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.

本文提出了一种新方法，用于对包含螺纹状不可变形不均匀性的各向同性固体的热弹性空间问题进行解析建模和数值分析。不均匀性从作为几何对象的考虑中去除，它对连续体的影响被沿着介质内的某条线（不均匀性的中线）分布的（热通量和机械力的）寻求函数所取代。推导了相应的积分方程，结果表明这种情况下的边界条件导致了不适定边界值问题。提出了对这些积分方程进行正则化的方法，该方法允许获得具有螺纹状不均匀性的固体的热弹性问题的近似（具有任意预定精度）解。开发了一种基于勒让德多项式求解所获得方程的分析方法。基于所进行的数值分析，本文证实了所提出的用于分析具有不可变形螺纹状不均匀性固体的热弹性平衡的方法的可靠性、收敛性和准确性。