Nonsingular boundary element flexural analysis of stiffened plates

This paper concerns a nonsingular formulation to deal with thin plates reinforced by beams using a BEM-FEM combination. The nonsingular formulation developed for the Kirchhoff׳s plate bending problem is extended to include the effect of the stiffener beams. In the proposed model, the plate is modelled by BEM using quadratic elements with transverse deflection and rotations in two orthogonal directions as the degrees of freedom (w, w,x and w,y). The beam is modelled by FEM using Timoshenko beam theory with quadratic elements and taking into account the transverse shear and bending and twisting moments (three degrees of freedom per node). As the plate and beam are modelled using C0 quadratic interpolation with the same set of three nodal values, these can be easily coupled. The nonsingular BEM formulation for thin plate bending problems is presented and the coupling of the BE equations of the plate and the FE equations of the beam is done by using the compatibility and equilibrium equations. A computer program has been developed using C++ with object oriented programming concepts. Several numerical examples are presented to illustrate the accuracy and efficiency of the present formulation.