Tensionless contact of a finite beam resting on Reissner foundation

A more generalized model of a beam resting on a tensionless Reissner foundation is presented. Compared with the Winkler foundation model, the Reissner foundation model is a much improved one. In the Winkler foundation model, there is no shear stress inside the foundation layer and the foundation is assumed to consist of closely spaced, independent springs. The presence of shear stress inside Reissner foundation makes the springs no longer independent and the foundation to deform as a whole. Mathematically, the governing equation of a beam on Reissner foundation is sixth order differential equation compared with fourth order of Winkler one. Because of this order change of the governing equation, new boundary conditions are needed and related discussion is presented. The presence of the shear stress inside the tensionless Reissner foundation together with the unknown feature of contact area/length makes the problem much more difficult than that of Winkler foundation. In the model presented here, the effects of beam dimension, gap distance, loading asymmetry and foundation shear stress on the contact length are all incorporated and studied. As the beam length increases, the results of a finite beam with zero gap distance converge asymptotically to those obtained by the previous model for an infinitely long beam.