Instability of variable-arc-length elastica subjected to end moment.

This article presents the instability of a variable-arc-length elastica where one end is attached on the hinged joint and the other end is placed on the sleeve support. The friction is also introduced at the sleeve end. At the hinged end, the concentrated moment is applied to turn the elastica around the joint. The system of governing differential equations is obtained from equilibrium equations, constitutive equation and nonlinear geometric relations. To extract the behaviour of this problem, the system of differential equations needs to be integrated from one end to the other and satisfied boundary conditions. In this problem, we utilise the Runge–Kutta scheme as an integration tool and the shooting method plays a vital role to compute the results. The results are interpreted by using the load-deflection diagram where the stiffness of the system can be observed. From the results, it can be found that there are two equilibrium points for a given end moment that is less than its critical value. This results from the non-monotonic load-deflection curves. There is a limit load point (buckling load) for each value of frictional coefficient. Beyond the buckling load, the elastica can lose its stability. Moreover, we discovered that, with presence of the friction (i.e. dry friction), the elastica shows more stable behaviour than its counterpart without friction since the buckling load increases when the frictional coefficient increases. [ABSTRACT FROM AUTHOR]