To solve many technical and economic problems, thin-walled coated structures are created. Coatings are usually formed directly on curved surfaces of structural elements and have a complex structure and complex surface relief. At the same time, some coatings are almost impossible to dismember from the substrate. An approach to study the stiffness properties of non-separable coatings on a thin-walled substrate of complex shape, based on the fact that the tensile stiffness of the coating is equal to the difference in the stiffness of the substrate with the coating minus the stiffness of the thin-walled substrate. The experimental-theoretical method is used to estimate the stiffness. A formula for estimating the Poisson’s ratio for the initially flat version of the substrate in the elastic formulation for cases of small deflection is obtained. An example of an assessment of the hardness of the coating with the flat substrate. It was found that the stiffness of the coating is 53.3 % of the substrate stiffness. The approach is effective in the study of the mechanical properties of coatings, especially when the stiffness of the coating and the substrate of the same order.

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The main stages of the birth of thin-walled structures, changes in their relative thickness and mass of a unit area are given; ways of creating perfect thin-walled structures are indicated. The problems arising during the operation of thin-walled structures of complex geometry, as well as approaches and methods of their calculation are noted. To ensure trouble-free operation of a thin-walled structure with a thin-layer coating, under load and exposed to physical fields and environments, it is necessary to correctly diagnose the condition of structural elements. The spline variant of the finite element method in two-dimensional (SV FEM-2) and three-dimensional (SV FEM-3) productions is noted, as well as the synthesis of these variants - SV FEM-2 + SV FEM-3. The combination of the idea of parametrization of the entire domain and approximation of the desired variables within the element by Hermitian cubic splines makes it possible to obtain high-precision consistent finite elements. The developed variants of the finite element method make it possible to evaluate the stress-strain state of structures of complex geometry, including the calculation of multilayer, thin-walled structures with coating and local defects, as well as to take into account specific surface properties other than those of the main array. Studies of stress concentration near local depressions are considered. Two-dimensional experimental and theoretical methods are noted for evaluating the stiffness properties and adhesion of thin-walled, thin-layer and composite structural elements of complex structure, which, along with a distributed complex structure, may have distributed defects. The developments were used in solving specific tasks of a number of enterprises.