539.3

interphase cross-sections, isotropic plate, elastic rib, transverse and longitudinal forces, bending moment, singular integral equations, contact efforts.

Under the conditions of generalized plane stress state, caused by forces uniformly distributed at infinity, mixed contact problem for infinity isotropic plate with curvilinear hole which contour is reinforced by closed elastic rib is considered when there are two symmetric interphase cross-sections with zero width on the boundary of the plate and rib materials. The system of singular integral-differential equations for determining the contact forces between the plate and the rib and the internal forces and moments in the rib is constructed due to the reinforced rib modelling by closed curved rod of the constant rectangular cross-section, the middle surface of which does not coincide with the plate hole surface, and the combination of the plate and the rib by ideal mechanical contact. The problem boundary conditions are formulated in the form of conditions for plate and rib joint deformation. In order to calculate the initial parameters in the statically indeterminate reinforcing rib, the conditions for the displacement uniqueness of the points of its axis and the cross sections rotation angles are used. Using a special approach to the representation of components of the stress state in a conditionally cut rib, the structure of the searched functions at the ends of the connection area of the plate and the rib are established. The approximate problem solution is constructed by mechanical quadratures and collocation method, by which the influence of the rib physical-geometric parameters and the type of external load on the stresses distribution in the plate and the reinforcing rib are investigated. It is determined that the components of the stress-strain deformed state in the rib at the ends of the junction area have restricted values.

1. Savin G. N. Plastinki i obolochki s rebrami zhestkosti / G. N. Savin, N. P. Fleyshman. – Kiyev: Nauk. dumka, 1964. – 384 s.
2. Savin G. N. Plastinki, podkreplennyye sostavnymi kol'tsami i uprugimi nakladkami / Savin G. N., Tul'chiy V. I. - Kiyev : Nauk. dumka, 1971. - 267 s.
3. Martyinovich T.L. Yurinets V.E. Kontaktnyie vzaimodeystviya plastin s uprugimi elementami. Lvov, Vyisshaya shkola, 1984. 160 p.
4. Pysarenko H.S.,Kvitka O.L.,Umanskyi Ye.S. Opir materialiv. Kyiv,Vyshcha shkola, 2004. 655p.
5. Filin A.P.,Tananayko O.D., Cherneva I.M., Shvarts M.A. Algoritmyi postroeniya razreshayuschih uravneniy mehaniki sterzhnevyih sistem. Leningrad, Stroyizdat, 1983. 232 p.
6. Bozhydarnik V.V.,Andreikiv O.Ye., Sulym H.T. Mekhanika ruinuvannia, mitsnisti dovhovichnist neperervno armovanykh kompozytsii. Vol. 2. Matematychni metody v zadachakh neperervno armovanykh kompozytiv. Lutsk, Nadstyrya, 2007. 410 p.
7. Siaskyi A.O., Shevtsova N.V., Dejneka O.Yu. Mizhfaznyi rozriz v izotropnii plastyntsi z kruvoliniynym konturom, pidsylenym pruzhnym rebrom – Visnyk Khmelnytskoho natsionalnoho universytetu, 2019, №3 (271), pp. 18 – 23.
8. Siaskyi A.O., Shevtsova N.V., Dejneka O.Yu. Mizhfaznyi rozriz v ortotropnii plastyntsi z eliptychnym konturom, pidsylenym pruzhnym rebrom – Visnyk Khmelnytskoho natsionalnoho universytetu, 2019, №1 (269), pp. 31 – 39.
9. Siaskyi A., Shevtsova N. Zastosuvannia metodu syl dlia statychnoho rozrakhunku zamknenykh kryvoliniinykh stryzhniv – Visnyk Ternopilskoho natsionalnoho tekhnichnoho universytetu, 2015,Vol. 79, №3, pp. 24 – 30.

1. Savin G. N. Plastinki i obolochki s rebrami zhestkosti / G. N. Savin, N. P. Fleyshman. – Kiyev: Nauk. dumka, 1964. – 384 s.
2. Savin G. N. Plastinki, podkreplennyye sostavnymi kol'tsami i uprugimi nakladkami / Savin G. N., Tul'chiy V. I. - Kiyev : Nauk. dumka, 1971. - 267 s.
3. Martyinovich T.L. Yurinets V.E. Kontaktnyie vzaimodeystviya plastin s uprugimi elementami. Lvov, Vyisshaya shkola, 1984. 160 p.
4. Pysarenko H.S.,Kvitka O.L.,Umanskyi Ye.S. Opir materialiv. Kyiv,Vyshcha shkola, 2004. 655p.
5. Filin A.P.,Tananayko O.D., Cherneva I.M., Shvarts M.A. Algoritmyi postroeniya razreshayuschih uravneniy mehaniki sterzhnevyih sistem. Leningrad, Stroyizdat, 1983. 232 p.
6. Bozhydarnik V.V.,Andreikiv O.Ye., Sulym H.T. Mekhanika ruinuvannia, mitsnisti dovhovichnist neperervno armovanykh kompozytsii. Vol. 2. Matematychni metody v zadachakh neperervno armovanykh kompozytiv. Lutsk, Nadstyrya, 2007. 410 p.
7. Siaskyi A.O., Shevtsova N.V., Dejneka O.Yu. Mizhfaznyi rozriz v izotropnii plastyntsi z kruvoliniynym konturom, pidsylenym pruzhnym rebrom – Visnyk Khmelnytskoho natsionalnoho universytetu, 2019, №3 (271), pp. 18 – 23.
8. Siaskyi A.O., Shevtsova N.V., Dejneka O.Yu. Mizhfaznyi rozriz v ortotropnii plastyntsi z eliptychnym konturom, pidsylenym pruzhnym rebrom – Visnyk Khmelnytskoho natsionalnoho universytetu, 2019, №1 (269), pp. 31 – 39.
9. Siaskyi A., Shevtsova N. Zastosuvannia metodu syl dlia statychnoho rozrakhunku zamknenykh kryvoliniinykh stryzhniv – Visnyk Ternopilskoho natsionalnoho tekhnichnoho universytetu, 2015,Vol. 79, №3, pp. 24 – 30.