Keywords: stiffened plate, ribbed plate, slab-and-beam structure, buckling, nonuniform torsion, warping, boundary element method.

The problem of the buckling of stiffened plates has been widely studied from both the analytical and the numerical point of view starting with the application of energy criteria to the study of the stability of stiffened plates under uniform compression, and continuing later with numerical tables for buckling loads of rectangular plates stiffened by longitudinal and transverse ribs. However, due to the mathematical complexity of the problem, the existing analytical solutions were limited to stiffened plates of simple geometry, loading and boundary conditions. In all these research efforts, the solution of the buckling problem of stiffened plates is not general since the shear longitudinal or transverse forces at the interfaces have been neglected or the torsional and warping behaviour of the stiffening beams has been ignored.

The boundary element method (BEM) on the other hand seems to be an alternative powerful tool for the solution of the aforementioned buckling problem. In recent years the boundary element method has been successfully applied to the solution of stability problems of unstiffened plate structures. Nevertheless, to the authors' knowledge, the boundary element method has not yet been used for the buckling analysis of stiffened plates.

In this paper a general solution for the elastic buckling analysis of plates stiffened by arbitrarily placed parallel beams of arbitrary doubly symmetric cross section subjected to an arbitrary inplane loading is presented, by improving the employed structural model of the authors in previous research efforts, so that a nonuniform distribution of the interface transverse shear force and the nonuniform torsional response of the beams are taken into account. According to the improved model, the stiffening beams are isolated from the plate by sections in the lower outer surface of the plate, 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 two interface lines, along which the loading of the beams as well as the additional loading of the plate is defined. The utilization of two interface lines for each beam enables the nonuniform torsional response of the beams to be taken into account as the angle of twist is indirectly equated with the corresponding plate slope. The unknown distribution of the aforementioned integrated tractions is established by applying continuity conditions in all directions at the two interface lines, while the analysis of both the plate and the beams is accomplished using their deformed shape. The method of analysis is based on the capability to establish the elastic and the corresponding geometric stiffness matrices of the stiffened plate with respect to a set of nodal points. Thus, the original eigenvalue problem for the differential equation of buckling is converted into a typical linear eigenvalue problem, from which the buckling loads are established numerically. For the calculation of the elastic and geometric stiffness matrices six boundary value problems are formulated and solved using the analog equation method (AEM), a boundary element based method. The adopted model permits the evaluation of the shear forces at the interfaces in both directions, the knowledge of which is very important in the design of prefabricated ribbed plates (estimation of bond, shear connectors or welding). The main conclusions that can be drawn from this investigation are:

a)

The validity of the proposed model and the accuracy of the results compared with those obtained from a three-dimensional FEM solution are noteworthy.

b)

The increment of the buckling factor with the increment of the plate thickness is easily verified.

c)

The influence of the inplane interface forces in the value of the buckling factor is also concluded.

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