Computational method for solving boundary problems of the theory of elasticity using non-orthogonal systems of functions

Abstract

A complete system of functions based on non-orthogonal sinuses and cosine was constructed. It has been proven that the continuous function can be approximated by a finite number of non-orthogonal functions in such a way that this amount does not enter the selected function of the non-orthogonal base. The numerical experiment confirmed the high accuracy of approximations of continuous functions by a small number of non-orthogonal functions. The flat problem of the theory of elasticity for the plate with variable elastic characteristics is considered. This equation is simplified when the characteristics of the material change insignificantly depending on the spatial coordinates. A new method of solving a boundary value problem has been developed for the fourth-order equation with variable coefficients. The proposed method is based on the separation of the stress state of the plate from an inhomogeneous material to the main and indignant state, the use of complete systems of non-orthogonal functions and a generalized quadratic form. A criterion under which the constructed approximate decision coincides with the exact solution was found.