Abstract A stochastic isogeometric analysis approach (SIGA) is presented for functionally graded porous plates with graphene platelets reinforcement (FGP-GPLs). Different kinds of random fields and variables are applied to describe the uncertain system inputs which are including material properties of the FGP matrix and graphene platelets, magnitudes and directions of applied loads. A Nystrom based Karhunen-Loeve expansion is presented for random field discretization within the IGA scheme. The arbitrary polynomial chaos-Kriging (aPCK) method is presented for uncertainty quantification. To sustain the robustness of the aPCK approach for engineering problems involving high-dimension of uncertainty, a new Dagum kernel function is introduced in Kriging. The mean, standard deviation, probability density function (PDF) and cumulative distribution function (CDF) of structural outputs can be effectively estimated. Three illustrative examples are investigated to assess the performance of the proposed method for mathematical and engineering applications.

中文翻译：

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基于元模型的复合板随机等几何分析

摘要 提出了一种用于具有石墨烯薄片增强功能的功能梯度多孔板 (FGP-GPL) 的随机等几何分析方法 (SIGA)。应用不同种类的随机场和变量来描述不确定的系统输入，包括 FGP 基质和石墨烯片的材料特性、施加载荷的大小和方向。针对 IGA 方案中的随机场离散化，提出了基于 Nystrom 的 Karhunen-Loeve 扩展。任意多项式混沌克里金 (aPCK) 方法用于不确定性量化。为了保持 aPCK 方法在涉及高维不确定性的工程问题上的稳健性，克里金法中引入了一个新的 Dagum 核函数。均值、标准差、可以有效地估计结构输出的概率密度函数（PDF）和累积分布函数（CDF）。研究了三个说明性示例，以评估所提出的方法在数学和工程应用中的性能。