Calculus of Long Rectangle Plate Articulated on Both Long Sides Charged with a Linear Load Uniformly Distributed on a Line Parallel to the Long Borders through the Transfer-Matrix Method

The Transfer-Matrix Method is very special and interesting for a lot of industrial fields. This paper presents a study for an application of rectangular long plate articulated at the two long borders and charged with an uniform linear load, that act on a line parallel to the long sides. The long rectangular plate is discretized in unit beams, a beam has width equal to the unit, thickness equal to the plate thickness and length equal to the plate width. The study is made for the unit beam in two cases: the first case, in which the load acts in a certain section x0 and the second case, a particularization of the first case, that is: the concentrated vertical force acts in the middle of the beam opening. All the elements for all state vectors for all the sections of the beam can be calculated and the stresses and the deformations in all sections of the beam too. By extension, the stresses and strains are calculated for the long rectangular plate articulated on both long borders. This work is original and very interesting for a lot of industrial fields.