## 1 Introduction  
A thermal protection system (TPS) is required to be lightweight, provide high strength under dynamic and acoustic pressures, and withstand aerodynamic heating during hypersonic flight. During its service lifetime, a hypersonic vehicle will operate in harsh conditions, such as high aerodynamic heating on the surface, which results in a thermal gradient across the thickness direction of the TPS panel [1; 2; 3; 4; 5]. In addition, thermal stress will increase, which causes the TPS panel to deflect outwardly and may damage the vehicle [6; 7]. The outward deflection of the TPS panel may cause a transition from laminar to turbulent boundary conditions, which may increase local aerodynamic heating [8; 9]. Thus, the design of the TPS panel must ensure a safe temperature for the vehicle structure at below the allowable temperature of the internal structure's material [10; 11]. It must also provide an acceptable surface deflection to prevent flow transition during flight [12]. Several studies have focused on the thermomechanical performance of the TPS panel to determine the deflection limit. [PERSON] et al. [12] theoretically calculated the deflection of a honeycomb panel for a TPS panel and evaluated the maximum deflections in terms of the boundary layer transition. [PERSON] et al. [13] investigated the thermomechanical performance of a TPS panel with a honeycomb panel at the top surface. They also presented an application of the finite element method for TPS panel optimization. Their TPS model followed the design of NASA's TPS panel [1; 12]. Most of the research focused on the goal of the temperature limit in the internal structure of the vehicle, and they determined the proper thickness and material for the TPS panel [11; 14; 15; 16]. Moreover, they also investigated whether the residual stress in the TPS panel remained at high levels [17]. Nevertheless, deformation due to thermal gradient has not received much attention. Thus, there remained a need for research on the deflection limit and permanent deformation of the TPS panel. In our previous design of the TPS panel [6], we employed a dense Inconel superalloy plate for the outer plate of the TPS panel, which was directly exposed to high aerodynamic heating, as shown in Figure 1. Note that the outer plate of the TPS panel is formed in the shape of the vehicle and its deformation can create roughness of the outer mold line of the vehicle. However, the dense plate used in our previous work [6], which was made of an Inconel superalloy, was heavy even though it guaranteed high strength for the TPS panel. Therefore, in this study, we developed lightweight structures that can be used as the exterior part of the TPS panel and ensure the high strength at a high temperature. One candidate for a lightweight structure is a sandwich structure, which has been widely used in the hypersonic vehicles as a thermal protection structure. Recently, sandwich structures consisting of two solid face sheets and a low-density core were inspired from biological structures [18; 19; 20]. Over the course of the long evolution of nature, biological structures have been optimized for survival and have adapted themselves to various environmental conditions. Thus, they were considered for a lightweight and high-strength structure for modern engineering applications. Many researchers have designed sandwich structures and investigated their thermal and mechanical performance under various conditions, such as crushing testing [18; 21], aerodynamic heating [10; 22], and thermal-acoustic analysis [23]. [PERSON] et al. [24] reviewed the most recent research on bio-inspired materials for energy absorption structure. [PERSON] et al. [25] computationally investigated the thermomechanical performance of honeycomb core panels for hot structure applications. [PERSON] et al. [26] introduced integral textile structures that were able to function in high-temperature working conditions with high specific strength.