## 1 Introduction  
Hybrid sandwich structures refer to metallic sandwich plates filled with stochastic foam [1]. Compared to traditional lightweight structures, the hybrid sandwich structures exhibit good mechanical performances as well as enhanced multi-functionality with respect to load bearing capacity, energy absorption and thermal protection [2]. Thus, they have demonstrated a wide range of applications in shipbuilding, train manufacturing and construction industry [3; 4; 5; 6]. Among various core topologies of the sandwich structures (e.g., pin-reinforced [7], truss [8], honeycomb [9]), corrugated cores have received major research attention because of their easy fabrication and cost-efficient maintenance [10]. In recent years, there has been growing interest in applying hybrid corrugated sandwich (HCS) plates to the novel thermal protection systems (TPS) of vehicles operating in extreme temperature environments [11; 12; 13]. Typical representatives are hypersonic vehicles which are exposed to severe thermal and aerodynamic loading. Due to the versatility of the HCS plates, the novel load-bearing TPS offers more weight saving than traditional TPS, leading to performance improvements of the hypersonic vehicles. A significant issue emerged is the mechanical stability of the HCS plates under thermal and aerodynamic loading, while a thorough understanding of the fluid-structure-thermal coupling effects is crucial for the novel TPS design. Prior research has mainly focused on the mechanical properties of HCS plates. [PERSON] et al. discovered the limited enhancement of filling foam in compressive strength and impact resistance due to the relatively weak and low-density foam material [14]. [PERSON] et al. [15,16] and [PERSON] et al. [17] utilized closed-cell aluminum foam instead of polymeric foam and demonstrated that foam filler effectively improved compressive and bending strength by stabilizing effects on the corrugated members against buckling. [PERSON] et al. [18] revealed that filling foam contributed to both enhanced buckling resistance and additional mass, and subsequently assessed the structural efficiency through optimization study. Furthermore, they derived the effective thermoelastic properties of the HCS plates using a homogenization method based on the Gibbs free energy [19]. [PERSON] et al. [20] compared modal characteristics of empty and foam-filled corrugated sandwich cylindrical panels by experiments and numerical analysis. [PERSON] et al. [21] evaluated compressive characteristics of composite sandwich panels with different corrugated core geometries under quasi-static out-of-plane loading. The promising application of the HCS plates to the novel TPS is an active research area, and recent studies have begun to explore the thermo-mechanical behaviors and the corresponding optimization design. Based on the solutions of 1D transient heat transfer and buckling analysis, [PERSON] et al. [22] developed response surface approximations to implement optimization studies for a preliminary design. [PERSON] et al. [23] acquired the optimal dimensions and the best materials for face sheets and web corrugations from a two-stage optimization method. [PERSON] et al. [24,25] conducted the stress and deflection analysis using a semi-analytical equivalent model subjected to combined mechanical-thermal loads. [PERSON] et al. [26] developed a finite-element based homogenization procedure and predicted the equivalent stiffness and strength properties for micromechanical analysis. [PERSON] et al. [27] carried out heat transfer and thermal-mechanical analysis to create an optimization procedure aiming at a minimum weight. [PERSON] et al. [28] performed bending and transient dynamic analysis with temperature-dependent materials, and [PERSON] et al. [29] employed the same equivalent model to conduct stress analysis under thermal and mechanical loads. [PERSON] et al. [13] gave the deflection and the thermal stress through thermo-mechanical analysis under simulated aerodynamic heating.