Application of numerical-analytical boundary element method to the calculation of orthotropic plates

Abstract

The solution of the problem of bending of orthotropic plates using numerical-analytical boundary element method is given. To reduce the dimensionality of the problem variational method of Kantorovich-Vlasov is used. The analytical expressions of the fundamental functions, Green’s functions and components of the load for all possible roots of the characteristic equation corresponding to the differential equation of plate bending are obtained. Examples of calculation are considered. Square plate OSB was considered with two versions of the boundary conditions. For each option two types of external load were considered: concentrated force applied at the center of the plate and the load uniformly distributed over the entire surface. Bending and tension in some characteristic points had to be determined. Numerical implementation of the algorithm for calculating is held in package SKILAB. The proposed approach provides a solution to the problem of bending of rectangular orthotropic plate with any character of external loads and fixing conditions of plate edges.