2D Green's function of orthotropic two-coating-substrate under a normal line force.

• Green's function of two-layer coating structure provides a theoretical basis for analysis of multicoating problem. • Analytical expressions, expressed as elementary functions, can be easily converted into numerical calculation codes. • Those solutions are the basis for analyzing the two-layer coating under distributed loading with numerical integration. The study of multi-layer coating structure is an important problem in the fields of machinery and materials. In this paper, a two-dimensional theoretical solution of the orthotropic double-coated substrate structure under the normal line force of the free surface is derived. The method in this paper is mainly aimed at orthotropic materials and falls within the scope of linear elasticity. Based on the general solution of two-dimensional orthotropic materials, the harmonic functions with undetermined constants corresponding to each region are constructed. With the equilibrium conditions, surface boundary conditions and interface continuity conditions, the full-field analytical solution (Green's function) expressed in elementary functions is determined with the method of mirror images, which is valuable to solve the full field analytical expression of layered structures for the linear elasticity problem. Compared with the existing theories, the effectiveness and accuracy of the method are verified. In the future, Green's function of the paper is the basis for the numerical integration of distributed loads, which can be used as the code basis for the development of special software to study ultra-precision coatings. [ABSTRACT FROM AUTHOR]