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3D CONTACT PROBLEM ON INTERACTION BETWEEN FLEXIBLE WEDGE AND TWO PUNCHES UNDER FRICTION

Abstract

The spatial contact problem for the flexible wedge is investigated in the quasi-static formulation when two identical elliptic rigid punches are symmetrically impressed into one face of the wedge under friction. The other wedge face is stress-free. The contact domain is accepted unknown. The motion of the punches perpendicular to the edge of the wedge is considered. In this case the punches can move either towards the edge or from the edge. Using the known Green function for the three-dimensional wedge, the contact problem is reduced to the integral equation with respect to the contact pressure. Galanov’s method is used for solving the integral equation which permits to determine the contact domain and the contact pressure simultaneously. The numerical analysis is made for different values of the friction coefficient, wedge angle, and the distance between the punches.

About the Authors

Dmitry Alexandrovich Pozharskiy
Don State Technical University.
Russian Federation


Anatoly Sergeyevich Polyakov
Don State Technical University.
Russian Federation


References

1. Alexandrov, V.M., Pozharskiy, D.A. Neklassicheskiye prostranstvennyye zadachi mekhaniki kontaktnykh vzaimodeystviy uprugikh tel. [Nonclassical spatial problems of elastic bodies contact interaction mechanics.] Moscow: Faktorial, 1998, 288 p. (in Russian).

2. Galanov, B.A. Metod granichnykh uravneniy tipa Gammershteyna dlya kontaktnykh zadach teorii uprugosti v sluchaye neizvestnykh oblastey kontakta. [Boundary equations method of Hammerstein type for elasticity theory contact problems in case of unknown contact domains.] Prikladnaya matematika i mekhanika, 1985, vol. 49, iss. 5, pp. 827–835 (in Russian).

3. Pozharskiy, D.A. O trekhmernoy kontaktnoy zadache dlya uprugogo klina pri uchete sil treniya. [On 3D contact problem for flexible wedge under friction.] Prikladnaya matematika i mekhanika, 2000, vol. 64, iss. 1, pp. 151–159 (in Russian).

4. Molchanov, A.A., Pozharskiy, D.A. Vzaimodeystviye shtampov na grani uprugogo klina. [Punches interaction on the edge of flexible wedge.] Prikladnaya matematika i mekhanika, 2010, vol. 74, iss. 4, pp. 681–690 (in Russian).

5. Sobol, B.V., Peshkhoyev, I.M. Prostranstvennaya zadacha o kontakte sistemy shtampov s uprugim sloyem. [Spatial problem on contact between punch system and elastic layer.] Ekologicheskiy vestnik nauchnykh tsentrov ChES, 2011, no. 1, pp. 69–76 (in Russian).


Review

For citations:


Pozharskiy D.A., Polyakov A.S. 3D CONTACT PROBLEM ON INTERACTION BETWEEN FLEXIBLE WEDGE AND TWO PUNCHES UNDER FRICTION. Vestnik of Don State Technical University. 2012;12(7):21-26. (In Russ.)

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