Shells I: Mechanics of Slender Structures

This lecture covers the linear and membrane theories of pressure vessels, differential geometry of surfaces, and the covariant and contravariant base vectors. It also introduces the first and second fundamental forms and the 3D metric tensor. The slides discuss the reduction of dimensionality from 3D to 2D, point identification, shell buckling, and knockdown factors. The lecture delves into the need for nonlinear theory, critical buckling pressure, and eigenvalue problems. It also explores the perturbation method, aperture motion, and the eigenvalue problem. The instructor explains the differential geometry of surfaces, parametrization, coordinate lines, and the Euclidean space. The lecture concludes with the representation of vectors on covariant and contravariant bases and the encoding of information about the surface metric and curvature.