Shells III: Nonlinear Theory and Zoelly's Solution

This lecture covers the nonlinear theory of spherical shells, including Donnell-Mushtari-Vlasov theory, shallow shells, and pressure buckling with Zoelly's solution. It explores the concepts of linear and nonlinear shell theory, Airy stress function, and the implications of shallow modes. The instructor discusses the point indentation of shells, the Airy stress function, and the equilibrium equations for shallow and deep shells. The lecture also delves into the concept of geometry-induced rigidity, the critical buckling pressure, and the implications of buckling under pressure.