539.214

coupling, plastic non-isothermal yielding theory, finite element method, stresses, optimization.

Within the plastic non-isothermal yielding theory the elastic-plastic thermal stresses has been investigated in a connective unit formed by means of thermal coupling shrinkage on tubes to be connected. The mathematical model for description of the thermomechanical processes has been proposed. The applicable mechanics problem has been formulated. The approximate approach for its solving based on the finite element method has been realized. The optimization of the coupling profile with variable thickness in axial direction has been fulfilled. A search of the optimal coupling variant has been executed for profiles restricted by piece-wise linear surfaces. The optimization criterion by minimization of inequality of normal contact pressure  distribution has been proposed.

1. Alian A.R., Shazly M., Megahed M.M. 3D finite element modeling of in-service sleeve repair welding of gas pipelines. International Journal of Pressure Vessels and Piping, 2016, Vol. 146, pp. 216 – 229.
2. Siddique M., Abid M. Finite element simulation of mechanical stress relieving in welded pipe-flange joint. Journal of Process Mechanical Engineering, 2006, Vol. 219, part 1, pp. 17 – 30.
3. Kopej B.V., Mykhailyuk V.V., Martynets’ O.R., Bublins’kyj Yu. Ya. Vplyv tekhnolohiyi vyhotovlennya na mitsnist’ riz’by nasosnoyi shtanhy. Naftohazova enerhetyka, 2014, No 2 (22), pp. 14 – 20 [In Ukrainian].
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5. Niu S. Numerical Simulation of Interference Assembly of Shaft and Sleeve. International Journal of Engineering and Advanced Research Technology (IJEART), 2015, Vol. 1, Issue 2, pp.3 – 15.
6. Shen J., Chen D., Liu G.F., Zhou D., Du X.D. FEM Analysis of Stress on Shaft-sleeve Interference Fits. Advanced Materials Research, 2013, Vol. 668, pp. 495 – 499.
7. Sulym G.T., Luchko J.J., Kuz’ O.N. Chyslove rozvyazuvannya osesymetrychnoyi zadachi zyednannya armaturnykh sterzhniv obtysknoyu vtulkoyu. Dorohy i mosty, 2008, Issue 8, K.: Derzhdor NDI, pp. 254 – 259 [In Ukrainian].
8. Sulym G.T., Kuz’ O.N. Matematychne modelyuvannya ta chyslovyj analiz formuvannya zyednannya pruzhnykh armaturnykh stryzhniv nahritoyu pruzhno-plastychnoyu muftoyu. Mizhvuzivs’kyj zbirnyk ”Naukovi notatky (za napryamom «Inzhenerna mekhanika»), 2011, Issue 35, Luts’k: Luts’kyj nacional’nyj tekhnichnyj universytet, pp. 181 – 186 [In Ukrainian].
9. Sulym G.T., Kuz’ O.N. Zistavlennya rezul’tativ eksperymental’nykh ta chyslovykh doslidzhen’ mekhanichnoho zyednannya armaturnykh stryzhniv obtysknoyu muftoyu. Visnyk TNTU, 2012, Vol. 67, No 3, pp. – 101 – 109 [In Ukrainian].
10. Yevdokimov A.P. Eksperimental’nye issledovaniya mnogoslojnoj uprugoj obolochki coyedinitel’noj mufty silovykh privodov. Informatsionno-tekhnologicheskij vestnik, 2015, No 5(3), pp. 68 – 80 [In Russian].
11. Sergeev S.A. Tsepnye mufty: analiz i sintez. Staryj Oskol, TNT, 2015, 392 p. ]In Russian].
12. Morozov Ye.M., Nikishkov G.P., Chernysh T.A. Neizotermicheskaya model’ uprugoplasticheskogo tela i yeyo primeneniye dlya MKE-raschyota tel s treshhinami. Analiticheskiye i chislennyye metody resheniya krayevykh zadach plastichnosti i vyazkouprugosti. Sverdlovsk, AN SSSR, Ural’sk. nauchn.. tsentr, 1986, pp. 87 – 94 [In Russian].
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15. Hachkevych O.R., Mykhailyshyn V.S. Matematychne modelyuvannya i doslidzhennya napruzhenoho stanu til v protsesi okholodzhennya pry vysokotemperaturnomu vidpali. Matematychni metody ta fizyko-mekhanichni polya, 2004, Vol. 47, No 3, pp. 186 – 198 [In Ukrainian].
