MODELING OF THE DEFORMED STATE OF MESH PLATES USING COMPLEX CONFIGURATION

Abstract

In this article, the deformed state processes of mesh plates with complex configurations are modeled mathematically. Specifically, a computational algorithm comprising of the R-function methods of V.L. Rvachev (RFM) and the Bubnov-Galerkin method is applied. The mathematical model describes the behavior of mesh plates under external loads by representing equilibrium equations in a Cartesian coordinate system. The solution structures are built using constructive RFM approaches, and discretization is carried out with the Bubnov-Galerkin technique. Computational experiments are conducted to determine the deformation characteristics of mesh plates with intricate geometries. The proposed approach significantly reduces the computational complexity and increases the accuracy of results when compared to conventional analytical methods. Furthermore, the algorithm enables numerical analysis of rhomboidal and hexagonal plate configurations under different boundary conditions. These results may be utilized in designing lightweight yet structurally efficient components in aerospace, civil, and mechanical engineering.