Analysis of plates stiffened by parallel beams

Abstract

SUMMARYIn this paper a general solution for the analysis of plates stiffened by parallel beams subjected to an arbitrary loading is presented. According to the proposed 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. The aforementioned integrated tractions result in the loading of the beams as well as the additional loading of the plate. Their distribution is established by applying continuity conditions in all directions at the interfaces. The analysis of both the plate and the beams is accomplished on their deformed shape taking into account second-order effects. Six boundary value problems with respect to the plate transverse deflection, to the plate inplane displacement components, to the beam transverse deflections, to the beam axial deformation and to the beam non-uniform angle of twist are formulated and solved using the analog equation method (AEM), a boundary element method (BEM)-based method employing a boundary integral equation approach. The solution of the aforementioned plate and beam problems, which are non-linearly coupled, is achieved using iterative numerical methods. The adopted model describes better the actual response of the plate beams system and 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. The evaluated lateral deflections of the plate-beams system are found to exhibit considerable discrepancy from those of other models, which neglect inplane and axial forces and deformations.

Shear deformation effect in plates stiffened by parallel beams

“…2). Integration of these tractions along each half of the width of the i-th beam results in line forces per unit length in all directions in two interface lines, which are denoted by q i x j , q i y j and q i zj ( j = 1, 2) encountering in this way the nonuniform distribution of the interface transverse shear forces q i y , which in the aforementioned model in [23] was ignored. The aforementioned integrated tractions result in the loading of the i-th beam as well as the additional loading of the plate.…”

“…The aforementioned integrated tractions result in the loading of the i-th beam as well as the additional loading of the plate. Their distribution is unknown and can be established by imposing displacement continuity conditions in all directions along the two interface lines, enabling in this way the nonuniform torsional response of the beams to be taken into account, which in the aforementioned model in [23] was also ignored.…”

“…1. The solution of the problem at hand is approached by an improved model of that proposed by Sapountzakis and Mokos in [23]. According to this model, the stiffening beams are isolated again from the plate by sections in its lower outer surface, taking into account the arising tractions at the fictitious interfaces (Fig.…”

“…The employed structural model is an improved one of that presented by Sapountzakis and Mokos in [23], 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 this model, the stiffening beams are isolated again 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.…”

“…Subsequently, in more refined approximations the adopted models for the analysis of the plate-beams system isolated the beams from the plate and employed numerical methods for the solution of the arising plate and beam problems with most frequently used the finite element method [15,17,21,27], the boundary element method [3,6,7,14,22,23,28,29] or a combination of these methods [2,13]. In all these approximations shear deformation effect is ignored, while with the exception of [23] the shear longitudinal and/or transverse forces at the interfaces have been neglected.…”