Shells I

This lecture covers linear pressure vessels and provides a brief primer on the differential geometry of surfaces, including covariant and contravariant base vectors, first and second fundamental forms, and the 3D metric tensor. The lecture delves into thin pressure vessels, thin shells, and critical buckling pressure, emphasizing the dimensional reduction from 3D to 2D. It also explores topics such as point indentation (Reissner), nonlinear theory, and obtaining equilibrium equations using linear theory. Additionally, the lecture discusses the geometric description of curved surfaces, the differential geometry of surfaces for plates, and the constitutive nonlinearities and geometric nonlinearities of shells.