## 4 Discussion  
The validation example in Section 3.1 has proved that the present layerwise finite element model possesses the advantages of both computational accuracy and efficiency compared to MSC.Nastran simulation. This model is thus conducive to the efficient parameter studies of the HCS plates. The frequency characteristics presented in Figure 9 demonstrate that the unsteady aerodynamic pressure causes two adjacent frequency to gradually coalesce with each other and the coalescence point indicates a critical stable state. The temperature change causes the decrease in natural frequencies which leads to an earlier occurrence of the structural instability. The geometric and material parameters, including number of unit cells, inclined angle, facesheet thickness, corrugation thickness as well as materials of foam and base structures, have been taken into consideration in the thermal buckling, pre-stressed modal and coupled fluid-structure-thermal analysis of the HCS plates. In general, the effects of the geometric parameters on the critical temperature change are similar to those on the natural frequency, but quite different from those on the critical dynamic pressure. As shown in Figures 8a and 11a, with the increase in the number of unit cells, the critical temperature change and the fundamental frequency in thermal environments firstly go up and then down, while the critical dynamic pressure keeps growing. As shown in Figures 8b and 11b, with the increase in the inclined angle, the critical temperature change and the fundamental frequency falls, and the critical dynamic rises. The improvement of the critical dynamic pressure due to the increase in inclined angle is obvious under no thermal loads or lower temperature changes. As shown in Figures 8c and 12, as the facesheet thickness increases, the critical temperature change and the fundamental frequency reaches a maximum when it is equal to the corrugation thickness, while the critical dynamic presents a great improvement. As shown in Figures 8d and 12, as the corrugation thickness increases, the critical temperature change and the fundamental frequency increase, while the critical dynamic decreases. It can be observed that for most cases, parameter changes improve static stabilities while deteriorates dynamic stabilities in coupled fluid-structure-thermal analysis. Due to the different influences of the geometric parameters on the critical temperature change and dynamic pressure, the final structural efficiency of the HCS plates is a trade-off between static and dynamic stabilities under fluid-structure-thermal coupling. Figure 13: Effects of (**a**) inclined angle and (**b**) corrugation thickness on equivalent density and dimensionless critical dynamic pressure under a linear or parabolic temperature field. Table 3 displays the effects of material properties of foam and base structures. The critical temperature change is closely related to both the foam and base materials and the critical dynamic pressure is mainly determined only by the base materials. Compared to the unfilled sandwich plates, the foam filling improves the structural efficiency to a certain degree. Among the materials adopted in the analysis, the best combination is a Ti-6 Al-4V-made corrugated sandwich plate fill with Rohacell 51 foam. Furthermore, additional investigations about the effects of airflow direction and aspect ratio on the critical dynamic pressure are conducted. Figure 10 indicates that regardless of the aspect ratio, the critical dynamic pressure is always slightly higher when the fiber or machine direction of the HCS plates is parallel to the streamwise than perpendicular to the streamwise. Finally, uneven temperature fields of linear and parabolic distributions are taken into the consideration. As can be seen in Figure 13, the critical dynamic pressure is smaller in the linear assumption than in the parabolic assumption, indicating that a linear distribution between the top and bottom face sheets brings about a conservative solution.