Large deflection analysis of plates stiffened by parallel beams

In this paper a general solution to the geometrically nonlinear analysis of plates stiffened by arbitrarily placed parallel beams of arbitrary doubly symmetric cross section, subjected to arbitrary 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 stiffening beams are isolated from the plate by sections in the lower outer surface of the plate, while the arising tractions in all directions at the fictitious interfaces are taken into account. These tractions are integrated with respect to each half of the interface width, yielding 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 at the interfaces, in all directions. 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. 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 system of nonlinear and coupled algebraic equations which is solved using iterative numerical methods. 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.