No abstract

No 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 = {ρ 0 < ρ < ρ 1, α 0 < α < α 1, 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.

An exact solution of the boundary value problems of thermoelastic equilibrium of a homogeneous isotropic rectangular parallelepiped is constructed. The parallelepiped is affected by a stationary thermal field and surface disturbances, in particular, on each side of the rectangular parallelepiped the following parameters are defined: a normal component of the displacement vector and tangential stresses (nonhomogeneous symmetry conditions) or normal stress and tangential stresses (nonhomogeneous antisymmetry conditions). The solution of the problems is constructed in series using the method of separation of variables.

No abstract