekh., 6, No. 3, 64–71 (1970).
B. Noble, Methods Based on the Wiener–Hopf Technique, Pergamon, New York (1958).
V. I. Ostrik and A. F. Ulitko, Wiener–Hopf Method in Contact Problems of the Theory of Elasticity [in Russian], Naukova Dumka, Kiev (2006).
V. I. Ostryk, “Problems of frictional contact of an elastic wedge and a cone with rigid extension,” Visn. Kyiv. Univ., Ser. Fiz.-Mat. Nauky, No. 4, 119–126 (2002).
V. Ostryk, “Contact with friction of an elastic wedge with rigid supports,” Mashynoznavstvo, No. 5, 28–32 (1999).
S. P. Timoshenko and J. N. Goodier, Theory of Elasticity, 3 rd edition, McGraw-Hill, New York (1970).
V. S. Tonoyan, “On one plane contact problem for an elastic quarter-plane,” Dokl. Akad. Nauk Arm. SSR, 37, No. 3, 121–130 (1963).
V. S. Tonoyan, “Plane contact problem for an elastic quarter-plane with fixed vertical edge,” Dokl. Akad. Nauk Arm. SSR, 37, No. 5, 249–258 (1963).
A. F. Ulitko and V. I. Ostrik, “Mixed problem of the theory of elasticity for a strip on a rigid base,” in: Proceedings of the III All-Russian Conference on the Theory of Elasticity with International Participation [in Russian], Novaya Kniga, Rostov-on-Don (2004), pp. 372–375.
A. F. Ulitko and V. I. Ostryk, “Contact of an elastic and a rigid wedges with regard for friction forces,” Visn. Kyiv. Univ., Ser. Fiz.-Mat. Nauky, No. 3, 129–137 (1999).
Ya. S. Uflyand, Integral Transformations in Problems of the Theory of Elasticity [in Russian], Nauka, Leningrad (1968).
M. V. Fedoryuk, Asymptotics: Integrals and Series [in Russian], Nauka, Moscow (1987).
M. Matczynski, “Elastic wedge with discontinuous boundary conditions,” Arch. Mech. Stosowanej, 15, No. 6, 833–855 (1963).
A. R. Shahani, S. Adibnazari, and D. Naderi, “Non-symmetrical plane contact of a wedge indenter,” J. Mech. Eng. Sci., 221, No. 11, 1233–1239 (2007).
Author information
Authors and Affiliations
Additional information
Translated from Matematychni Metody ta Fizyko-Mekhanichni Polya, Vol. 53, No. 4, pp. 143–150, October–December, 2010.
Rights and permissions
About this article
Cite this article
Ostryk, V.I., Shchokotova, O.M. Plane contact problem of the indentation of a stamp into an elastic wedge. J Math Sci 181, 470–480 (2012). https://doi.org/10.1007/s10958-012-0699-1
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10958-012-0699-1