Abstract
Integral representations of the components of the displacement vector and the stress tensor and the corresponding system of boundary integral equations are derived for a piecewise-homogeneous body. A numerical scheme is developed that allows for the specific behavior of the stress fields in the neighborhood of the corner points of the inclusions. As an example, we consider the thermally stressed state of an elastic half-plane with inclusions of various shapes.
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References
V. G. Balan, Analysis of the Thermally Stressed State of Plane Piecewise-Homogeneous Bodies [in Russian], thesis, Kiev (1989).
P. Benerjee and R. Butterfield, Boundary Element Methods in Applied Science [Russian translation], Moscow (1984).
C. Brebbia, J. Telles, and L. Vroubel, Boundary Element Methods [Russian translation], Moscow (1987).
V. S. Vladimirov, Generalized Functions in Mathematical Physics [in Russian], Moscow (1979).
V. D. Kupradze, Potential Methods in Elasticity Theory [in Russian], Moscow (1963).
V. I. Lavrenyuk, "Solving the spatial quasi-static problem of thermoelasticity for piecewise-homogeneous bodies," Izv. Akad. Nauk SSSR, Mekh. Tverd. Tela, No. 3, 63–69 (1979).
V. I. Lavrenyuk, "Solving problems of thermomechanics of piecewise-homogeneous bodies," in: Mechanics of Nonhomogeneous Structures [in Russian], Kiev (1986), pp. 117–122.
V. A. Lomakin, Elasticity Theory of Nonhomogeneous Bodies [in Russian], Moscow (1976).
N. I. Muskhelishvili, Singular Integral Equations [in Russian], Moscow (1968).
V. Novatskii, Elasticity Theory [in Russian], Moscow (1975).
K. S. Chobanyan and S. Kh. Gevorkyan, "Behavior of the stress field near the corner point of the contact line in the problem of planar strain of a composite elastic body," Izv. Akad. Nauk Arm. SSR, Mekhanika,24, No. 5, 16–24 (1971).
Additional information
Kiev University. Translated from Vychislitel'naya i Prikladnaya Matematika, No. 75, pp. 87–98, 1991.
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Lavrenyuk, V.I., Balan, V.G. Boundary element methods in problems of thermoelasticity for piecewise-homogeneous bodies. J Math Sci 72, 3120–3128 (1994). https://doi.org/10.1007/BF01259483
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DOI: https://doi.org/10.1007/BF01259483