Technical Paper
An Efficient Methodology to Predict the Dynamic Instabilities of a Frictional System
2022-06-15
2022-01-0984
Stochastic Finite Elements Method (SFEM) is applied in many fields. For instance, in frictional systems, it helps quantify uncertainties about the parameters controlling the involved process and thus, provides a more reliable prediction of the dynamic instabilities. Usually, SFEM is coupled with sensitivity theory to investigate the effect of a given input on the output. However, the available methods which often couple Monte-Carlo (MC) algorithm with the Finite Element (FE) method have a computational cost that scales linearly as a number of stochastic iteration N and input parameters k (i.e., t ~ N x k). To achieve convergence, the magnitude of N must be on the order of thousands or even millions. Hence, for a frictional system with 5 random variables and requiring 15 min of CPU time per run, the computational cost will exceed 52 days (!). Such a method cannot be applied in an industrial design framework with a high number of random variables since its CPU time becomes prohibitive.