Dimensional Analysis and Scaling Laws

This lecture covers the concepts of dimensional analysis and scaling laws, focusing on two exercises. The first exercise explores Euler buckling in columns, emphasizing the critical buckling load and the impact of imperfections. The second exercise delves into the periodic folding of a sheet of paper, drawing an analogy with viscous fluids. Through dimensional analysis, students will determine the fold length as a function of system parameters and establish an analogy between folding of thin elastic sheets and viscous fluids. The lecture also discusses the flexural-bending behavior of paper and the scaling law governing the fold length in different scenarios.