<abstract xmlns="http://www.w3.org/1999/xhtml"><p>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.</p></abstract>

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.

Mixed Boundary Value Problem for an Anisotropic Thermoelastic Half-Space Containing Thin Inhomogeneities

Acta Mechanica et Automatica

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

The paper presents a rigorous and straightforward approach for obtaining the 2D boundary integral equations for a thermoelastic half-space containing holes,...

Mixed Boundary Value Problem for an Anisotropic Thermoelastic Half-Space Containing Thin Inhomogeneities

Publié en ligne: 30 janv. 2020

Pages: 238 - 244

Reçu: 16 mai 2019

Accepté: 13 déc. 2019

DOI: https://doi.org/10.2478/ama-2019-0032

Mots clés
thermoelasticity, anisotropic half-space, boundary element method, thin inclusion, crack, stress intensity factors, Stroh formalism

© 2019 Heorhiy Sulym et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Mixed Boundary Value Problem for an Anisotropic Thermoelastic Half-Space Containing Thin Inhomogeneities

Publié en ligne: 30 janv. 2020

Pages: 238 - 244

Reçu: 16 mai 2019

Accepté: 13 déc. 2019

DOI: https://doi.org/10.2478/ama-2019-0032

Mots clésthermoelasticity, anisotropic half-space, boundary element method, thin inclusion, crack, stress intensity factors, Stroh formalism

© 2019 Heorhiy Sulym et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Mots clés
thermoelasticity, anisotropic half-space, boundary element method, thin inclusion, crack, stress intensity factors, Stroh formalism