Buckling of Plates: Post-Buckling Deformation Analysis

This lecture covers the critical force required to buckle a rectangular plate, assuming a sinusoidal deformed shape. The post-buckling deformation behavior is investigated by considering in-plane stretching energy. The lecture derives the bending energy and curvature tensor, as well as the bending energy density equation. It also explores the stretching energy using the strain tensor and derives the total energy. The solutions for in-plane displacements and stress resultants are discussed, along with the potential energy due to bending and the shear force required for buckling. The aspect ratio for minimal shear force and the solvability of certain parameters are also addressed.