## 5 Numerical Examples  
In order to account for the feasibility and validity of the proposed non-probabilistic uncertainty quantification method for composite laminates, two numerical examples are carried out in this section on the basis of micro and macro scales. One is the uncertainty quantification of macro elastic mechanical parameters for graphite-fiber/epoxy-matrix fiber-reinforced composites at the lamina level, where the proposed method is compared with the reference [29] based on the probabilistic thought. The other is the uncertainty quantification of T300/QY8911 composite laminated plates at the component level, where some experimental data points are taken good advantage of. Uncertainty Quantification for Elastic Parameters of Graphite--Fiber/Epoxy-Matrix Fiber-Reinforced Laminae  
In this section, firstly, the uncertainty quantification of the graphite-fiber/epoxy-matrix fiber-reinforced lamina is considered [29]. It is generally acknowledged that obtaining the statistical information for micro-scale modeling is a challenging task because of complex manufacturing processes and experimental constraints. As a result, uncertain input parameters at the micro scale are treated as independent interval variables, whose uncertain information are listed in Table 1. Uncertain information can consist of the nominal values, stand deviations and lower and upper bounds of uncertain parameters. For the sake of carrying out the uncertainty quantification of macro elastic mechanical properties for the lamina, the series model formulated as (1), the parallel model as (3), the combined model as (4) and [PERSON]'s model as (6) are adopted, where the results of \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Variables** & **Nominal Values** &
\begin{tabular}{c} **Stand** \\ **Deviations** \\ \end{tabular} & **Lower Bounds** & **Upper Bounds** \\ \hline \(E_{11}^{f}(\text{GPa})\) & 213.7000 & 10.3400 & 182.6800 & 244.7200 \\ \(E_{22}^{f}(\text{GPa})\) & 13.8000 & 0.6900 & 11.7300 & 15.8700 \\ \(v_{12}^{f}\) & 0.2000 & 0.0100 & 0.1700 & 0.2300 \\ \(G_{12}^{f}(\text{GPa})\) & 13.8000 & 0.6900 & 11.7300 & 15.8700 \\ \(E_{m}(\text{GPa})\) & 3.4500 & 0.1720 & 2.9340 & 3.9660 \\ \(v_{m}\) & 0.3500 & 0.0175 & 0.2975 & 0.4025 \\ \(V_{f}\) & 0.6600 & 0.0132 & 0.6204 & 0.6996 \\ \(V_{V}\) & 0.0200 & 0.0010 & 0.0170 & 0.0230 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Uncertain information at the micro scale for graphite–fiber/epoxy–matrix lamina. Figure 3: The flowchart of the proposed method. reference [29] are listed for comparisons. The corresponding quantification results are listed in Table 2, where the nominal values and variation coefficients under different quantification models are included. Herein, the values before the symbol '/' are nominal values and the values after the symbol '/' are variation coefficients. Through making comparisons between the results under different quantification models, it can be easily seen that the quantified results of the longitudinal tension modulus \(E_{1}\) for different models are absolutely the same. However, the quantified results for the transverse tension modulus \(E_{2}\), the Poisson's ratio \(v_{12}\) and the gear modulus \(G_{12}\) are different whereas the results under the combined model and [PERSON]'s model are approximately identical. As a result, we will take good advantage of the two kinds of models to be used for further study. Furthermore, by comparing the results under [PERSON]'s model in this paper based on non-probabilistic thoughts and the reference [29] by [PERSON] based on probabilistic idea, it can be concluded that the nominal values are closely the same, but the non-probabilistic variation coefficients are bigger than the probabilistic ones. That is to say, the dispersions of uncertain macro elastic properties on the basis of non-probabilistic thoughts will be larger.