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An Alternative Unsteady Adaptive Stochastic Finite Elements Formulation Based On Interpolation At Constant Phase

机译:基于恒相插值的非定常自适应随机有限元公式

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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.
机译:基于时间无关参数化(UASFE-ti)的非稳态自适应随机有限元方法是一种解决非稳态仿真中随机参数影响的有效方法。与其他方法通常需要快速增加的样本数量相比,它在样本数量恒定的情况下可以达到恒定的时间精度。本文提出了一种基于恒定相位插值的非稳态自适应随机有限元公式(UASFE-cp),以进一步提高精度并扩展UASFE-ti的适用性。除了在时间上获得恒定数量的样本外,在恒定相位处进行插值:(1)消除了与时间无关的参数化的参数化误差; (2)解决了时间相关的功能,这些功能无法通过参数化来建模; (3)捕获样本的瞬态行为,这是时间相关功能的重要特例。通过将UASFE-cp应用于质量弹簧阻尼器系统中的随机参数,阻尼非线性Duffing振荡器以及在流动和结构中具有非线性的弹性安装翼型,可以说明这三点。将不同类型的概率分布的结果与UASFE-ti和Monte Carlo模拟的结果进行比较。

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