Abstract Due to the inherent uncertainties in various systems, deterministic approaches may not be able to satisfactorily characterize their response. In such cases, stochastic approaches that can systematically consider uncertainties have to be employed. In the past, many stochastic finite element analysis (SFEA) methods have been developed for uncertainty quantification (UQ), among which the perturbation methods, intrusive and non-intrusive polynomial chaos expansion (IPCE/NIPCE) methods and stochastic collocation (SC) methods have received considerable attention. However, in mechanics, most of the applications of these methods are confined to relatively simple problems, and the applicability and performance of these methods to complex nonlinear mechanics problems are not clear. To this end, this study carried out an investigation on the performance of different SFEA methods in linear and nonlinear problems. Numerical studies show that the NIPCE and SC methods are superior in terms of accuracy among other methods in the linear elastic case. The NIPCE method is also used for UQ in stochastic models with plasticity and nonlocal elastoplastic damage. The results demonstrate that the stochastic averages can be significantly different from the deterministic results, which indicates the necessity of considering UQ for improving response predictions.

中文翻译：

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关于线性和非线性问题中随机有限元的性能评估

摘要 由于各种系统固有的不确定性，确定性方法可能无法令人满意地表征其响应。在这种情况下，必须采用可以系统地考虑不确定性的随机方法。过去，已经开发了许多用于不确定性量化（UQ）的随机有限元分析（SFEA）方法，其中扰动方法、侵入式和非侵入式多项式混沌展开（IPCE/NIPCE）方法和随机搭配（SC）方法受到了极大的关注。然而，在力学中，这些方法的应用大多局限于相对简单的问题，这些方法对复杂非线性力学问题的适用性和性能尚不清楚。为此，本研究对不同 SFEA 方法在线性和非线性问题中的性能进行了调查。数值研究表明，在线性弹性情况下，NIPCE 和 SC 方法在精度方面优于其他方法。NIPCE 方法也用于具有塑性和非局部弹塑性损伤的随机模型中的 UQ。结果表明随机平均值可能与确定性结果显着不同，这表明考虑 UQ 以改进响应预测的必要性。NIPCE 方法也用于具有塑性和非局部弹塑性损伤的随机模型中的 UQ。结果表明随机平均值可能与确定性结果显着不同，这表明考虑 UQ 以改进响应预测的必要性。NIPCE 方法也用于具有塑性和非局部弹塑性损伤的随机模型中的 UQ。结果表明随机平均值可能与确定性结果显着不同，这表明考虑 UQ 以改进响应预测的必要性。