Plyta Ortotropowa z Cienkościennymi Żebrami Niesymetrycznymi - Wilde, P. (Engineering Transactions, 1959)
The problem under consideration is that of an orthotropic plate with asymmetric ribs constituting a monolithic structure with the plate. The assumptions of the theory of thin plates are assumed for the plate. For the ribs, it is assumed that they are thin-walled bars with open cross-section and that the angle between the plate and the rib does not change under the influence of the load. To solve the problem, the mathematical model of infinite number of ribs is assumed. In this respect, this paper is a generalization of the work by Pflüger, [12], to the case of ribs of any cross-section. The procedure consists in deriving equations for the reactions of the ribs and then in loading the orthotropic plate by these reactions. A system of three differential equations is obtained, determining the displacements in the plate with given boundary conditions. The equations take into consideration the inertia forces and describe. the buckling problem (2.17), (2.35), (2.36) and (2.37). The solution for arbitrary ribs is obtained by means of the displacement function in the case of cylindrical loading. The general solution expressed by double trigonometric series is obtained with any boundary conditions by means of the Fourier transformation for a plate with symmetric ribs. An analogous solution for an orthotropic plate was given by the author in the Ref. [8]. The differential equations of the problem with given boundary conditions in the form (3.8) reduce after the trans- formation (3.9) to a system of algebraic equations (3.10), the coefficients being determined by the Eqs. (3.11) and the free terms by the relations (3.12). For a plate with symmetric ribs, a number of particular solutions are given. The problem of determining the frequency of free vibration and that of buckling of a simply supported or clamped plate is discussed. For a. sinusoidal load, an equation for the co-working width of a ribbed plate with two main girders is obtained. The solutions are illustrated by numerical examples.