An Iterative Numerical Solution for the Elastica With Causally Mixed Inputs

Abstract

An iterative numerical solution is given for the case of a thin elastic rod whose inputs are simultaneously the positions of the two ends and an applied moment at one end. The development begins by considering the real rod as an end section of a longer fictitious rod loaded with end forces only. Newton’s method is then used to obtain both the shape of the real road and its vector restoring force. The results show that both the magnitude and the direction of the restoring force are changed considerably from the zero-moment case, especially when the percent deflection of the elastica is small. Such a model is a useful alternative to a pure force-deflection one because it accounts not only for the direct effect of the applied moment on the reaction rigid body but the indirect contribution to the reaction force as well.