Numerical-analytical method to determine the stress state of an elastic rectangular plate

A numerical-analytical method for solving the plane problem of elasticity is proposed. Systems of nonorthogonal functions are used. The method involves the minimization of a quadratic form that is equal to the integral of the sum of squared residuals of the solution and given forces. An explicit expression for stresses is derived. Bessel's inequality and the convergence of the solution are proved. The accuracy of the boundary conditions is estimated. The stress and strain distribution in the plate depending on the maximum magnitude of distributed forces and the size of their localization area is analyzed numerically. New quantitative and qualitative features of the stress distribution in the plate are established.