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A data driven polynomial chaos based approach for stochastic analysis of CFRP laminated composite plates

机译：基于数据驱动的基于多项式混沌的CFRP叠层复合板随机分析方法

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摘要

A polynomial chaos (PC) based stochastic finite element methodology is developed for uncertainty quantification and failure probability estimation in CFRP laminated composite plates. The methodology is based on modelling the spatial inhomogeneities in the material properties as 2D non-Gaussian random fields and representing them as PC expansions. Constructing the PC representation requires knowledge of the marginal probability density function (mpdf) and the autocorrelation function. In reality, only measurements at discrete points are available from experiments. Treating this data as a finite dimensional approximation of the random fields, corresponding PC representations are developed using a sequence of Rosenblatt's transformations that lead to matching target mpdfs and target correlation defined through the Spearman's rank correlation coefficient, both of which are estimated from the observed measurements. Subsequently, a stochastic finite element framework is developed that enable quantification of the uncertainty propagation in the developed local stresses. The proposed methodology enables representing the structure matrices as functions of vector random variables which can be easily simulated using Monte Carlo simulations. Estimates of the failure probability are obtained from a relative frequency definition applied to the Tsai-Hill criterion. Discussions on the salient features of the proposed methodology are highlighted using numerical examples. (C) 2015 Elsevier Ltd. All rights reserved.
机译：开发了一种基于多项式混沌（PC）的随机有限元方法，用于CFRP层压复合板的不确定性量化和失效概率估计。该方法基于将材料属性中的空间不均匀性建模为2D非高斯随机场并将其表示为PC展开。构建PC表示需要了解边际概率密度函数（mpdf）和自相关函数。实际上，实验只能提供离散点的测量结果。将这些数据视为随机场的有限维近似值，使用一系列Rosenblatt变换开发相应的PC表示，这些变换导致匹配的目标mpdf和通过Spearman秩相关系数定义的目标相关性，两者均从观察到的测量值中进行估算。随后，建立了一个随机的有限元框架，该框架可以量化在已发展的局部应力中不确定性的传播。所提出的方法使得能够将结构矩阵表示为向量随机变量的函数，其可以使用蒙特卡洛模拟容易地模拟。失败概率的估计值是从应用于Tsai-Hill标准的相对频率定义中获得的。使用数值示例突出了对所提出方法的突出特征的讨论。 （C）2015 Elsevier Ltd.保留所有权利。

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