Studying the material orthotropy effect under the plane stress state of triangular plates

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.