Abstract
The article deals with the plane stress state of elastic thin orthotropic plates in the form of irregular triangles; orthotropy is assumed to be both physical and constructive. The research method used is the numerical finite difference method using a grid of scalene triangles. For such a grid, the authors have obtained resolving finite difference equations; in difference form they have obtained correct records of boundary conditions on the plate edges through the stress function based on the frame analogy taking into account the material orthotropy; typical finite difference equations are presented that allow solving problems of the plane stress state of triangular plates with a high degree of automation. As an illustrative example, a numerical calculation of triangular plates with a grid density of N = 8 is performed using a computer; the result of the study is the analysis of the stress state in the calculated grid nodes with a wide variation in the values of the a lateral edges angles of inclination to the base of the triangle, the orthotropy coefficients. The results obtained demonstrate the feasibility and effectiveness of using a finite difference scheme on irregular triangular grids for analyzing the plane stress state of orthotropic plates. The developed approach provides a solid theoretical foundation for modeling stress distributions in structures with geometric and material anisotropy. The flexibility of the method allows adapting it to a wide range of boundary conditions and geometric configurations, laying the groundwork for further analytical development and integration into engineering software tools for structural analysis.