THERMOELASTIC EQUILIBRIUM OF BODIES IN GENERALIZED CYLINDRICAL COORDINATES

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Abstract

ABSTRACT

Using the method of separation of variables, an exact solution is constructed for some boundary value and boundary-contact problems of thermoelastic equilibrium of one- and multilayer bodies bounded by the coordinate surfaces of generalized cylindrical coordinates ρ, α, z. ρ, α are the orthogonal coordinates on the plane and z is the linear coordinate. The body, occupying the domain Ω = {ρ0 < ρ < ρ1, α0 < α < α1, 0 < z < z1}, is subjected to the action of a stationary thermal field and surface disturbances (such as stresses, displacements, or their combinations) for z = 0 and z = z1. Special type homogeneous conditions are given on the remainder of the surface. The elastic body is assumed to be transversally isotropic with the plane of isotropy z = const and nonhomogeneous along z. The same assumption is made for the layers of the multilayer body which contact along z = const.

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