Keywords: elastic stiffened plate, reinforced plate with beams, bending, nonuniform torsion, warping, ribbed plate, boundary element method, slab-and-beam structure, nonlinear analysis.

Structural plate systems stiffened by beams are widely used in buildings, bridges, ships, aircraft and machines. However, these structures are prone to failure of the bond between the plate and the beams. It is the behavior of this bond that gives composite construction its unique peculiarities, while interface slip can cause significant redistribution of strain and stress. Besides, having in mind the importance of weight saving in engineering structures, the study of nonlinear effects on the analysis (large deflection analysis) of stiffened plates becomes essential. This non-linearity results from retaining the squares of the slopes in the strain-displacement relations (intermediate non-linear theory), thus avoiding the inaccuracies arising from a linearized second-order analysis.

In this chapter, a model is proposed for the large deflection analysis of stiffened plates, while the small deflection one is treated as a special case. According to this model, the 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 (i.e. uplift neglected) and taking into account the tractions arising 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 as well as the additional loading of the plate is defined. The unknown distribution of the aforementioned integrated tractions is established by applying continuity conditions in all directions at the two interface lines taking into account their relation with the interface slip through the shear connector stiffness. Any distribution of connectors in each direction of the interfaces can be handled. Six boundary value problems are formulated and solved using the analog equation method (AEM), a boundary element based method. The solution of the aforementioned plate and beam problems, which are nonlinearly coupled, is achieved using iterative numerical methods. The model adopted permits the evaluation of the shear forces at the interfaces in both directions, knowledge of which is very important in the design of prefabricated ribbed plates. Numerical examples of great practical interest demonstrate the improved accuracy of this model which better describes the actual response of the plate-beams system. The utilization of two interface lines for each beam describes better the actual response of the plate beams system since the beam angle of twist is indirectly equated with the corresponding plate slope.

Future works will be devoted to considering the analysis of the stiffened plate material nonlinearities as well as viscoelastic material.

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