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Plane mixed thermoelasticity problem for a semi-strip. (Ukrainian, English) Zbl 1363.74024

Mat. Metody Fiz.-Mekh. Polya 58, No. 4, 87-98 (2015); translation in J. Math. Sci., New York 228, No. 2, 105-121 (2018).
The authors study the stress state of a semi-strip. Smooth contact conditions are given on one lateral side of the semi-strip while coupling conditions are given on the other side, and the external normal loading and temperature are applied to its end. By means of the method of integral transforms, the initial problem is reduced to a one-dimensional vector boundary value problem. The apparatus of matrix differential calculus and Green’s matrix function are applied to reduce the obtained problem to a singular integral equation with respect to the derivative of displacements at the semi-strip end. The equation is solved by the method of orthogonal polynomials. Stress and displacement fields in the semi-strip are analyzed numerically. Zones of tensile stresses on the lateral side of the semi-strip are determined and conditions of their occurrence are established.

MSC:

74F05 Thermal effects in solid mechanics
74A15 Thermodynamics in solid mechanics
74K35 Thin films
74S30 Other numerical methods in solid mechanics (MSC2010)
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[1] N. D. Vaisfel’d, G. Ya. Popov, and A. V. Reut, “Axisymmetric problem of stressed state for a twice truncated cone,” Mat. Met. Fiz.-Mekh. Polya,56, No. 1, 185-196 (2013); English translation:J. Math. Sci., 201, No. 2, 229-244 (2014). · Zbl 1313.74011
[2] A. I. Veremeichik, V. V. Garbachevskii, and V. M. Khvisevich, “On the solution of plane boundary-value problems of thermoelasticity of inhomogeneous bodies by the potential method,” Teor. Prikl. Mekh.: Mezhdunarod. Nauch.-Tekh. Zh., Issue 30, 184-189 (2015).
[3] G. Gabrusev, “Problem of thermoelasticity for a transversally isotropic layer with circular separation lines of boundary conditions on its surface,” Visn. Ternopil. Nats. Tekh. Univ., 73, No. 1, 57-67 (2014).
[4] I. S. Gradshtein and I. M. Ryzhik, Tables of Integrals, Sums, Series, and Products [in Russian], Fizmatgiz, Moscow (1963).
[5] T. V. Denisova, V. S. Protsenko, and Ya. P. Buz’ko, “Problem of stationary heat conduction for a semistrip with circular hole,” Otkryt. Inform. Komp’ut. Integr. Tekhnol., No. 42, 159-163 (2009).
[6] W. Kecs and P. P. Teodorescu, Introducere în Teoria Distribuţiilor cu Aplicaţii in Tehnică, Editura Tehnică, Bucureşti (1975).
[7] G. S. Kit and M. G. Krivtsun, Plane Problems of Thermoelasticity for Bodies with Cracks [in Russian], Naukova Dumka, Kiev (1983). · Zbl 0517.73006
[8] G. S. Kit and R. M. Martynyak, “Thermoelasticity of structures with heat-conducting cracks,” Mat. Met. Fiz.-Mekh. Polya, 46, No. 1, 11-20 (2003). · Zbl 1108.74300
[9] G. V. Kolosov, Application of Complex Variables in the Theory of Elasticity [in Russian], ONTI, Leningrad-Moscow (1935).
[10] G. B. Kolchin, Sh. N. Plyat, and N. Ya. Sheinker, Some Problems of Thermoelasticity for Rectangular Domains [in Russian], Shtiintsa, Kishinev (1980).
[11] Yu. M. Kolyano and L. M. Zatvarskaya, “The method of continuation of functions in a problem of thermoelasticity for a semistrip,” Izv. Vyssh. Uchebn. Zaved., Mat., No. 8, 84-86 (1987); English translation:Sov. Math., 31, No. 8, 109-111 (1987). · Zbl 0850.73035
