On the calculation of anisotropic plates by the numerical-analytical boundary elements method

Abstract

The differential equation for anisotropic plate bending is not always solvable analytically due to mathematical difficulties. Local loads, and the conditions for securing the plate’s edges have a significant impact. Analytical processes based on numbers are often utilized, but there is no universal methodology. This study aimed to investigate the bendable anisotropic plates using the numerical-analytic boundary element method. Even though the numerical-analytic boundary element approach was only established recently, it has already proven beneficial in tackling various issues [15, 16]. The method allows constructing a central system of solutions for the differential equations of isotropic and orthotropic plate bending [15, 16] without limitation on load properties or fixing circumstances. The Kantorovich-Vlasov variation technique reduces two-dimensional to a one-dimensional problem. It is recommended that a dynamic or static function of the lateral deflection distribution be selected. In general form, characteristic equations and fundamental functions are given. As a result, the problem of bending an anisotropic plate managed to four different root combinations of the equation’s characteristic, implying that 64 primary function analytical expressions will give the total solution. The numerical-analytic approximation algorithm for boundary elements [15, 16, 18, 19] can be used to determine all principal functions, generate Green’s functions, and so on after solving the Cauchy problem to determine constants. The proposed method solves the problem of anisotropic rectangular plate bending under homogeneous and inhomogeneous constraints, regardless of the load applied.