An unsteady adaptive stochastic finite elements formulation for rigid-body fluid–structure interaction

An adaptive stochastic finite elements approach for unsteady problems is developed. Time-dependent solutions of dynamical systems are known to be sensitive to small input variations. Stochastic finite elements methods usually require a fast increasing number of elements with time to capture the effect of random input parameters in these unsteady problems. The resulting large number of samples required for resolving the asymptotic stochastic behavior, results for computationally intensive fluid–structure interaction simulations in impractically high computational costs. The unsteady adaptive stochastic finite elements (UASFE) formulation proposed in this paper maintains a constant interpolation accuracy in time with a constant number of samples. The approach is based on a time-independent parametrization of the sampled time series in terms of frequency, phase, amplitude, reference value, damping, and higher-period shape function. This parametrization is interpolated using a robust adaptive stochastic finite elements method based on Newton–Cotes quadrature in simplex elements. The effectiveness of the UASFE approach is illustrated by applications to a mass–spring–damper system, the Duffing equation, and a rigid-airfoil fluid–structure interaction problem with multiple random input parameters. The results are verified by comparison to those of Monte Carlo simulations.