Elastic and Viscoelastic Foundation Models

TLDR

The paper critically examines various foundation models and further develops key concepts. The authors focus on rigorous mathematical formulation of the physical problems. The study shows that the Pasternak foundation is a mechanical model for the generalized foundation, its kernel matches Wieghardt’s exponential kernel in plane stress/strain and a modified Bessel function in 3D, and that finite beam or plate problems on continuous foundations are solvable for any load distribution allowed by classical plate theory.

Abstract

The present paper contains a critical study of a number of foundation models as well as a further development of some of the ideas involved. Among others it is shown that the Pasternak foundation is a mechanical model for the so-called “generalized” foundation. It is also demonstrated that the kernel for the Pasternak foundation in plane stress or plane strain is identical with Wieghardt’s exponential kernel, and that for the three-dimensional case the kernel is a modified Bessel function. It is also shown that the “non solvability” of the problem of a finite beam or plate resting on a continuous foundation as posed by Wieghardt and further elaborated by Pflanz is not correct, and that problems of this type are solvable for any load distribution permissible in classical plate theory. Throughout the paper, emphasis is placed on the proper mathematical formulation of the physical problems in question.