Stochastic arbitrary Lagrangian–Eulerian formalism for stochastic rolling contact analysis

This article presents a stochastic ALE framework to solve rolling contact problems with uncertainties. To this end, the classical ALE method used for deterministic rolling contact analysis is extended to a stochastic framework. Within the proposed stochastic ALE framework, stochastic finite element equations are derived and efficiently solved by an iterative algorithm. Specifically, the stochastic solution is approximated by a set of products of random variables and deterministic vectors. An alternating iteration is presented to solve each component of random variable and deterministic vector one by one. Based on a set of obtained deterministic vectors, an equivalent stochastic rolling contact interface system is further constructed, which transforms the original problem into a stochastic rolling contact problem on an interface. Thus, its solution involves fewer degrees of freedom and is cheap enough. The proposed framework is not sensitive to stochastic dimensions and can be applied to high-dimensional stochastic rolling contact problems. Numerical examples demonstrate the promising performance of the proposed framework.