DOI: https://doi.org/10.20535/SRIT.2308-8893.2020.1.10

Моделювання контактної взаємодії двох трансверсально-ізотропних пружних півпросторів за наявності жорсткого дископодібного включення між ними і тиску на ділянці розшарування

Vitaly S. Kirilyuk, Olga I. Levchuk

Анотація


Використано строгу математичну модель для аналізу контактної взаємодії двох різних за властивостями трансверсально-ізотропних пружних півпросторів під час стискання за наявності жорсткого дископодібного включення між ними і тиску в ділянці розшарування матеріалів. Розв’язок задачі отримано на основі подання загального розв’язку системи рівнянь рівноваги для трансверсально-ізотропного тіла через гармонічні функції, зведення крайової задачі до розгляду інтегрального рівняння, розкладу шуканої функції по малому параметру. Як окремий випадок зі знайдених виразів випливають основні параметри контакту для двох пружних ізотропних півпросторів (за наявності включення між ними і тиску в ділянці розшарування). Отримано числові результати, вивчено вплив пружних властивостей півпросторів, геометричних розмірів включення і навантажень на параметри контактної взаємодії.

Ключові слова


математичне моделювання; трансверсально-ізотропний матеріал; пружний півпростір; жорстке дископодібне включення; тиск в області розшарування; параметри контактної взаємодії

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Посилання


Kirilyuk V.S. Modeling of contact interaction of piezoelectric half-space and elastic isotropic base with surface groove of circular section / V.S. Kirilyuk, O.I Levchuk // System research and information technologies. — 2016. — № 4. — P. 120–132.

Kirilyuk V.S. Mathematical modeling of contact interaction of two electroelastic half-spaces under compression with rigid disc-shaped inclusion between them / V.S. Kirilyuk, O.I. Levchuk, O.V. Gavrilenko // System research and information technologies. — 2018. — № 2. — P. 89–98. DOI: 10.20535/SRIT.2308-8893.2018.2.09

Podil’chuk Yu.N. Boundary value problems of statics of elastic bodies [in Russian] / Yu.N. Podil’chuk. — K.: Nauk. dumka, 1984. — 304 p.

Podil’chuk Yu.N. Exact analytic solutions of three-dimensional boundary-value problems of the statics of a transversely isotropic body of canonical form (Survey) / Yu.N. Podil’chuk // International Applied Mechanics. — 1997. — 33, № 10. — P. 763–787.

Borodich F.M. The JKR-type adhesive contact problems for transversely isotropic elastic solids / F.M. Borodich , B.A. Galanov , L.M. Keer , M.M. Suarez-Alvarez // Mechanics of Materials. — 2014. — 75. — P. 34–44.

Chai Y.S. Local tangential contact of elastically similar, transversely isotropic elastic bodies / Y.S. Chai, I.I. Argatov // Meccanica. — 2018. — 53, N 11–12. — P. 3137–3143.

Chen W.Q. 3D point force solution for a permeable penny-shaped crack embedded in an infinite transversely isotropic piezoelectric medium / W.Q. Chen, C.W. Lim // Int. J. Fract. — 2005. — 131, N 3. — P. 231–246.

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Dai L. Stress concentration at an elliptic hole in transversely isotropic piezoelectric solids / L. Dai, W. Guo, X. Wang // Int. J. Solids and Struct. — 2006. — 43, N 6. — P. 1818–1831.

Davtyan D.B. Action of an elliptic punch on a transversally isotropic half-space/ D.B. Davtyan , D.A. Pozharskii // Mechanics of Solids. — 2014. — 49, N 5. — P. 578–586.

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Freund L.B. Thin Film Materials / L.B. Freund, S. Suresh. — Cambridge: Cambridge University Press, 2003. — 802 p.

Gladwell G.M.L. On Inclusions at a Bi-Material Elastic Interface / G.M.L. Gladwell // Journal of Elasticity. — 1999. — 54, N 1. — P.27–41.

Hou P.F. Three-dimensional exact solutions of homogeneous transversely isotropic coated structures under spherical contact / P.F. Hou, W.H. Zhang, J.-Y. Chen // Int. J. Solids Structures. — 2019. — 161. — P. 136–173.

