On the contact problem of beams resting on tensionless two-parameter foundations

In the present work, the tensionless contact problem of an Euler-Bernoulli beam of finite length resting on a two-parameter foundation is investigated, with special regard to the Reissner soil model. Owing to the tensionless nature of the contact, the beam may lift-off the foundation and the condition setting the point where contact ceases and detachment begins, named contact locus, needs to be assessed. Such condition is in the form of a homogeneous second-order form in the displacement and its derivatives, which gives the problem a nonlinear feature. Moreover, the loading and the beam length may be such that the beam rests entirely supported on the foundation, which situation is governed by a different set of boundary conditions (BCs).Through a variational approach, the proper set of BCs at the contact loci have been determined elsewhere and some numerical examples given, with special regard to the Pasternak foundation. In this work, the BCs are put to advantage to discuss a number of relevant situations concerning beams on a Reissner foundation. Indeed, the Reissner simplified continuum (RSC) model is often regarded, for instance in the realm of soil-structure interaction, as the most effective soil model which retains a certain degree of simplicity. Symmetric as well as non-symmetric contact scenarios are considered and the elastic energy of the system is plotted onto the equilibrium candidates, showing that the alleged solutions are indeed energy stationary points. The problem of finding the limiting loading at equilibrium, on the verge of complete detachment, is also touched upon.