ABSTRACT
This chapter investigates the equilibrium stability of various structural elements such as beams, plates, and shells, and as far as possible, the general elastic continuum in the framework of the previously stated theory. It also investigates some fundamental smoothness properties of the potential energy functionals of various structural elements in their energy spaces. The chapter describes the equilibrium stability of the axially loaded inextensible elastic rod, according to the classical model of the “Elastica” and analyses both plane flexural buckling and stability. Buckling and stability problems of shafts under constant torque and of deep beams under transversal loads are then worked out as particular examples. Some basic stability problems of plates and shells are then studied extensively by analyzing special properties of their strain energy functionals into the corresponding energy spaces. The chapter examines the energy space of the elastic continuum, together with the convergences of the strain and stress tensors.
