Elastic Foundation Displacement Approximations

Abstract

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.

Shape-Adaptive Universal Soft Parallel Gripper for Delicate Grasping Using a Stiffness-Variable Composite Structure

“…As described in the previous section, the soft supporting layer consisting of a honeycomb structure plays a vital role in deforming the tip surface to match the shape of the target object. The shape of deformed soft supporting layer due to the target object can be described using the Filonenko-Borodich model which uses the individual spring elements in the Winkler model and the elastic membrane connecting the spring element under a constant tension T [26], [27]. The surface deformation w of the structure due to a pressure q in the elastic half space is described as follows:…”