Abstract. The thermoelastic state of a composite cylinder is analyzed. The classical generalized problems defined on classes of discontinuous functions are presented. The explicit expressions are obtained for residual gradients (using the solution of direct and adjoint problems) for the implementation of Alifanov’s gradient methods; the functions of finite element method are used to construct highly accurate computation schemes for the numerical sampling of direct and adjoint problems. The numerical results for some model examples are presented.

Keywords: mathematical modeling, thermoelastic state, cylindrical composite body, finite element method, discontinuous solution, gradient method of identification.