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Title of the article

ANALYTICAL METHOD OF SOLVING PROBLEMS OF THERMOELASTICITY WITH PERIODIC CONDITIONS FOR MULTILAYER FOUNDATION

Authors

VELICHKO Igor G., Cand. Phys.-Math. Sc., Associate Professor, Head of the Department "Higher Mathematics and Physics", e-mail: This email address is being protected from spambots. You need JavaScript enabled to view it., Tavria State Agrotechnological University, Melitopol, Ukraine

In the section MECHANICS OF DEFORMED SOLIDS
Year 2015 Issue 4 Pages 42-49
Type of article RAR Index UDK 536.21+539.3 Index BBK  
Abstract

A method for solving the two-dimensional stationary problem of thermoelasticity for multilayer foundations. The upper boundary of the temperature and pressure are described by periodic functions. At the lower boundary temperature and displacement zero. On the common boundary layers of the conditions of continuity of the temperature field and the equality of heat fluxes. The desired function in each layer are written in the form of Fourier series. To ensure the fulfillment of the conditions at the common borders layers of a modification of the method of compliance matrices. An algorithm for solving the problem. It is shown that the method gives the exact solution of the problem for any finite number of layers. According to the results of theoretical studies, numerical experiments. Formulate conclusions concerning the identified thermoelastic effects.

Keywords

multilayer foundation, thermoelasticity, recurrence relations, compliance matrix, Fourier series, Fourier law

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Bibliography
  • Podstryhach J.S. Teploupruhost tel neodnorodnoy struktury [Heat elastic bodies of the inhomogeneous structure]. Moscow, Nauka, 1984. 368 p.
  • Kovalenko A.D. Osnovy termoupruhosty [Fundamentals of heat elastic]. Kyev, Scientific thought, 1970. 307 p.
  • Kudynov V.A. Analytycheskye reshenyya zadach teplomassoperenosa y termoupruhosty dlya mnohosloynykh konstruktsyy [Analytical solving of problem of heat and mass transfer and thermoelasticity for multilayer designs]. Moscow, High school, 2005. 430 p.
  • Ukhyn D.V. Matematycheskaya model rascheta temperatury mnohosloynoy konstruktsyy dorozhnoy odezhdy v uslovyyakh peremeny temperatur [Mathematical model for calculating the temperature of the multilayer structure of the pavement in a temperature change]. Vestn. VolgASU. Serii storitelstvo i arhitektura [Journal of the VolgASU. Series building and architecture], 2010, vol. 17(36), pp. 66-69.
  • Altukhov E.V. Metod odnorodnykh reshenyy v trekhmernykh zadachakh termoupruhosty dlya transportnykh plastyn [Method of uniform decisions in three-dimensional problems of thermoelasticity for transport plates]. Teoreticheskaya I prikladnaya mekhanika [Theoretical and applied mechanics]. Kyev, 2003, vol. 37, pp. 8-13.
  • Altukhov, E.V. Odnorodnye reshenyya trekhmernykh zadach o rasprostranenyy harmonycheskykh voln v transportnykh termoupruhykh plastynakh [Uniform solutions of three-dimensional tasks on distribution of harmonious waves in transport thermoelastic plates]. Dopovidi of the NAS of Ukraine [News of the NAS of Ukrain], 2007, vol. 4, pp. 49-53.
  • Protsyuk B.V. Metod funktsiy Hrina v osesymetrychnykh zadach pruzhnosti ta termopruzhnosti kuskovo-odnoridnykh ortotropnykh til [Method of green’s functions for axisymmetric problems of elasticity and thermoelasticity piecewise-homogeneous bodies orthotropic]. Matematicheskie metody physichesko-mekhanicheskogo polya [Mathematical methods of physical-mechanical field], 2000, vol. 43, pp. 94-101.
  • Horynyn H.L. Metod zhestkostnykh funktsyy v zadachakh rascheta mnohosloynykh sterzhney pry temperaturnykh nahruzkakh [Method stiffness functions in problems of calculation of clad rods with temperature loads]. Matematicheskie metody physichesko-mekhanicheskogo polya [Mathematical methods of physical-mechanical field], 2012, vol. 2, pp. 144-155.
  • Neng-Hus Zhang. Thermoelastic stresses in multilayered beams. Thin Solid Films, 2007, pp. 8402-8406.
  • Velychko O.V. Ploska deformatsiya pruzhnoyi bahatosharovoyi plyty pid diyeyu periodychnoyi systemi navantazhen [Plane strain elastic multilayered plates under the action of the periodic system loads]. Vestnik Dnepropetrovskogo yniversiteta. Serii mekhanika [Bulletin of Dnepropetrovsk University. Series mechanics]. Dnepropetrovsk, Dnepropetrovsk University publishing house, 2004, no. 8, vol. 1, pp.162-170.
  • Velychko I.G. Prostorova termopruzhna deformatsiya bahatosharovoyi [Spatial thermoprene deformation of multilayer framework]. Vestnik Dnepropetrovskogo yniversiteta. Serii mekhanika [Bulletin of Dnepropetrovsk University. Series mechanics], 2004, no. 8, vol. 1, pp.154-161.
  • Velychko I.H. Prostorova ta osesymetrychna termopruzhna deformatsiya bahatosharovoyi osnovy [Spatial and axisymmetric thermoprene deformation of multilayer framework]. Vestnik Dnepropetrovskogo yniversiteta. Serii mekhanika [Bulletin of Dnepropetrovsk University. Series mechanics], 2004, no. 8, vol. 2, pp. 36-43.
  • Tkachenko I.H. Dvomirna mishana zadacha termopruzhnosti dlya bahatosharovoyi osnovy [Two-dimensional mixed problem of thermoelasticity for laminated foundation]. Prikladnye problemy mekhaniki i matematiki [Applied problems of mechanics and mathematics], 2005, vol. 3, pp. 70-78.
  • Kovalenko A.D. Vvedenye v termoupruhost [Introduction to thermoelasticity]. Kyev, Scientific Thought, 1965. 204 p.