Shells II: 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, and the relationship between covariant and contravariant components. The lecture also delves into the formal definition of the trace of a tensor, bulk modulus, Lagrangian-Green strain, and the invariance of energy. Special emphasis is placed on shells, their strain energy, and the reduction of 3D strain energy to a 2D form.