Literature cited
K. R. Chobanyan and A. S. Khachikyan, “Plane strain state of an elastic body with a thin-wall flexible inclusion,” Izv. Akad. Nauk ArmSSR, No. 6, 19–29 (1967).
D. V. Grilitskii and G. T. Sulim, “A periodic problem for an elastic plane with thinwall inclusions,” Prikl. Mat. Mekh.,39, No. 3, 520–529 (1975).
R. Chez, “Mechanical equilibrium and the form of small crystals,” Helvetica Phys. Acta,41, No. 3, 287–309 (1968).
O. V. Sotkilava and G. P. Cherepanov, “Some problems of the heterogeneous theory of elasticity,” Prikl. Mat. Mekh.,38, No. 3, 539–550 (1974).
V. V. Panasyuk, O. E. Andreikiv, and M. M. Stadnik, “Elastic equilibrium of an unrestricted body with a fine inclusion,” Dopov. Akad. Nauk Ukr. RSR Ser. A, No. 7, 636–639 (1976).
Ya. S. Pidstrigach, “The effect of the level of stresses and displacements on a thinwalled elastic inclusion in a solid environment,” Dopov. Akad. Nauk Ukr. RSR Ser. A, No. 12, 29–31 (1982).
D. V. Grilitskii, V. K. Opanasovich, and L. O. Tisovskii, “Elastic state of a plate with a circular disk and a rectilinear inclusion,” Prikl. Mat. Mekh., No. 6, 993–1000 (1982).
V. M. Aleksandrov and S. M. Mkhitaryan, Contact Problems of Bodies with Thin Coatings and Interlayers [in Russian], Nauka, Moscow (1983).
S. K. Kanaun, “A thin defect in a homogeneous elastic medium,” in: Investigations into Theoretical Fundamentals of Calculations of Engineering Structures, a Collection of Works, Leningrad Engineering and Constructional Institute, Leningrad (1983), pp. 75–84.
A. B. Movchan and S. A. Nazarov, “Asymptotics of the stress-strain state in the vicinity of the spatial peak-shaped inclusion,” Mekh. Kompozitn. Mater., No. 5, 792–800 (1985).
V. V. Panasyuk, A. E. Andreikiv, M. M. Stadnik, and Ya. Yu. Morozovich, “Limiting equilibrium state of elastoplastic bodies with thin inclusions subjected to the effect of pores and temperature factors,” in: Proceedings of 3rd All-Union Conference of Mechanics of Heterogeneous Structures, Lvov, September 6–8, 1983, Naukova Dumka, Kiev (1983), pp. 170–171.
M. M. Stadnik, “Integrodifferential equations of the three-dimensional problem of elasticity theory for a solid with a system of thin inclusions,” Fiz.-Khim. Mekh. Mater., No. 1, 15–21 (1984).
M. V. Khai, “Integral equations of the problem for determining loads in a body with a fine peak-shaped inclusion,” Dopov. Akad. Nauk Ukr. RSR Ser. A, No. 3, 43–46 (1984).
M. V. Khai, “Determination of the temperature fields and stresses in bodies with fine heat-conducting inclusions,” Dopov. Akad. Nauk. Ukr. RSR Ser. A, No. 11, 48–52 (1984).
M. M. Stadnik and A. E. Andreikiv, “Strength of materials containing systems of thin inclusions,” Fiz.-Khim. Mekh. Mater., No. 1, 29–35 (1986).
M. M. Stadnik and Ya. Yu. Morozovich, “A thermoelastic problem for a convex polyhedron with a system of thin inclusions,” Fiz.-Khim. Mekh. Mater., No. 2, 39–43 (1986); No. 3, 89–96 (1986).
G. P. Cherepanov, Mechanics of Brittle Fracture [in Russian], Nauka, Moscow (1974).
V. V. Panasyuk, Limiting Equilibrium of Brittle Bodies with Cracks [in Russian], Naukova Dumka, Kiev (1968).
V. V. Panasyuk, M. P. Savruk, and A. P. Datsyshin, Distribution of Stresses Around Cracks in Plates and Shells [in Russian], Naukova Dumka, Kiev (1976).
P. C. Paris and G. C. Shih, “Stress analysis of cracks,” in: Fracture Toughness Testing and its Applications, ASTM STP No. 381, Philadelphia (1965), pp. 30–81.
N. I. Muskhelishvili, Some Main Problems of Mathematical Theory of Elasticity [in Russian], Nauka, Moscow (1966).
G. T. Sulim, “The effect of the form of a thin-wall inclusion on stress concentration in a plate,” Fiz.-Khim. Mekh. Mater., No. 3, 64–68 (1981).
G. Ashelby, Continual Dislocation of Theory [Russian translation], IL, Moscow (1983).
N. J. Hardiman, “Elliptic elastic inclusion in an infinite plate,” Q. J. Mech. Appl. Math.,2, No. 2, 25–43 (1954).
G. P. Cherepanov, Fracture Mechanics of Composite Material [in Russian], Nauka, Moscow (1983).
G. I. Bil'chenko and S. I. Gubenko, Nonmetallic Inclusions and Quality of Steel [in Russian], Tekhnika, Kiev (1980).
I. P. Volchok, “Examination of the processes of deformation and failure of cast steel,” Fiz.-Khim. Mekh. Mater., No. 2, 88–91 (1976).
L. T. Berezhrnitskii, V. V. Panasyuk, and N. G. Stashchuk, Interaction between Hard Linear Inclusions and Cracks in the Deformed Solid [in Russian], Naukova Dumka, Kiev (1983).
M. K. Kassir and G. C. Sih, “Some three-dimensional inclusion problems in elasticity,” Int. J. Solids Struct.,4, 225–241 (1968).
V. P. Silovanyuk, “A hard plate-shaped inclusion in the elastic space,” Fiz.-Khim. Mekh. Mater., No. 5, 80–84 (1984).
R. N. Edwards, “Stress concentration around spheroidal inclusions and cavities,” Trans. ASME, J. Appl. Mech. Sec.,75, No. 1, 19–30 (1951).
Yu. N. Podil'chuk, Three-Dimensional Problems of Elasticity Theory [in Russian], Naukova Dumka, Kiev (1979).
Author information
Authors and Affiliations
Additional information
Translated from Fiziko-Khimicheskaya Mekhanika Materialov, No. 1, pp. 53–65, January–February, 1988.
Rights and permissions
About this article
Cite this article
Stadnik, M.M. A method of approximate solution of a three-dimensional elastic problem for a body with a thin inclusion. Mater Sci 24, 49–60 (1988). https://doi.org/10.1007/BF00722580
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF00722580