The Navier solution for partly loaded rectangular plate

The Navier solution for deflection function in the problem of bending of a rectangular simply supported plate is studied. The plate is supposed to be loaded by a uniform pressure distributed on the rectangle with the sides, parallel to the sides of the plate. The author brings and uses his universal method, which belongs to the classical theory of functions. It is proved that: a) all the derivatives of the Navier solution of biharmonic operator are continuous functions in set $E$, which coincides with subtraction from closed rectangle $G$ of the plate the lines passing through the sides of the rectangle of the load application b) In $E$ these derivatives can be calculated by differentiating the Navier series term by term under both symbols of summing. The cutting forces in repeated series of accelerated convergence are given.