Stability Evaluation of Clamped – Clamped Variable-Arc-Length Elastica using External Force: Theory and Experiment

Abstract

This paper presents the study of the stability of an elastica under the gravitational field using the horizontal force at mid-length of the elastica. One end of the elastica is initially fixed while the other end can increase the length through the sleeve support. At the mid-length of the elastica, there is a horizontal force served as a tool for investigating the stability of the elastica. The stability of the elastica can be observed from the signs of the stiffness of the elastica against the horizontal force. The governing differential equations consist of equilibrium equations of the elastica segment, moment-curvature relationship, and geometric relations of the elastica. Solutions of the problem can be calculated by employing the shooting method. The governing differential equations are integrated numerically (i.e., Runge-Kutta method) to satisfy boundary conditions. The results from the computation would be compared to the experimental results. From the study, the gravitational field in terms of self-weight of the elastica causes the instability when the total arc-length is increased beyond a critical value. Moreover, the results from the experiment using the high flexibility specimens (i.e., polycarbonate sheets) exhibit the good agreement with those from the theoretical results.