Physics of Deflection

Abstract

Deflection remains one of the most critical and yet least intuitively understood phenomena in structural engineering. Newtonian mechanics provide consistent and powerful framework for static deflection analysis. However, Newtonian formalism falls short to fully explaining subtleties of dynamic vibrations and even worse, buckling. In the everyday life of a machine design engineer the triad of static, dynamic and buckling deflection analysis and optimization is fundamental. However, engineers typically stop at static because of a murky understanding of dynamics and buckling. Of the two misunderstood phenomena the buckling is the more elusive. Common explanations why buckling deflection does not follow the direction of applied force revolve around minute geometric and material imperfections. Experimental evidence contradicts this theory as the nature of displacement is predictable and can be calculated or simulated with great fidelity. To align with experimental data these small imperfections would have to occur every time with the same distribution and magnitude. The imperfections theory not only fails to resolve this contradiction but also lacks the capacity to foster accurate intuition about the actual behavior of structures under load. This theoretical research aims to develop a first principles understanding of the physics underlying deflection.