An alternative unsteady adaptive stochastic finite elements formulation based on interpolation at constant phase

The unsteady adaptive stochastic finite elements method based on time-independent parametrization (UASFE-ti) is an efficient approach for resolving the effect of random parameters in unsteady simulations. It achieves a constant accuracy in time with a constant number of samples, in contrast with the usually fast increasing number of samples required by other methods. In this paper, an alternative unsteady adaptive stochastic finite elements formulation based on interpolation at constant phase (UASFE-cp) is developed to further improve the accuracy and extend the applicability of UASFE-ti. In addition to achieving a constant number of samples in time, interpolation at constant phase: (1) eliminates the parametrization error of the time-independent parametrization; (2) resolves time-dependent functionals, which cannot be modeled by the parametrization; and (3) captures transient behavior of the samples, which is an important special case of time-dependent functionals. These three points are illustrated by the application of UASFE-cp to random parameters in a mass–spring–damper system, the damped nonlinear Duffing oscillator, and an elastically mounted airfoil with nonlinearity in the flow and the structure. Results for different types of probability distributions are compared to those of UASFE-ti and Monte Carlo simulations.