Optimal loading conditions for non-linear deflections

Abstract

Some mechanical systems, such as compliant mechanisms, require large deflections to perform their function, and it is important to obtain these deflections as efficiently as possible. The purpose of this work is to determine the optimal angle of an applied end load on a cantilever beam to maximize large, non-linear elastic deflections. Elliptic integral equations for large deflection are used to determine the optimal angle for angular, vertical, and total deflection. A simplified model (the pseudo-rigid-body model) is introduced for quick but accurate approximations. This approximation method complements the analytical solution by providing a physical model that is useful in both easily predicting the deflection and in visualizing it.