INVESTIGATION OF THE DISTRIBUTION OF STRESSES IN A RECTANGULAR PLATE UNDER THE ACTION OF DISTRIBUTED LOADS

摘要

We propose a new numerical-analytic method for the solution of a plane problem of the theory of elasticity based on the application of systems of nonorthogonal functions. The method is based on the minimization of a quadratic form equal to the integral of the sum of squares of the discrepancy of the obtained solution and given forces. We establish the representation of a stress function in the form of a series in eigenfunctions and prove the Bessel inequality and the convergence of the solution of the obtained infinite system of equations. The accuracy of satisfying of the boundary conditions is estimated and the numerical analysis of the distribution of stresses and strains in the plate is performed. New quantitative and qualitative features of the distribution of stresses are established.