A random field of homogeneous and multi-material structures with uncertain scenarios is addressed by constructed the generalized stochastic cell-based smoothed finite element model. Smoothed finite element method (S-FEM) is “Jacobian-free”, which is not only overcomes the limitations of “overly-stiff” and low accuracy of the standard FEM, but also demonstrates strong resistance to mesh distortion. This paper proposes an efficient non-intrusive stochastic smoothed finite element method (SS-FEM) based on cell-based smoothing domains (SD) for the stochastic analysis of elastic problems, which describe much more realistically real physical systems under uncertain scenarios. This SS-FEM starts from the Gaussian random field based on representation related to the spatial variability in material parameters based on the Karhunen-Loève (KL) expansion, and then establishes the basic formulation that considers the effects of uncertainties. A generalized solving framework based on numerical integration is further developed. The non-intrusive dimension reduction method is also adopted to obtain the statistical moments and probability density function. The proposed SS-FEM can capture the structural stochastic responses under uncertainty condition by combining gradient smoothing technology and uncertainty quantification. A number of engineering examples are compared with the solution of Monte Carlo simulation to demonstrate both the accuracy and the efficiency of the proposed method.

中文翻译：

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采用平滑有限元法和 Karhunen-Loève 展开的均质和多材料结构的随机场


通过构建基于广义随机单元的平滑有限元模型来解决具有不确定场景的同质和多材料结构的随机场。平滑有限元法（S-FEM）是“无雅可比”的，不仅克服了标准有限元法“过于僵硬”和精度低的局限性，而且具有很强的抗网格畸变能力。本文提出了一种基于单元平滑域（SD）的高效非侵入式随机平滑有限元方法（SS-FEM），用于弹性问题的随机分析，可以更真实地描述不确定场景下的真实物理系统。该SS-FEM从基于Karhunen-Loève (KL)展开的材料参数空间变异性表示的高斯随机场开始，然后建立考虑不确定性影响的基本公式。进一步开发了基于数值积分的广义求解框架。还采用非侵入式降维方法来获得统计矩和概率密度函数。所提出的SS-FEM可以通过结合梯度平滑技术和不确定性量化来捕获不确定性条件下的结构随机响应。通过多个工程实例与蒙特卡罗模拟的解决方案进行了比较，证明了该方法的准确性和效率。