Thin elastic inclusions in a transversally isotropic material
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Abstract
We propose a model of thin elastic inclusions that reduces the problem to the treatment of plane surfaces of discontinuity of displacements in a transtropic space. By representing the solution of the equilibrium equations in terms of harmonic functions and applying the technique of integral Fourier transformation, the problem is reduced to the solution of a system of two-dimensional singular integral equations relative to displacement jumps of the discontinuity surfaces. For illustration we consider an ellipsoidal inclusion in a homogeneous uniaxial tension field for which exact solutions of the integral equations are found and expressions for the stresses within the inclusion and in its neighborhood are obtained in explicit form.
Keywords
Fourier Fourier Transformation Integral Equation Exact Solution Harmonic FunctionPreview
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Literature cited
- 1.S. G. Lekhnitskii, Elasticity Theory of an Anisotropic Body [in Russian], Nauka, Moscow (1977).Google Scholar
- 2.Ya. S. Pidstrigach, “Discontinuity conditions on stresses and displacements in a thin-walled isotropic body in a continuum,” Dokl. Akad. Nauk UkrSSR, Ser. A, No. 12, 29–31 (1982).Google Scholar
- 3.V. P. Silovanyuk, “Solution of problem of elasticity theory for a transversally isotropic body with plane surface of discontinuity,” Dokl. Akad. Nauk UkrSSR, Ser. A, No. 2, 63–66 (1987).Google Scholar
- 4.H. A. Elliot, “Axial symmetric stress distribution in allotropie hexagonal crystals,” Proc. Camb. Philos. Soc.,45, 621–630 (1949).Google Scholar
- 5.M. M. Stadnik, “Integrodifferential equations of a three-dimensional problem of elasticity theory for a body with system of thin inclusions,” Fiz.-Khim. Mekh. Mater.,20, No. 1, 15–21 (1984).Google Scholar
- 6.G. P. Cherepanov, R. S. Kocharov, and O. V. Sotkilava, “On a cracklike defect in an elastic plane,” Prikl. Mekh.,13, No. 2, 48–52 (1977).Google Scholar
- 7.M. K. Kassir and G. S. Sih, “Three-dimensional stress around elliptical cracks in transversally isotropic solid,” Eng. Fract. Mech.,1, 327–345 (1968).Google Scholar
- 8.V. V. Panasyuk, M. M. Stadnik, and V. P. Silovanyuk, Concentration of Stresses in Solids with Thin Inclusions [in Russian], Naukova Dumka, Kiev (1987).Google Scholar