elastic foundation displacement approximations

Interaction of an elastic foundation and structures like beams, plates and frames plays an essential role in investigating soil media in contact and impact mechanics. The solution to this interaction problem is complicated even the foundation is assumed as a linear elastic medium. E. Winkler suggested the fair representation of the foundation in 1867, and then, to bring it closer to reality, an interaction between the spring elements was introduced. In this paper, a relatively simple membrane-spring system is investigated, where an ideal gas is added under or above the membrane. In many cases, this constant pressure in the cavity modifies the solution and accuracy of the approximation is significantly increased. The cases of concentrated normal force and uniform distributed load are examined. The results of elastic half-space line displacements and the membrane displacements are presented.