16. Hachkevych O., Mykhailyshyn V., Ravs’ka-Skotnichna A. Chyslova metodyka rozv’yazuvannya zadach termomekhaniky til u razi okholodzhennya v protsesi vysokotemperaturnoho vidpalyuvannya. Visnyk L’vivs’koho universytetu. Seriya prykladna matematyka ta informatyka, 2007, Issue 12, pp. 78 – 92 [In Ukrainian].
17. Mykhailyshyn V.S. Iteratsijni procedury v zadachakh neizotermichnoyi pruzhnoplastychnosti z izotropno-kinematychnym zmitsnennyam. Fizyko-khimichna mekhanika materialiv, 1999, Vol. 35, No 4, pp. 102 – 112 [In Ukraunian].
18. (Mykhailyshyn V.S. Iterative Procedures for Problems of Nonisothermal Elastoplasticity with Isotropic Kinematic Hardening. Materials Science, 1999, Vol. 35, No 4, pp. 561–571).
19. Sakharov A.S., Al’tenbakh I. Metod konechnykh elementov v mekhanike tvyordykh tel. Kyiv, Vyshcha shkola, 1982, 480 p. [In Russian].
20. Feodos’yev V.I. Soprotivleniye materialov. Moskva, Nauka, 1972, 544 p. [In Russian].
21. Mykhailyuk V.V. Rozroblennya riz’bovoho zyednannya nasosnykh shtanh z rivnomirnym rozpodilom zusyl’ mizh vytkamy riz’by. Naukovyj visnyk IFNTUNG, 2010, No 4 (26), pp. 61 – 65 [In Ukrainian].
22. Halushkin D.V., Odarchenko I.B., Tkachyov V.M., Bobarikin Yu.L., Selyutin A.M. Tekhnika i tekhnologiya polucheniya mekhanicheskikh muftovykh soedinenij armatury s parallel’noj res’boj. Vestnik Homel’skoho HTU im. P.O. Sukhoho, 2017, No 4, pp. 53 – 62 [In Russian].

1. Alian A.R., Shazly M., Megahed M.M. 3D finite element modeling of in-service sleeve repair welding of gas pipelines. International Journal of Pressure Vessels and Piping, 2016, Vol. 146, pp. 216 – 229.
2. Siddique M., Abid M. Finite element simulation of mechanical stress relieving in welded pipe-flange joint. Journal of Process Mechanical Engineering, 2006, Vol. 219, part 1, pp. 17 – 30.
3. Kopej B.V., Mykhailyuk V.V., Martynets’ O.R., Bublins’kyj Yu. Ya. Vplyv tekhnolohiyi vyhotovlennya na mitsnist’ riz’by nasosnoyi shtanhy. Naftohazova enerhetyka, 2014, No 2 (22), pp. 14 – 20 [In Ukrainian].
4. Tribel’skii I.A., Zubarev A.V. Stress-strain state and thermal state of rubber-cord casing of highly elastic couplings. Russian Engineering Research, 2008, Vol. 28, No 12, pp.1159 – 1164.
5. Niu S. Numerical Simulation of Interference Assembly of Shaft and Sleeve. International Journal of Engineering and Advanced Research Technology (IJEART), 2015, Vol. 1, Issue 2, pp.3 – 15.
6. Shen J., Chen D., Liu G.F., Zhou D., Du X.D. FEM Analysis of Stress on Shaft-sleeve Interference Fits. Advanced Materials Research, 2013, Vol. 668, pp. 495 – 499.
7. Sulym G.T., Luchko J.J., Kuz’ O.N. Chyslove rozvyazuvannya osesymetrychnoyi zadachi zyednannya armaturnykh sterzhniv obtysknoyu vtulkoyu. Dorohy i mosty, 2008, Issue 8, K.: Derzhdor NDI, pp. 254 – 259 [In Ukrainian].
