Mechanics of Slender Structure

This lecture covers the expression of the Kirchhoff-St. Venant energy in a covariant setting, dimensional reduction for shells, equilibrium equations for spherical shells, linear shell theory, covariance and contravariance of vectors, covariant and contravariant components, and extending linear elastic models to 3D. The lecture delves into the concepts of covariant and contravariant components of vectors, the second fundamental form, extending linear elastic models to 3D, and the Kirchhoff-St. Venant model. It also explores the dimensional reduction of strain energy for shells, the extension of linear elastic models to 3D, and the energy invariants of shells.