[12] R. M. Kushnir, M. M. Nykolyshyn, U. V. Zhydyk, and V. M. Flyachok, “Modeling of thermoelastic processes in heterogeneous anisotropic shells with initial deformations,” Mat. Met. Fiz.-Mekh. Polya, 53, No. 2, 122-136 (2010); English translation:Math. Sci., 178, No. 5, 512-530 (2011). · Zbl 1230.74057
[13] R. M. Kushnir, M. M. Nykolyshyn, U. V. Zhydyk, and V. M. Flyachok, “Thermomechanical model of inhomogeneous anisotropic shells with initial strains,” Dop. Nats. Akad. Nauk Ukr., No. 11, 45-50 (2010). · Zbl 1224.74076
[14] N. I. Muskhelishvili, Some Basic Problems of the Mathematical Theory of Elasticity, Springer, Noordhoff-Gröningen (1977).
[15] W. Nowacki, Thermoelasticity, Pergamon Press, Oxford (1962).
[16] V. V. Novozhilov, Theory of Elasticity, Pergamon Press, Oxford (1961). · Zbl 0098.37604
[17] P. F. Papkovich, Theory of Elasticity [in Russian], Oborongiz, Leningrad-Moscow (1939). · JFM 65.0922.02
[18] G. Ya. Popov, Selected Works [in Russian], Vol. 1, VMV, Odessa (2007).
[19] G. Ya. Popov, Concentration of Elastic Stresses Near Punches, Cuts, Thin Inclusions, and Reinforcements [in Russian], Nauka, Moscow (1982).
[20] G. Ya. Popov, “New transforms for the resolving equations in elastic theory and new integral transforms, with applications to boundary-value problems of mechanics,” Prikl. Mekh., 39, No. 12, 46-73 (2003); English translation:Int. Appl. Mech., 39, No. 12, 1400-1424 (2003). · Zbl 1130.74324
[21] G. Ya. Popov, Exact Solutions of Some Boundary-Value Problems of the Mechanics of Deformable Solids [in Russian], Astroprint, Odessa (2013).
[22] G. Ya. Popov, S. A. Abdymanapov, and V. V. Efimov, Green Functions and Matrices of One-Dimensional Boundary-Value Problems [in Russian], Rauan, Almaty (1999).
[23] G. Ya. Popov, V. V. Reut, and N. D. Vaisfel’d, Equations of Mathematical Physics. Method of Integral Transforms: A Textbook [in Russian], Astroprint, Odessa (2005).
[24] Ya. S. Uflyand, Integral Transforms in Problems of the Theory of Elasticity [in Russian], Nauka, Leningrad (1968).
[25] L. A. Fil’shtinskii and A. V. Bondar, “Problem of coupled thermoelasticity for a half layer with a tunnel cavity: an antisymmetric case,” Prikl. Mekh., 44, No. 10, 28-36 (2008); English translation:Int. Appl. Mech., 44, No. 10, 1098-1105 (2008). · Zbl 1187.74046
[26] A. D. Shamrovskii and G. V. Merkotan, “Dynamic problem of generalized thermoelasticity for an isotropic half space,” Vost.-Evrop. Zh. Peredov. Tekhnol., 3, No. 7(51), 56-59 (2011).
[27] M. S. Abou-Dina and A. F. Ghaleb, “On the boundary integral formulation of the plane theory of thermoelasticity (analytical aspects),” J. Therm. Stresses, 25, No. 1, 1-29 (2002).
[28] R. V. N. Melnik, “Discrete models of coupled dynamic thermoelasticity for stress-temperature formulations,” Appl. Math. Comput., 122, No. 1, 107-132 (1999). · Zbl 1058.74029
[29] P. P. Teodorescu, Probleme Plane în Teoria Elasticităţii, Vol. I, Editura Academiei Republicii Populare Romane, Bucureşti (1960), Vol. II, Editura Academiei Republicii Socialiste România, Bucureşti (1966). · Zbl 0096.09201
[30] Yu. Tokovyy and C.-C. Ma, “An explicit-form solution to the plane elasticity and thermoelasticity problems for anisotropic and inhomogeneous solids,” Int. J. Solids Struct., 46, No. 21, 3850-3859 (2009). · Zbl 1176.74024
[31] R. Xia, Ya. Guo, and W. Li, “Study on generalized thermoelastic problem of semiinfinite plate heated locally by the pulse laser,” Int. J. Eng. Pract. Res., 3, No. 4, 95-99 (2014).
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