THE APROXIMATE ROOTS FOR THE RECTANGULAR PLATES USING THE VARIATIONAL RITZ METHOD

The energy methods for solutions of boundary value problems of plates, subjected to static loading have already been study from the XVIII century. Using the energy methods for solution of boundary value problem of plates represent an important method to find approximate solutions to static or dynamic plate problems when exact solutions are unavailable or too cumbersome for practical application. Also there are well known for the Ritz method the solution who use the product of beam shape (trigonometrycal functions). For this case we choose for study the all sides clamped rectangular plate having a static loading. The Ritz methods consist in selecting a suitable infinite series expression of the shape functions who satisfies the geometrical boundary conditions, and the differential equation motion is not required. The unknown coefficients in shape functions equations are obtained from the minimum total energy principle. We use for the displacement expression the approximate function