**N. Khomasuridze**

## Effective Solution of a Class Of Boundary Value
Problems of Thermoelasticity

in Generalized Cylindrical Coordinates

**Abstract:**

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 $z$.

**Keywords:**

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

**MSC 2000:** 74B05, 74F05