The stability of functionally graded porous plates with graphene platelets reinforcement (FGP-GPLs) is investigated in this paper. Combining with a new metamodeling approach, namely the Kriging enhanced Neural Network, a stochastic isogeometric analysis (SIGA) framework is proposed for assessing the structural stability. The uncertainties of material properties of both FGP matrix and graphene platelets are considered in the form of random fields and variables. Karhunen-Loève expansion based Nyström method is applied to random field discretization. The Dagum function is adopted as a new kernel function to further improve the performance of the proposed approach. Statistical information including but not limited to statistical moments, probability density function (PDF), and cumulative distribution function (CDF) of the critical buckling load of the plate structure can be effectively estimated through a non-intrusive fashion. In order to illustrate the effectiveness and applicability of the proposed stochastic computational analysis, both theoretical and real-life engineering examples have been investigated in this study.

本文研究了石墨烯增强功能梯度多孔板（FGP-GPLs）的稳定性。结合一种新的元建模方法，即Kriging增强神经网络，提出了一种随机等几何分析（SIGA）框架来评估结构稳定性。FGP基质和石墨烯血小板的材料性能不确定性以随机场和变量的形式考虑。基于Karhunen-Loève展开的Nyström方法被应用于随机场离散化。Dagum函数被用作新的内核函数，以进一步提高所提出方法的性能。统计信息，包括但不限于统计矩，概率密度函数（PDF），板结构的临界屈曲载荷的累积分布函数（CDF）可以通过非侵入式有效地估算。为了说明所提出的随机计算分析的有效性和适用性，本研究对理论和实际工程实例进行了研究。