Vacancy defects are unavoidable in graphene sheets, and the random distribution of vacancy defects has a significant influence on the mechanical properties of graphene. This leads to a crucial issue in the research on nanomaterials. Previous methods, including the molecular dynamics theory and the continuous medium mechanics, have limitations in solving this problem. In this study, the Monte Carlo-based finite element method, one of the stochastic finite element methods, is proposed and simulated to analyze the buckling behavior of vacancy-defected graphene. The critical buckling stress of vacancy-defected graphene sheets deviated within a certain range. The histogram and regression graphs of the probability density distribution are also presented. Strengthening effects on the mechanical properties by vacancy defects were detected. For high-order buckling modes, the regularity and geometrical symmetry in the displacement of graphene were damaged because of a large amount of randomly dispersed vacancy defects.

In practical engineering and industry fields, complicated and correlated problems are often descripted by implicit expression. The Kriging model is one of the popular spatial interpolation models to surrogate the numerical relationship between input and output variables. But the efficiency of the Kriging surrogate model is limited when confronting with large databases. The subset simulation is a promising selection method to provide more important and typical samples. By the subset simulation, the Kriging surrogate model can significantly reduce the computational cost in regression, since much fewer samples are required. Besides, more reliable prediction results can be obtained because of the emphasis on the samples that are more representative in the Kriging fitting process. Examples are performed to confirm the properties of the Kriging surrogate model based on the subset simulation.

Because of the unignoring line-impedance, distorted grid voltage, high penetration and the increased parallel-connected grid-connected converters (GCC) in vehicle-to-grid (V2G) system, the stability of the grid with electric vehicle (EV) faces new challenges. To deal with the stability problem, this paper proposes a numerator-denominator-model (NDM) based H-infinity controller combined with an adaptive capacitive-current-feedback active damping method with explicitly robust stability in terms of variations on filter parameters, time-delay and grid-impedance. Simulation results are investigated in two parallel-connected GCC in EV and show the validity of the proposed method.

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