Kaloerov S.A. Problem of Electromagnet viscoelasticity for Multiply Connected Plates / S.A. Kaloerov, A.A. Samodurov // International Applied Mechanics. — 2015. — 51, N 6. — P. 623–639.

Kaloerov S.A. Determining the intensity factors for stresses, electric-flux density, and electric-field strength in multiply connected electroelastic anisotropic media / S.A. Kaloerov // Int. Appl. Mech. — 2007. — 43, N 6. — P. 631–637.

Kirilyuk V.S. On stressed state of transversely isotropic medium with an arbitraly orientated spheroidal void or penny-shaped crack under internal pressure / V.S. Kirilyuk, O.I. Levchuk // Strength of Materials. — 2005. — 37, N 5. — P. 480–488.

Kirilyuk V.S. Elastic state of a transversely isotropic piezoelectric body with an arbitrarily oriented elliptic crack / V.S. Kirilyuk // Int. Appl. Mech. — 2008. — 44, N 2. — P. 150–157.

Kirilyuk V.S. Stress state of a piezoceramic body with a plane crack opened by a rigid inclusion / V.S. Kirilyuk // Int. Appl. Mech. — 2008. — 44, N 7. — P. 757–768.

Kotousov A. On a rigid inclusion pressed between two elastic half spaces / A. Kotousov, L.B. Neto, A. Khanna // Mechanics of Materials. — 2014. — 68, N 1. — P. 38–44.

Kumar R. Green's function for transversely isotropic thermoelastic diffusion bimaterials / R. Kumar , V. Gupta // Journal of Thermal Stresses. — 2014. — 37, N 10. — P. 1201–1229.

Marmo F. Analytical formulas and design charts for transversely isotropic half-spaces subject to linearly distributed pressures / F. Marmo, F. Toraldo, L. Rosati // Meccanica. — 2016. — 51, N 11. — P. 2909–2928.

Podil’chuk Yu.N. Representation of the general solution of statics equations of the electroelasticity of a transversally isotropic piezoceramic body in terms of harmonic functions / Yu.N. Podil’chuk // International Applied Mechanics. — 1998. — 34, N 7. — P. 623–628.

Selvadurai A.P.S. A unilateral contact problem for a rigid disc inclusion embedded between two dissimilar elastic half-spaces / A.P.S. Selvadurai // Q. J. Mech. Appl. Math. — 1994. — N 3. — P. 493–509.

Tokovyy Yu.V. Three-Dimensional Elastic Analysis of Transversely-Isotropic Composites / Yu.V. Tokovyy, C.C. Ma // Journal of Mechanics. — 2018. — 33, N 6. — P. 821–830.

Wang Y.J. The anti-plane solution for the edge cracks originating from an arbitrary hole in a piezoelectric material / Y.J. Wang, C.F. Gao, H.P. Song // Mechanics Research Communications. — 2015. — Vol. 65. — P. 17–23.

Wang Z.K. The general solution of three-dimension problems in piezoelectric media / Z.K. Wang, B.L. Zheng // Int. J. Solids Structures. — 1995. — 32, N 1. — P. 105–115.

Yu H.Y. A concise treatment of indentation problems in transversely isotropic half-spaces / H.Y. Yu // Int. J. Solids Struct. — 2001. — 38, N 7. — P. 2213–2232.

Zhao M. Three-dimensional steady-state general solution for transversely isotropic hygrothermoelastic media / M. Zhao, H. Dang, C. Fan, Z. Chen // Journal of Thermal Stresses. — 2018. — 41, N 8. — P. 951–972.

Zhao M.H. Singularity analysis of planar cracks in three-dimensional piezoelectric semiconductors via extended displacement discontinuity boundary integral equation method / M.H. Zhao, Y. Li, Y. Yan, C.Y. Fan // Engineering Analysis with Boundary Elements. — 2016. — Vol. 67. — P. 115–125.

