The fundamental relations of the quasi-static problem of thermoelasticity are written for a finite layered orthotropic cylindrical shell of an antisymmetric structure. Under convective heat transfer on the surfaces of this shell and under a linear dependence of temperature on the transverse coordinate, the basic system of equations for the integral characteristics of temperature is given. The method is proposed for solving the formulated problems of thermoelasticity and thermal conductivity, using the double finite integral Fourier transform with respect to the corres
For rectangular layered shallow cylindrical shells of irregular structure, the quasi-static problem of unbound thermoelasticity is formulated. As a mathematical model, the equations of the shear theory of shallow shells of Timoshenko type are used. The closed solution for the formulated problem is found by the methods of integral transformations. The distribution of temperature, displacements, forces and moments in a two-layer cylindrical shell under local convective heating is analyzed numerically.