DOI: https://doi.org/10.20535/SRIT.2308-8893.2020.3.10

Моделювання контактної взаємодії нагрітого жорсткого еліптичного штампа з трансверсально-ізотропним пружним півпростором

Vitaly S. Kirilyuk, Olga I. Levchuk, Olena V. Gavrilenko, Mykhailo B. Viter

Анотація


На основі строгої математичної моделі досліджено задачу контактної взаємодії нагрітого плоского штампа еліптичного перерізу з трансверсально-ізотропним пружним півпростором. Припускається, що поверхня півпростору є площиною ізотропії трансверсально-ізотропного матеріалу, а також має гладкий (без тертя) контакт. У явному вигляді знайдено вирази контактних напружень і переміщення нагрітого плоского еліптичного штампа. У вигляді простої нерівності отримано умову відділення пружного матеріалу від поверхні плоского еліптичного штампа. Виконано числові розрахунки. Вивчено контактну взаємодію нагрітого плоского штампа з урахуванням відділення матеріалу від штампа.

Ключові слова


математична модель; контактна взаємодія; пружний півпростір; трансверсально-ізотропний матеріал; плоский еліптичний штамп; нагрівання; розподіл напружень; ділянка відділення матеріалу

Повний текст:

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Посилання


J.R. Barber, Contact Mechanics. New York, USA: Springer, 2018.

K.L. Johnson, Contact Mechanics. Cambridge, Great Britain: Cambridge Univ. Press, 1985.

A.I. Lurie, Theory of Elasticity. Berlin, Germany: Springer, 2005.

L.A. Galin and G.M.L. Gladwell (Editor) Contact Problems. Dordrecht, Germany: Springer, 2008.

L.A. Galin, Development of the Theory of Contact Problems in the USSR [in Rus-sian]. Moscow, USSR: Nauka, 1976.

N.M. Borodachev, “On solving the contact problem of thermoelasticity in the case of axial symmetry”, Izv. AN SSSR, Otd.Tekhn. Nauk Mekh. Mashinost, no. 5, pp. 86–90, 1962.

J.R. Barber, “Indentation of an elastic half space by a cooled flat punch”, Q.J. Mech. Appl. Math., vol. 35, no.1, pp. 141–154, 1982.

Yu.N. Podil'chuk, V.F. Tkachenko, Ya.I. Sokolovskii, “Thermoelastic contact prob-lem on the penetration of a transversely isotropic half-space by a heated die elliptical in plan”, Int. Appl. Mech., vol. 32, no. 11, pp. 851–857, 1996.

D.V. Grilitsky and Ya.M. Kizyma, Axisymmetric contact problems of the theory of elasticity and thermoelasticity [in Russian]. Lvov, Ukraine: Vyshcha Shkola, 1981.

B.G. Shelestovskii and G.V. Gabrusev, “Thermoelastic state of transversely isotropic layer between two annular punches”, Int. Appl. Mech., vol. 40, no. 4, pp. 417–425, 2004.

Y.S. Chai and I.I. Argatov, “Local tangential contact of elastically similar, trans-versely isotropic elastic bodies”, Meccanica, vol. 53, no. 11–12, pp. 3137–3143, 2018.

V.I. Fabrikant, “Contact problem for an arbitrarily oriented transversely isotropic half-space”, Acta Mechanica, vol. 228, no. 4, pp. 1541–1560, 2017.

P.F. Hou, W.H. Zhang and J.-Y.Chen, “Three-dimensional exact solutions of homo-geneous transversely isotropic coated structures under spherical contact”, Int. J. Solids Structures, vol. 161, no. 5, pp. 136–173, 2019.

F. Marmo, F. Toraldo and L. Rosati, “Analytical formulas and design charts for transversely isotropic half-spaces subject to linearly distributed pressures”, Meccanica, vol. 51, no. 11, pp. 2909–2928, 2016.

Yu.V. Tokovyy and C.C. Ma, “Three-dimensional elastic analysis of transversely-isotropic composites”, Journal of Mechanics, vol. 33, no. 6, pp. 821–830, 2018.

V.S. Kirilyuk, “On the relationship between the solutions of static contact problems of elasticity and electroelasticity for a half-space”, Int. Appl. Mech., vol. 42, no. 11, pp. 1266–1269, 2006.

V.S. Kirilyuk and O.I. Levchuk, “Indentation of punches into a piezoceramic body: Two-dimensional contact problem of electroelasticity”, Int. Appl. Mech., vol. 44, no. 11, pp. 1244–1257, 2008.

V.S. Kirilyuk, “Stress state of a piezoceramic body with a plane crack opened by a rigid inclusion”, Int. Appl. Mech., vol. 44, no. 7, pp. 757–768, 2008.

V.S. Kirilyuk and O.I. Levchuk, “Stress state of an orthotropic piezoelectric material with an elliptic crack”, Int. Appl. Mech., vol. 53, no. 3, pp. 305–312, 2017.

V.S. Kirilyuk, O.I. Levchuk, and H. Altenbach, “Calculation of stress intensity fac-tors for an arbitrary oriented penny-shaped crack under inner pressure in an orthotropic electroelastic material”, Advanced Structured Materials, vol. 108, pp. 211–222, 2019.

Yu.N. Podil’chuk, “Exact analytical solutions of static electroelastic and thermoelec-troelastic problems for a transversely isotropic body in curvilinear coordinate sys-tems”, Int. Appl. Mech., vol. 39, no. 2, pp. 132–170, 2003.

