Shells III: Nonlinear Theory and Pressure Buckling

This lecture delves into the nonlinear theory of spherical shells, exploring concepts such as Donnell-Mushtari-Vlasov theory and Zoelly's solution for pressure buckling. The slides cover topics like linear shell theory, strain measures, Airy stress function, and the covariant framework for shells. The instructor discusses the implications of shallow shells and shallow modes, as well as the critical buckling pressure for different shell geometries. The lecture also touches on the history of shell buckling research and the importance of precision in modeling imperfections for experimental studies.