ABSTRACT
This chapter presents a new formulation of the theory of equilibrium stability of infinite-dimensional elastic structural systems loaded by conservative forces. In a first general statement of the theory, the norm of the space of the configurations of the system will not be explicitly chosen and stability criteria will be only formally given. On the other hand, the requirement of stability of the unstressed initial state in the context of the energy method implies that the definition of stability properly has to be given by assuming the “energy norm” as the measure of distances among configurations. In this framework, stability, as well as instability, is analyzed using the second differential energy criterion. Moreover, the chapter examines the undecided case of stability at the critical state. For infinite-dimensional elastic structures the existence of a “potential well” at the equilibrium state is sufficient to stability.
