Nonlinear Dynamic Analysis of Plates Stiffened By Parallel Beams With Deformable Connection

Abstract eng:
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 arbitrary 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 (i.e. uplift neglected) 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 as well as the additional loading of the plate is defined. Their unknown distribution is established by applying continuity conditions in all directions at the interfaces taking into account their relation with the interface slip through the shear connector stiffness. The utilization of two interface lines for each beam enables the nonuniform distribution of the interface transverse shear forces and the nonuniform torsional response of the beams to be taken into account describing better in this way the actual response of the plate– beams system. Six boundary value problems are formulated and solved using the Analog Equation Method (AEM), a BEM-based method. Application of the boundary element technique leads to a nonlinear coupled system of equations of motion, which is solved employing a distributed mass model. 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. 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.

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