A modular nonlinear stochastic finite element formulation for uncertainty estimation
A modular nonlinear stochastic finite element formulation for uncertainty estimation
复制标题
用于不确定性估计的模块化非线性随机有限元公式
DOI：
10.1016/j.cma.2022.115044
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发表时间：
2022
影响因子：
7.2
通讯作者：
Ammouche Y
中科院分区：
文献类型：
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作者：
Ammouche Y
蒙特卡罗方法广泛用于机械工程设计中不确定性的估计。然而，虽然灵活，但这种方法在计算时间和可扩展性方面仍然不切实际。为了绕过这些限制，人们提出了其他更有效的方法，例如伽辽金随机有限元法（GSFEM）或配置法。 GSFEM 提供准确的输出统计数据，具有采样独立的优点，并且在操作方面可以模块化，尽管代码具有侵入性。虽然线性弹性已在文献中广泛讨论，但 GSFEM 在非线性机械行为中的应用仍然相对未经探索，部分原因是使用传统的 GSFEM 插值法难以捕获非线性效应。为此，我们提出了一个无缝且高效的模块化框架，避免了先验地了解物质定律的需要。特别是，该方法利用基于小波的公式能够同时捕获连续和不连续的行为，并且提出随机算子来直接适应任何材料模型。最后，通过两个问题说明了该方法的灵活性：(i) 具有由屈曲不确定性引起的非线性行为的 3D 超弹性示例，以及 (ii) 根据已知的外部可访问结构变形量来评估结构内点的位移。
The Monte Carlo method is widely used for the estimation of uncertainties in mechanical engineering design. However, while flexible, this method remains impractical in terms of computational time and scalability. To bypass these limitations, other more efficient approaches such as the Galerkin stochastic finite element method (GSFEM) or the collocation method have been proposed. GSFEM provides accurate output statistics, has the advantage of being sampling independent and can be modular in terms of operations, albeit code intrusive. While linear elasticity has been extensively covered in the literature, the application of GSFEM to nonlinear mechanical behaviour remains relatively unexplored, in part due to the difficulty to capture nonlinear effects with the traditional GSFEM interpolants. To this end, we propose a seamless and efficient modular framework avoiding the need to know a priori the material law. In particular, the method makes use of a wavelet based formulation able to capture simultaneously continuous and discontinuous behaviours, and stochastic operators are proposed to straightforwardly adapt any material model. Finally, the flexibility of this approach is illustrated with two problems: (i) a 3D hyperelastic example with nonlinear behaviour arising from buckling uncertainty, and (ii) the evaluation of the displacement of a point within a structure based on how much of the external accessible structural deformation is known.