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Influence of imperfect interface of anisotropic thermomagnetoelectroelastic bimaterial solids on interaction of thin deformable inclusions

Sulym Heorhiy, Vasylyshyn Andrii, Pasternak Iaroslav

Acta Mechanica et Automatica

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2022

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Vol. 16, no. 3

242--249

EN

This work studies the problem of thermomagnetoelectroelastic anisotropic bimaterial with imperfect high-temperature conducting coherent interface, whose components contain thin inclusions. Using the extended Stroh formalism and complex variable calculus, the Somigliana-type integral formulae and the corresponding boundary integral equations for the anisotropic thermomagnetoelectroelastic bimaterial with high-temperature conducting coherent interface are obtained. These integral equations are introduced into the modified boundary element approach. The numerical analysis of new problems is held and results are presented for single and multiple inclusions.

2

Mixed boundary value problem for an anisotropic thermoelastic half-space containing thin inhomogeneities

Sulym Heorhiy, Pasternak Iaroslav, Smal Mariia, Vasylyshyn Andrii

Acta Mechanica et Automatica

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2019

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Vol. 13, no. 4

238--244

EN

The paper presents a rigorous and straightforward approach for obtaining the 2D boundary integral equations for a thermoelastic half-space containing holes, cracks and thin foreign inclusions. It starts from the Cauchy integral formula and the extended Stroh formalism which allows writing the general solution of thermoelastic problems in terms of certain analytic functions. In addition, with the help of it, it is possible to convert the volume integrals included in the equation into contour integrals, which, in turn, will allow the use of the method of boundary elements. For modelling of solids with thin inhomogeneities, a coupling principle for continua of different dimensions is used. Applying the theory of complex variable functions, in particular, Cauchy integral formula and Sokhotski–Plemelj formula, the Somigliana type boundary integral equations are constructed for thermoelastic anisotropic half-space. The obtained integral equations are introduced into the modified boundary element method. A numerical analysis of the influence of boundary conditions on the half-space boundary and relative rigidity of the thin inhomogeneity on the intensity of stresses at the inclusions is carried out.

3

Heat conduction in anisotropic medium with perfectly conductive thread-like inclusions

Sulym Heorhiy, Ilchuk Nataliia, Pasternak Iaroslav

Acta Mechanica et Automatica

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2019

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Vol. 13, no. 4

251--254

EN

The paper presents a novel approach for the analysis of steady-state heat conduction of solids containing perfectly conductive thread-like inhomogeneities. Modelling of a thread-like heat conductive inhomogeneity is reduced to determination of density of heat distributed along a spatial curve, which replaces the inclusion. Corresponding boundary integral equations are obtained for anisotropic solids with thread-like inclusions. Non-integral terms are computed in a closed form. It is shown that, nevertheless the singularity of the equation is 1/r, it is hypersingular, since the kernel is symmetric. Boundary element approach is adopted for solution of the obtained equations. Numerical example is presented for a rectilinear conductive thread, which verifies derived boundary integral equations.