The Second Variation of the Potential Energy and the Theory of Elastic Stability

Abstract

We remember and comment on the research scenario of the theory of elastic stability that accompanied all the course of studies, carried out with enthusiasm and passion, of Prof. Marcello Pignataro, who we still miss and to whom our affectionate memory goes. Marcello was in continuous contact with Professor Koiter in Delft, to study, with a new approach, the many and still open problems of the nonlinear theory of elastic stability. In those times, the entire approach used in the study of the equilibrium stability of elastic structures was in question and its basis seemed to need to be reformulated. The central theme was the definition of the stability criterion of the second variation of the potential energy and how it being definite positive could effectively imply stability.

Keywords

• elastic stability
• potential energy criterion
• lyapunov stability
• functional analysis