Plates II: Föppl-von Kármán Equations

This lecture covers the framework for the theory of plates, including the curvature tensor, nonlinear strain components, and bending and stretching energies. It delves into the variation of bending and stretching energies, leading to the Föppl-von Kármán Equations of equilibrium. The lecture explores the interpretation of mean and Gaussian curvatures of surfaces, the curvature tensor, and the determinants related to curvature. It discusses the assumptions and implications of Kirchhoff-Love hypothesis, the Einstein notation, and the principal curvatures. The lecture concludes with the analysis of bending and stretching energies, emphasizing the importance of Gaussian curvature in deforming thin elastic plates.