539.3

interfacial incisions, orthotropic plate, reinforcing rib, contact forces, singular integral-differential equations.

In the conditions of a generalized flat stress state created by uniformly distributed tensile forces at infinity, the mixed contact problem for an infinite orthotropic plate with an elliptical hole, the contour of which is strengthened by a closed elastic rib, in the presence two symmetrical interphase incisions with edges which are not in contact during deformation, is considered. The deformation tensor components (relative elongation and normal angle of rotation) at the points of the contour of the plate hole are represented by integral dependences on the contact forces. By modeling strengthening of a closed elastic rod of a constant rectangular cross section and using the basic equations of the linear theory of curvilinear rods, which takes into account the deformations of the transverse shear, the mathematical model of the problem is constructed as a system of singular integral-differential equations with Hilbert cores to find the contact forces between the plate and the rib and the internal forces and moments in the reinforcemen. To determine the initial parameters of a statically indeterminate rod, the conditions of unambiguity of displacements and angles of rotation at points of its axis were used. The structure of the required functions in the areas of interconnection of the plate and the reinforcing rib is established. The approximate solution of the problem is constructed by the combined method of me chanical quadratures and collocations, which investigates the influence of the magnitude of the interphase cuts and the shape of the hole in the plate on the stress state of the plate and the reinforcing rib. It is established that in the vicinity of the ends of the interphase sections, the normal stresses in the longitudinal fibers of the rib have first-order jumps, while remaining limited, and the contact and annular efforts in the plate take unlimited values.

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7. Syaskyi A. O., Shevtsova N. V., Deyneka O. Yu. Mizhfaznyy rozriz v ortotropniy plastyntsi z pidsylenym kruhovym konturom. Visnyk Khmelnytskoho natsionalnoho universytetu. Tekhnichni nauky. Khmelnytskyi. 2018. No. 5. P. 176–181.
8. Syaskyi A. O., Shevtsova N. V., Deyneka O. Yu. Mizhfaznyy rozriz v ortotropniy plastyntsi z eliptychnym konturom, pidsylenym zamknenym pruzhnym rebrom. Visnyk Khmelnytskoho natsionalʹnoho universytetu. Tekhnichni nauky. Khmelnytskyi. 2019. No. 1. P. 31–39.
9. Syasky A., Dejneka O. Interphase incision on the limit welding of orthotropic plate with elliptical hole and closed elastic rib. Scientific Journal of TNTU (Ternopil). 2019. Vol. 95. No. 3. P. 26–33.
10. Syasky A., Dejneka O., Shevtsova N. Interphase gross – sections in the infinity plate with curvilinear contour reinforced by closed rib. Scientific Journal of TNTU (Ternopil). 2019. Vol. 96. No. 4. P. 23–31.
11. Lekhnytskyi S. H. Anyzotropnye plastynky. M.: Gostekhyzdat, 1957. 464 p.

1. Pysarenko H. S., Kvitka O. L., Umanskyi E. S. Opir materialiv. K.: Vyshcha shkola, 2004. 655 p.
2. Martynovych T. L. K reshenyyu zadach o napryazhennom sostoyanyy v anyzotropnykh plastynkakh s podkreplennym kraem. Prykl. matematyka y mekhanyka. 1971. T. 35. No. 1. P. 172–178.
3.  Fylyn A. P., Tananayko O. D., Cherneva Y. M., Shvarts M. A. Alhorytmy postroenyya razreshayushchykh uravnenyy mekhanyky sterzhnevyykh system. L.: Stroyizdat, 1983. 232 p.
4. Syaskyi A., Shevtsova N. Zastosuvannya metodu syl dlya statychnoho rozrakhunku zamknenykh kryvoliniynykh stryzhniv. Visnyk TNTU. 2015. No. 3 (79). P. 24–30.
5. Bozhydarnik V. V., Andreykiv O. E., Sulym H. T. Mekhanika ruynuvannya, mitsnist i dovhovichnist neperervno armovanykh kompozytiv. Monohrafiya. U 2–kh t. T. 2. Matematychni metody v zadachakh mekhaniky ruynuvannya neperervno armovanykh kompozytiv. Lutsk: Nadstyya, 2007. 424 p.
6. Martynovych T. L., Yurynets V. E. Kontaktnye vzaymodeystvyya plastyn s upruhymy élementamy. Lvov : Vyshcha shkola. Yzd-vo Lvov. un-ta, 1984. 160 p.
7. Syaskyi A. O., Shevtsova N. V., Deyneka O. Yu. Mizhfaznyy rozriz v ortotropniy plastyntsi z pidsylenym kruhovym konturom. Visnyk Khmelnytskoho natsionalnoho universytetu. Tekhnichni nauky. Khmelnytskyi. 2018. No. 5. P. 176–181.
8. Syaskyi A. O., Shevtsova N. V., Deyneka O. Yu. Mizhfaznyy rozriz v ortotropniy plastyntsi z eliptychnym konturom, pidsylenym zamknenym pruzhnym rebrom. Visnyk Khmelnytskoho natsionalʹnoho universytetu. Tekhnichni nauky. Khmelnytskyi. 2019. No. 1. P. 31–39.
9. Syasky A., Dejneka O. Interphase incision on the limit welding of orthotropic plate with elliptical hole and closed elastic rib. Scientific Journal of TNTU (Ternopil). 2019. Vol. 95. No. 3. P. 26–33.
10. Syasky A., Dejneka O., Shevtsova N. Interphase gross – sections in the infinity plate with curvilinear contour reinforced by closed rib. Scientific Journal of TNTU (Ternopil). 2019. Vol. 96. No. 4. P. 23–31.
11. Lekhnytskyi S. H. Anyzotropnye plastynky. M.: Gostekhyzdat, 1957. 464 p.