Determination of thermoelastic state of piecewise inhomogeneous thermosensitive bodies with cylindrical interfaces (Q2808479)

The author proposes a method for determining the thermoelastic state caused by plane one-dimensional temperature fields and surface loads in layered isotropic bodies with cylindrical interfaces. The temperature and coordinate dependences of the elastic modulus, linear expansion coefficients and Poisson coefficients are taken into account. The method involves the solution of integro-algebraic equations with respect to radial displacements. In the case of a cylinder, the equations are obtained from the integral representation of the solution to the problem for ordinary differential equations with generalized derivatives. To this end, the Green function of the elasticity problem for homogeneous cylinder is used. For the layered space with a cylindrical cavity, solid cylinder and solid space the corresponding equations and other relations necessary for determining the thermoelastic state are found by a passage to the limit. The relations for thermal stress determination are given in the case of the corresponding one-layer bodies. A numerical study is conducted for the three-layered cylinders with a functionally graded layer.