In this paper a recently developed discretization method, which was already used for one-dimensional structures, is shown to be a valid tool for the static and dynamic analysis of plates. The stiffness matrix and the mass matrix of the structure are calculated, so that a straight forward application of the Lagrange equation allows us to obtain the equation of motion.

The method seems to have two interesting features: it is very easy to allow for non-uniform thickness and elastic constraints at the edges, and, from the computational point of view, it is possible to take full advantage from the particular structure of the matrices. In fact, the mass matrix is diagonal, and the stiffness matrix has a well-defined banded form.

First of all, the discretization method is briefly described, and the lagrangian coordinates are defined. Then, the bending strain energy is calculated in detail, with particular emphasis on the boundary conditions. The torsional strain energy of the panels, and the axial strain energy of the Winkler soil are also calculated, to obtain the global stiffness matrix of the structure. The mass matrix is immediately obtained by lumping the mass at discrete points.

Some numerical examples end the paper, in which comparisons with some known results of the literature are offered, together with the convergence curves.

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