Stochastic Version of the Arc-Length Method

The solution of a nonlinear algebraic system using the incremental method, based on pre-defined loading steps, fails in the vicinity of local extrema as well as around bifurcation points.The solution involved the derivation of the so-called 'Arc-Length' method.Its essence lies in not incrementing the system parameter or any of the independent variables but rather the length of the response curve.The stochastic variant of this method allows for working with a system where system parameters include random imperfections.This contribution presents a variant that tracks the first two stochastic moments.Even in this simple case, interesting phenomena can be observed, such as the disappearance of the energy barrier against equilibrium jump due to random imperfections in the system.