Nonlinear Dynamic Analysis of Plates Stiffened by Parallel Beams with Deformable Connection

In this paper a general solution to the geometrically nonlinear dynamic analysis of plates stiffened by arbitrarily placed parallel beams of arbitrary doubly symmetric cross-section, subjected to dynamic loading, is presented. The plate-beam structure is assumed to undergo moderate large deflections and the nonlinear analysis is carried out by retaining nonlinear terms in the kinematical relations. According to the proposed model, the arbitrarily placed parallel stiffening beams are isolated from the plate by sections in the lower outer surface of the plate, making the hypothesis that the plate and the beams can slip in all directions of the connection without separation and taking into account the arising tractions in all directions at the fictitious interfaces. These tractions are integrated with respect to each half of the interface width resulting in two interface lines, along which the loading of the beams and the additional loading of the plate are defined. Six boundary value problems are formulated and solved using the analog equation method (AEM), a BEM-based method. Both free and forced transverse vibrations are considered and numerical examples with great practical interest are presented demonstrating the effectiveness, wherever possible, the accuracy, and the range of applications of the proposed method. 1. Introduction Stiffened plate panels are structural elements of practical importance in applications such as ship superstructures, bridge decks, and aircraft structures. Stiffening of the plate provides the benefit of added load-carrying capability with a relatively small additional weight penalty, while buckling is prevented especially in case of inplane loading. The unique peculiarities of the aforementioned structures are obtained due to the behavior of the bond between the plate and the beams; however, this bond is the usual reason why these structures are prone to failure. Moreover, since these stiffened plates are frequently subjected to dynamic loading such as air blasts or underwater explosions, a clear understanding of the dynamic response requires development of an efficient dynamic analysis capability. When the deflections of the structure are small, a wide range of linear analysis tools, such as modal analysis, can be used and some analytical results are possible. As the deflections become larger, the induced geometric nonlinearities result in effects that are not observed in linear systems, making therefore the determination of an analytical solution extremely difficult and in most cases impossible. Moreover, having in mind the