RESEARCH PAPER
Mathematical Modelling of Stationary Thermoelastic State for a Plate with Periodic System of Inclusions and Cracks
1
Department of Mathematics, Institute of Applied Mathematics and Fundamental Sciences, Lviv Polytechnic National University, S. Bandery str., 12, 79013, Lviv, Ukraine
Submission date: 2018-11-08
Acceptance date: 2019-03-07
Online publication date: 2019-04-18
Publication date: 2019-03-01
Acta Mechanica et Automatica 2019;13(1):11-15
KEYWORDS
ABSTRACT
Two-dimensional stationary problem of heat conduction and thermoelasticity for infinite elastic body containing periodic system of inclusions and cracks is considered. Solution of the problem is constructed using the method of singular integral equations (SIEs). The numerical solution of the system integral equations are obtained by the method of mechanical quadrature for a plate heated by a heat flow, containing periodic system elliptic inclusions and thermally insulated cracks. There are obtained graphic dependences of stress intensity factors (SIFs), which characterise the distribution of intensity of stresses at the tops of a crack, depending on the length of crack, elastic and thermoelastic characteristics inclusion, relative position of crack and inclusion.
REFERENCES (22)
1.
Brock L.M. (2016), Contours for planar cracks growing in three dimensions: Coupled thermoelastic solid (planar crack growth in 3D), Journal of Thermal Stresses, 39(3), 345–359.
2.
Cheesman B.A., Santare M.H. (2000), The interaction of a curved crack with a circular elastic inclusion, Int. J. Fract.,103, 259-278.
3.
Chen H., Wang Q., Liu G., Sun J. (2016), Simulation of thermoe-lastic crack problems using singular edge-based smoothed finite element method, Int. J. of Mech. Sci., 115,116, 23-134.
4.
Choi H.J. (2014), Thermoelastic interaction of two offset interfacial cracks in bonded dissimilar half-planes with a functionally graded interlayer, Acta Mechanica , 225(7),2111–2131.
5.
Elfakhakhre N.R.F., Nik L., Eshkuvatov N.M.A. (2017), Stress intensity factor for multiple cracks in half plane elasticity, AIP Conference, 1795(1).
6.
Erdogan F., Gupta B.D., Cook T.S. (1973), The numerical solutions of singular integral equations, Methods of analysis and solutions of crack problems. Leyden: Noordhoff Intern. publ., 368-425.
7.
Havrysh V.I. (2015), Nonlinear boundary-value problem of heat conduction for a layered plate with inclusion, Phis.-chim. mechanica materialiv (Materials Science), 51(3), 331–339.
8.
Havrysh V.I. (2017) Investigation of temperature fields in a heat-sensitive layer with through inclusion, Phis.-chim.mechanica materialiv (Materials Science), 52(4), 514–521.
9.
Kit H.S., Chernyak M.S. (2010), Stressed state of bodies with thermal cylindrical inclusions an cracks (plane deformation), Phis.-chim. mechanica materialiv (Materials Science), 46(3), 315–324.
10.
Kit, G.S., Ivas’ko, N.M. (2013), Plane deformation of a semi-infinite body with a heat-active crack perpendicular to its boundary, Teoret. I prikl. Mehanika, 53(7), 30–37.
11.
Matysiak S.J., Evtushenko A.A., Zelenjak V.М. (1999), Frictional heating of a half–space with cracks. I. Single or periodic system of subsurface cracks, Tribology Int., 32, 237-243.
12.
Panasyuk V.V., Savruk M.P., Datsyshyn O.P. (1976), Distribution tense neighborhood of cracks in the plates and shells (in Russian), Kiev, Naukova dumka.
13.
Rashidova E.V., Sobol B.V. (2017), An equilibrium internal transverse crack in a composite elastic half-plane, Journal of Applied Mathmatics and Mechanics, 81(3), 236‒247.
14.
Savruk M.P., Zelenyak V.M.(1986), Singular integral equations of plane problems of thermal conductivity and thermoelasticity for a piecewise–uniform plane with cracks, Phis.-chim. mechanica materialiv (Materials Science), 22(3), 297–307.
15.
Savruk M.P. (1981), Two-dimensional elasticity problem for bodies with cracks (in Russian), Kiev, Naukova dumka.
16.
Sekine H. (1975), Thermal stress singularities at tips of a crack in a semi-infinite medium under uniform heat flow, Eng. Fract. Mech., 7 (4), 713-729.
17.
Sushko O.P. (2013), Thermoelastic state of a body with two coplanar thermally active circular cracks, Journal of Mathematical Sciences, 190(5), 725–739.
18.
Tweed I., Lowe S. (1979), The thermoelastic problem for a half-plane with an internal line crack, Int. J. Eng. Sci., 17(4), 357-363.
19.
Xiao Z..M., Chen B.J. (2001), Stress intensity factor for a Griffith crack interacting with a coated inclusion, Int. J. Fract., 108, 193-205.
20.
Zelenyak B.M. (2015), Thermoelastic equilibrium of a three-layer circular hollow cylinder weakened by a crack, Phis.-chim. mechanica materialiv (Materials Science), 50(1), 14–19.
21.
Zelenyak V.M. (2012), Thermoelastic interaction of a two–component circular inclusion with a crack in the plate, Phis.-chim. mechanica materialiv (Materials Science), Materials Science, 48(3), 301–307.
22.
Zelenyak, V.M., Kolyasa, L.I. (2016). Thermoelastic state of a half plane with curvilinear crack under the conditions of local heating, Phis.-chim. mechanica materialiv (Materials Science), 52(3), 315-322.
Share
RELATED ARTICLE
| eISSN: | 2300-5319 |
| ISSN: | 1898-4088 |
We process personal data collected when visiting the website. The function of obtaining information about users and their behavior is carried out by voluntarily entered information in forms and saving cookies in end devices. Data, including cookies, are used to provide services, improve the user experience and to analyze the traffic in accordance with the Privacy policy. Data are also collected and processed by Google Analytics tool (more).
You can change cookies settings in your browser. Restricted use of cookies in the browser configuration may affect some functionalities of the website.
You can change cookies settings in your browser. Restricted use of cookies in the browser configuration may affect some functionalities of the website.
