An extended BEM formulation for plates reinforced by rectangular beams

This article presents a BEM formulation developed particularly for analysis of plates reinforced by rectangular beams. This is an extended version of a previous paper that only took into account bending effects. The problem is now re-formulated to consider bending and membrane force effects. The effects of the reinforcements are taken into account by using a simplified scheme that requires application of an initial stress field to locally correct the bending and stretching stiffness of the reinforcement regions. The domain integrals due to the presence of the reinforcements are then transformed to the reinforcement/plate interface. To reduce the number of degrees of freedom related to the presence of the reinforcement, the proposed model was simplified to consider only bending and stretching rigidities in the direction of the beams. The complete model can be recovered by applying all six internal force correctors, corresponding to six degrees of freedom per node. Examples are presented to confirm the accuracy of the formulation and to illustrate the level of simplification introduced by this strong reduction in the number of degrees of freedom.