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

Abstract

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.