ABSTRACT

A shell resting on an elastic foundation can in certain cases be viewed as resting on distributed elastic springs that have spring rates k1, k2, and k3N/m

3 and act in 1, 2, and 3 directions. If the foundation is a homogeneous material of uniform thickness hF m that is defined by a modulus of elasticity EN/m2 and Poisson’s ratio , a very approximate first-order estimate is k1=k2=G/hF , and k3=E/hF , where G is the shear modulus of the foundation. Usually, the spring rates are identified experimentally. It should be remembered that the concept of an elastic foundation is an approximation by itself. In cases where a high degree of accuracy is required, or where Young’s modulus of the foundation approaches that of the shell, the foundation will have to be modeled as an elastic continuum (see Chapter 20).