ABSTRACT
This chapter describes the study of the “linear” or “perfect” elastic structures, represented by those elastic systems that exhibit a linear behavior during loading up to the critical state. It provides a unified analysis of the equilibrium states that occur in the neighborhood of the critical state of elastic continuous structural systems in the framework of the results. Thompson and others made further contributions to the snapping and bifurcation analysis of discrete elastic systems. At the critical state a general elastic system, because of nonlinear geometrical effects, in fact, becomes incapable of sustaining any further small increase of load and fails. The chapter explains the study of the behavior of the “quasi-linear” or “quasi-perfect” elastic structures. It investigates some examples that are developed and the equilibrium bifurcations of elastic rods, deep beams, and frames, and provides the analysis of the imperfection sensitivity of thin cylinders under external pressure.
