3D Linear Elasticity & Beams

This lecture covers the fundamentals of 3D linear elasticity, including stress transformations, principal stresses, and mean stress. It also delves into the mechanics of slender structures, focusing on beams, internal loads, bending, and torsion. The instructor provides insights into the dimensional analysis, scalings, calculus of variations, and Euler's elastica. Additionally, the lecture explores the concepts of plates, Kirchhoff rods, and shells, discussing bending stiffness, wrinkling, and buckling. The course emphasizes analytical methods for modeling the mechanics of slender structures, with a strong focus on mathematical and theoretical approaches.