V.S. Kirilyuk, “The thermoelastic equilibrium of a transversally isotropic medium with an elliptic crack under symmetric loading”, Int. Appl. Mech., vol. 36, no. 4, pp. 509–517, 2000.

V.S. Kirilyuk, “Equilibrium of a transversally isotropic body with an elliptic crack under thermal action”, Int. Appl. Mech., vol. 37, no. 10, pp. 1304–1310, 2001.

V. Pauk, “Plane contact of hot flat-ended punch and thermoelastic half-space involv-ing finite friction”, J. Appl. Mech., vol. 74, no. 6, pp. 1172–1177, 2007.


Пристатейна бібліографія ГОСТ


1. J.R. Barber, Contact Mechanics. New York, USA: Springer, 2018.

2. K.L. Johnson, Contact Mechanics. Cambridge, Great Britain: Cambridge Univ. Press, 1985.

3. A.I. Lurie, Theory of Elasticity. Berlin, Germany: Springer, 2005.

4. L.A. Galin and G.M.L. Gladwell (Editor) Contact Problems. Dordrecht, Germany: Springer, 2008.

5. L.A. Galin, Development of the Theory of Contact Problems in the USSR [in Rus-sian]. Moscow, USSR: Nauka, 1976.

6. N.M. Borodachev, “On solving the contact problem of thermoelasticity in the case of axial symmetry”, Izv. AN SSSR, Otd.Tekhn. Nauk Mekh. Mashinost, no. 5, pp. 86–90, 1962.

7. J.R. Barber, “Indentation of an elastic half space by a cooled flat punch”, Q.J. Mech. Appl. Math., vol. 35, no.1, pp. 141–154, 1982.

8. Yu.N. Podil'chuk, V.F. Tkachenko, Ya.I. Sokolovskii, “Thermoelastic contact prob-lem on the penetration of a transversely isotropic half-space by a heated die elliptical in plan”, Int. Appl. Mech., vol. 32, no. 11, pp. 851–857, 1996.

9. D.V. Grilitsky and Ya.M. Kizyma, Axisymmetric contact problems of the theory of elasticity and thermoelasticity [in Russian]. Lvov, Ukraine: Vyshcha Shkola, 1981.

10. B.G. Shelestovskii and G.V. Gabrusev, “Thermoelastic state of transversely isotropic layer between two annular punches”, Int. Appl. Mech., vol. 40, no. 4, pp. 417–425, 2004.

11. Y.S. Chai and I.I. Argatov, “Local tangential contact of elastically similar, trans-versely isotropic elastic bodies”, Meccanica, vol. 53, no. 11–12, pp. 3137–3143, 2018.

12. V.I. Fabrikant, “Contact problem for an arbitrarily oriented transversely isotropic half-space”, Acta Mechanica, vol. 228, no. 4, pp. 1541–1560, 2017.

13. P.F. Hou, W.H. Zhang and J.-Y.Chen, “Three-dimensional exact solutions of homo-geneous transversely isotropic coated structures under spherical contact”, Int. J. Solids Structures, vol. 161, no. 5, pp. 136–173, 2019.

14. F. Marmo, F. Toraldo and L. Rosati, “Analytical formulas and design charts for transversely isotropic half-spaces subject to linearly distributed pressures”, Meccanica, vol. 51, no. 11, pp. 2909–2928, 2016.

15. Yu.V. Tokovyy and C.C. Ma, “Three-dimensional elastic analysis of transversely-isotropic composites”, Journal of Mechanics, vol. 33, no. 6, pp. 821–830, 2018.

16. V.S. Kirilyuk, “On the relationship between the solutions of static contact problems of elasticity and electroelasticity for a half-space”, Int. Appl. Mech., vol. 42, no. 11, pp. 1266–1269, 2006.

17. V.S. Kirilyuk and O.I. Levchuk, “Indentation of punches into a piezoceramic body: Two-dimensional contact problem of electroelasticity”, Int. Appl. Mech., vol. 44, no. 11, pp. 1244–1257, 2008.

18. V.S. Kirilyuk, “Stress state of a piezoceramic body with a plane crack opened by a rigid inclusion”, Int. Appl. Mech., vol. 44, no. 7, pp. 757–768, 2008.

19. V.S. Kirilyuk and O.I. Levchuk, “Stress state of an orthotropic piezoelectric material with an elliptic crack”, Int. Appl. Mech., vol. 53, no. 3, pp. 305–312, 2017.

20. V.S. Kirilyuk, O.I. Levchuk, and H. Altenbach, “Calculation of stress intensity fac-tors for an arbitrary oriented penny-shaped crack under inner pressure in an orthotropic electroelastic material”, Advanced Structured Materials, vol. 108, pp. 211–222, 2019.

21. Yu.N. Podil’chuk, “Exact analytical solutions of static electroelastic and thermoelec-troelastic problems for a transversely isotropic body in curvilinear coordinate sys-tems”, Int. Appl. Mech., vol. 39, no. 2, pp. 132–170, 2003.

22. V.S. Kirilyuk, “The thermoelastic equilibrium of a transversally isotropic medium with an elliptic crack under symmetric loading”, Int. Appl. Mech., vol. 36, no. 4, pp. 509–517, 2000.

23. V.S. Kirilyuk, “Equilibrium of a transversally isotropic body with an elliptic crack under thermal action”, Int. Appl. Mech., vol. 37, no. 10, pp. 1304–1310, 2001.

24. V. Pauk, “Plane contact of hot flat-ended punch and thermoelastic half-space involv-ing finite friction”, J. Appl. Mech., vol. 74, no. 6, pp. 1172–1177, 2007.