Zhao M.H. Extended displacement discontinuity method for analysis of cracks in 2D piezoelectric semiconductors / M.H. Zhao, Y.B. Pan, C.Y. Fan, G.T. Xu // International Journal of Solids and Structures. — 2016. — Vol. 94–95. — P. 50–59.


Пристатейна бібліографія ГОСТ


1. Kirilyuk V.S. Modeling of contact interaction of piezoelectric half-space and elastic isotropic base with surface groove of circular section / V.S. Kirilyuk, O.I Levchuk // System research and information technologies. — 2016. — № 4. — P. 120–132.

2. Kirilyuk V.S. Mathematical modeling of contact interaction of two electroelastic half-spaces under compression with rigid disc-shaped inclusion between them / V.S. Kirilyuk, O.I. Levchuk, O.V. Gavrilenko // System research and information technologies. — 2018. — № 2. — P. 89–98. DOI: 10.20535/SRIT.2308-8893.2018.2.09

3. Podil’chuk Yu.N. Boundary value problems of statics of elastic bodies [in Russian] / Yu.N. Podil’chuk. — K.: Nauk. dumka, 1984. — 304 p.

4. Podil’chuk Yu.N. Exact analytic solutions of three-dimensional boundary-value problems of the statics of a transversely isotropic body of canonical form (Survey) / Yu.N. Podil’chuk // International Applied Mechanics. — 1997. — 33, № 10. — P. 763–787.

5. Borodich F.M. The JKR-type adhesive contact problems for transversely isotropic elastic solids / F.M. Borodich , B.A. Galanov , L.M. Keer , M.M. Suarez-Alvarez // Mechanics of Materials. — 2014. — 75. — P. 34–44.

6. Chai Y.S. Local tangential contact of elastically similar, transversely isotropic elastic bodies / Y.S. Chai, I.I. Argatov // Meccanica. — 2018. — 53, N 11–12. — P. 3137–3143.

7. Chen W.Q. 3D point force solution for a permeable penny-shaped crack embedded in an infinite transversely isotropic piezoelectric medium / W.Q. Chen, C.W. Lim // Int. J. Fract. — 2005. — 131, N 3. — P. 231–246.

8. Chen W.Q. General solutions for elasticity of transversely isotropic materials with thermal and other effects: A review / W.Q. Chen, J. Zhu, X.Y. Li // Int. J. Mech. Sciencis. — 2019. — 151. — P. 471–497.

9. Dai L. Stress concentration at an elliptic hole in transversely isotropic piezoelectric solids / L. Dai, W. Guo, X. Wang // Int. J. Solids and Struct. — 2006. — 43, N 6. — P. 1818–1831.

10. Davtyan D.B. Action of an elliptic punch on a transversally isotropic half-space/ D.B. Davtyan , D.A. Pozharskii // Mechanics of Solids. — 2014. — 49, N 5. — P. 578–586.

11. Elliott H.A. Three-dimensional stress distributions in hexagonal aeolotropic crystals / H.A. Elliott, N.F. Mott // Mathematical Proceedings of the Cambridge Philosophical Society. — 1948. — 44, N 4. — P.522–533.

12. Fabrikant V.I. Contact problem for an arbitrarily oriented transversely isotropic half-space/ V.I. Fabrikant // Acta Mechanca. — 2017. — 228, N 4. — P. 1541–1560.

13. Freund L.B. Thin Film Materials / L.B. Freund, S. Suresh. — Cambridge: Cambridge University Press, 2003. — 802 p.

14. Gladwell G.M.L. On Inclusions at a Bi-Material Elastic Interface / G.M.L. Gladwell // Journal of Elasticity. — 1999. — 54, N 1. — P.27–41.

15. Hou P.F. Three-dimensional exact solutions of homogeneous transversely isotropic coated structures under spherical contact / P.F. Hou, W.H. Zhang, J.-Y. Chen // Int. J. Solids Structures. — 2019. — 161. — P. 136–173.

16. Kaloerov S.A. Problem of Electromagnet viscoelasticity for Multiply Connected Plates / S.A. Kaloerov, A.A. Samodurov // International Applied Mechanics. — 2015. — 51, N 6. — P. 623–639.

