ABSTRACT
The objective of this chapter is to present the equations that model the elastic
behavior of shell-like bodies in terms of physical components as an application
of the theory developed in the previous chapter. In order to do so, however,
it is worthwhile to start by giving a summary of the theories of elasticity
for general materials and for shells in particular. The notion of elasticity
originated in the form of the law announced by Robert Hooke and succinctly
explained by him in 1678 as “the power of any springy body is in the same
proportion with the extension.”This statement, whose precise meaning is not
clear in this original form, can now be understood as the constitutive law for
linear elastic materials and it was the work of great mathematical physicists of
the last three centuries to develop a mathematical theory of elasticity extended
to other sort of materials. The load-deflection relationship established by this
law can be stated as a tensor equation relating the stress and strain, and the
first two sections of this chapter are concerned with presenting this relationship
for elastic bodies in general.
