Static analysis of shear flexible beams and frames in adhesive contact with an isotropic elastic half-plane using a coupled FE-BIE model

Shear deformable beams and frames in perfect adhesion with an isotropic elastic half-space are analysed in plane strain or plain stress states. By means of a mixed variational formulation, the beam elements are described in terms of nodal displacements and rotations using locking-free shape functions, whereas the soil substrate is represented in terms of surface tractions through a boundary integral equation that incorporates a suitable Green's function. The formulation ensures full continuity between structure and substrate in terms of displacements and rotations. A variety of numerical examples is presented to show the effectiveness of the proposed model. For very stiff beams subjected to a point force or moment, comparisons are made with available closed-form solutions to the contact problem of a rigid indenter. For foundation beams bonded to the substrate and loaded by a vertical point force the proposed model exhibits a superior convergence rate in comparison with other standard numerical models. Moreover, the shear deformations are shown to play a crucial role on both beam displacements and soil surface tractions. Finally, the soil-structure interaction analysis of a two-bay plane frame is presented.