17. Kaloerov S.A. Determining the intensity factors for stresses, electric-flux density, and electric-field strength in multiply connected electroelastic anisotropic media / S.A. Kaloerov // Int. Appl. Mech. — 2007. — 43, N 6. — P. 631–637.

18. Kirilyuk V.S. On stressed state of transversely isotropic medium with an arbitraly orientated spheroidal void or penny-shaped crack under internal pressure / V.S. Kirilyuk, O.I. Levchuk // Strength of Materials. — 2005. — 37, N 5. — P. 480–488.

19. Kirilyuk V.S. Elastic state of a transversely isotropic piezoelectric body with an arbitrarily oriented elliptic crack / V.S. Kirilyuk // Int. Appl. Mech. — 2008. — 44, N 2. — P. 150–157.

20. Kirilyuk V.S. Stress state of a piezoceramic body with a plane crack opened by a rigid inclusion / V.S. Kirilyuk // Int. Appl. Mech. — 2008. — 44, N 7. — P. 757–768.

21. Kotousov A. On a rigid inclusion pressed between two elastic half spaces / A. Kotousov, L.B. Neto, A. Khanna // Mechanics of Materials. — 2014. — 68, N 1. — P. 38–44.

22. Kumar R. Green's function for transversely isotropic thermoelastic diffusion bimaterials / R. Kumar , V. Gupta // Journal of Thermal Stresses. — 2014. — 37, N 10. — P. 1201–1229.

23. Marmo F. Analytical formulas and design charts for transversely isotropic half-spaces subject to linearly distributed pressures / F. Marmo, F. Toraldo, L. Rosati // Meccanica. — 2016. — 51, N 11. — P. 2909–2928.

24. Podil’chuk Yu.N. Representation of the general solution of statics equations of the electroelasticity of a transversally isotropic piezoceramic body in terms of harmonic functions / Yu.N. Podil’chuk // International Applied Mechanics. — 1998. — 34, N 7. — P. 623–628.

25. Selvadurai A.P.S. A unilateral contact problem for a rigid disc inclusion embedded between two dissimilar elastic half-spaces / A.P.S. Selvadurai // Q. J. Mech. Appl. Math. — 1994. — N 3. — P. 493–509.

26. Tokovyy Yu.V. Three-Dimensional Elastic Analysis of Transversely-Isotropic Composites / Yu.V. Tokovyy, C.C. Ma // Journal of Mechanics. — 2018. — 33, N 6. — P. 821–830.

27. Wang Y.J. The anti-plane solution for the edge cracks originating from an arbitrary hole in a piezoelectric material / Y.J. Wang, C.F. Gao, H.P. Song // Mechanics Research Communications. — 2015. — Vol. 65. — P. 17–23.

28. Wang Z.K. The general solution of three-dimension problems in piezoelectric media / Z.K. Wang, B.L. Zheng // Int. J. Solids Structures. — 1995. — 32, N 1. — P. 105–115.

29. Yu H.Y. A concise treatment of indentation problems in transversely isotropic half-spaces / H.Y. Yu // Int. J. Solids Struct. — 2001. — 38, N 7. — P. 2213–2232.

30. Zhao M. Three-dimensional steady-state general solution for transversely isotropic hygrothermoelastic media / M. Zhao, H. Dang, C. Fan, Z. Chen // Journal of Thermal Stresses. — 2018. — 41, N 8. — P. 951–972.

31. Zhao M.H. Singularity analysis of planar cracks in three-dimensional piezoelectric semiconductors via extended displacement discontinuity boundary integral equation method / M.H. Zhao, Y. Li, Y. Yan, C.Y. Fan // Engineering Analysis with Boundary Elements. — 2016. — Vol. 67. — P. 115–125.

32. Zhao M.H. Extended displacement discontinuity method for analysis of cracks in 2D piezoelectric semiconductors / M.H. Zhao, Y.B. Pan, C.Y. Fan, G.T. Xu // International Journal of Solids and Structures. — 2016. — Vol. 94–95. — P. 50–59.