Thermoelastic Analysis of Solids with Thread-Like Inhomogeneities

The book presents a novel approach for analysis of thermoelasticity problems for solids with deformable thread-like (wired textile) 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.