N. Khomasuridze

Effective Solution of a Class Of Boundary Value Problems of Thermoelasticity
in Generalized Cylindrical Coordinates

A class of static boundary value problems of thermoelasticity is effectively solved for bodies bounded by coordinate surfaces of generalized cylindrical coordinates $\rho,$ $\alpha,$ $z$ ($\rho$, $\alpha$ are orthogonal curvilinear coordinates on the plane and $z$ is a linear coordinate). Besides in the Cartesian system of coordinates some boundary value thermoelasticity problems are separately considered for a rectangular parallelepiped. An elastic body occupying the domain $\Omega=\{\rho_0<\rho <\rho_1,\, \alpha_0<\alpha<\alpha_1,\,0<z<z_1\},$ is considered to be weakly transversally isotropic (the medium is weakly transversally isotropic if its nine elastic and thermal characteristics are correlated by one or several conditions) and non-homogeneous with respect to $z$.

Thermoelasticity, symmetry condition, curvilinear coordinates, Laplace field, Fourier method.

MSC 2000: 74B05, 74F05