A Universal Method for Solving the Problem of Bending of Plates of Any Shape

Abstract

This paper presents a universal algorithm for solving boundary value problems of bending plates of arbitrary shape. To solve the problem of bending, the method of sources and sinks is used. According to this method, sources and sinks are distributed continuously along a line located outside the area occupied by the plate and similar to the contour of the original plate. By choosing their powers, the conditions at the plate boundary are satisfied.In this paper, we use an elementary solution for the problem of bending a round supported plate and fundamental solutions from a unit transverse force and moment concentrated at a point. Mathematical expressions corresponding to various boundary conditions are given. The boundary value problem is reduced to a system of integral equations. To obtain a stable solution to the system of integral equations, the regularization method with minimization of the Tikhonov functional is applied, the numerical implementation of which will lead to systems of algebraic equations. An algorithm for solving the problem in the MATLAB system is proposed.