8. Sulym G.T., Kuz’ O.N. Matematychne modelyuvannya ta chyslovyj analiz formuvannya zyednannya pruzhnykh armaturnykh stryzhniv nahritoyu pruzhno-plastychnoyu muftoyu. Mizhvuzivs’kyj zbirnyk ”Naukovi notatky (za napryamom «Inzhenerna mekhanika»), 2011, Issue 35, Luts’k: Luts’kyj nacional’nyj tekhnichnyj universytet, pp. 181 – 186 [In Ukrainian].
9. Sulym G.T., Kuz’ O.N. Zistavlennya rezul’tativ eksperymental’nykh ta chyslovykh doslidzhen’ mekhanichnoho zyednannya armaturnykh stryzhniv obtysknoyu muftoyu. Visnyk TNTU, 2012, Vol. 67, No 3, pp. – 101 – 109 [In Ukrainian].
10. Yevdokimov A.P. Eksperimental’nye issledovaniya mnogoslojnoj uprugoj obolochki coyedinitel’noj mufty silovykh privodov. Informatsionno-tekhnologicheskij vestnik, 2015, No 5(3), pp. 68 – 80 [In Russian].
11. Sergeev S.A. Tsepnye mufty: analiz i sintez. Staryj Oskol, TNT, 2015, 392 p. ]In Russian].
12. Morozov Ye.M., Nikishkov G.P., Chernysh T.A. Neizotermicheskaya model’ uprugoplasticheskogo tela i yeyo primeneniye dlya MKE-raschyota tel s treshhinami. Analiticheskiye i chislennyye metody resheniya krayevykh zadach plastichnosti i vyazkouprugosti. Sverdlovsk, AN SSSR, Ural’sk. nauchn.. tsentr, 1986, pp. 87 – 94 [In Russian].
13. Allen D.H., Haisler W.E. A theory for analysis of thermoplastic materials. Comput. & Struct., 1981, Vol.. 13, No 1, pp. 129 – 135.
14. Vasidzu K. Variatsionnye metody v teorii uprugosti i plastichnosti. Moskva, Mir, 1987, 542 p. [In Russian].
15. Hachkevych O.R., Mykhailyshyn V.S. Matematychne modelyuvannya i doslidzhennya napruzhenoho stanu til v protsesi okholodzhennya pry vysokotemperaturnomu vidpali. Matematychni metody ta fizyko-mekhanichni polya, 2004, Vol. 47, No 3, pp. 186 – 198 [In Ukrainian].
16. Hachkevych O., Mykhailyshyn V., Ravs’ka-Skotnichna A. Chyslova metodyka rozv’yazuvannya zadach termomekhaniky til u razi okholodzhennya v protsesi vysokotemperaturnoho vidpalyuvannya. Visnyk L’vivs’koho universytetu. Seriya prykladna matematyka ta informatyka, 2007, Issue 12, pp. 78 – 92 [In Ukrainian].
17. Mykhailyshyn V.S. Iteratsijni procedury v zadachakh neizotermichnoyi pruzhnoplastychnosti z izotropno-kinematychnym zmitsnennyam. Fizyko-khimichna mekhanika materialiv, 1999, Vol. 35, No 4, pp. 102 – 112 [In Ukraunian].
18. (Mykhailyshyn V.S. Iterative Procedures for Problems of Nonisothermal Elastoplasticity with Isotropic Kinematic Hardening. Materials Science, 1999, Vol. 35, No 4, pp. 561–571).
19. Sakharov A.S., Al’tenbakh I. Metod konechnykh elementov v mekhanike tvyordykh tel. Kyiv, Vyshcha shkola, 1982, 480 p. [In Russian].
20. Feodos’yev V.I. Soprotivleniye materialov. Moskva, Nauka, 1972, 544 p. [In Russian].
21. Mykhailyuk V.V. Rozroblennya riz’bovoho zyednannya nasosnykh shtanh z rivnomirnym rozpodilom zusyl’ mizh vytkamy riz’by. Naukovyj visnyk IFNTUNG, 2010, No 4 (26), pp. 61 – 65 [In Ukrainian].
22. Halushkin D.V., Odarchenko I.B., Tkachyov V.M., Bobarikin Yu.L., Selyutin A.M. Tekhnika i tekhnologiya polucheniya mekhanicheskikh muftovykh soedinenij armatury s parallel’noj res’boj. Vestnik Homel’skoho HTU im. P.O. Sukhoho, 2017, No 4, pp. 53 – 62 [In Russian].