Thermoelasticity of solids containing thread-like inhomogeneities. I. Nondeformable thread-like inclusions

Abstract

The paper presents a novel approach for analytic modeling and numerical analysis of spatial problems of thermoelasticity for isotropic solids containing thread-like nondeformable inhomogeneities. The inhomogeneity is removed from consideration as a geometric object, and its influence on the continuum is replaced by sought functions (of heat flux and mechanical forces) distributed along some line (the midline of inhomogeneity) inside the medium. The corresponding integral equations are derived and it is shown that the boundary conditions in this case results in the ill-posed boundary-value problem. A method for regularization of these integral equations is proposed, which allows obtaining an approximate (with arbitrary predetermined accuracy) solution of the problems of thermoelasticity for solids with thread-like inhomogeneities. An analytical approach to solving the obtained equations on the basis of Legendre polynomials is developed. Based on the performed numerical analysis the paper substantiates reliability, convergence and accuracy of the proposed method for the analysis of thermoelastic equilibrium of solids with nondeformable thread-like inhomogeneities.