## 1 Introduction  
Thermal protection system (TPS) is one of the most important sub-systems for hypersonic vehicles suffering extremely high aerodynamic heating and pressure during flights. For the purpose of performing both thermal protection and load-bearing functions, the integrated thermal protection system [1] was developed. Compared to a parasitic TPS with cold structures and hot structures with insulations, the ITPS has better weight efficiency under the same thermal and structural loads [2, 3]. Traditional ITPSs are mostly fabricated by metallic materials [4] with the service temperature around 1300 K. By using C/SiC and SiC/SiC composites, the operable temperature of such systems can be extended to 1800 K [5]. All these advantages make the ITPS a promising concept for future hypersonic vehicles. A typical ITPS consists of three components: a top face sheet (TFS), a bottom face sheet (BFS) and insulation cores (webs and insulation materials). The webs not only connect and integrate the TFS and the BFS but also transfer the thermal and mechanical loads between two surfaces [6]. Although the webs help enhance the structural stiffness and maintain the configuration of the ITPS, they simultaneously induce the thermal short effect due to the high thermal conductivity. Furthermore, when the TFS reaches a high temperature during flight, the BFS remains at a relatively low temperature, leading to the thermal expansion mismatch of the webs [7]. For some configurations of the ITPS, local buckling occurs on the webs due to the existence of thermal compressive stresses and in-plane mechanical compressive loads, which might lead to catastrophic failure indirectly. The layout design of the web is the key factor in the design of the ITPS. Many analytical and numerical methods have been developed focusing on analyzing and optimizing the structure of the ITPS. [PERSON] et al. [8, 9, 10] developed a micromechanical method to homogenize the sandwich panel as an equivalent orthotropic plate to calculate the structural responses of the ITPS. [PERSON] et al. [11] conducted coupled fluid-structure thermal analysis on an innovative layer-wise finite element model of a hybrid corrugated sandwich panel and found that mechanical instability would be aggravated by the cross-coupling effect. [PERSON] et al. [12; 13] established an optimization procedure to optimize the geometric dimensions of the ITPS with the globally convergent method of moving asymptotes. [PERSON] et al. [14] strengthened the thermal protection performance of the ITPS by incorporating shape-stabilized composite phase-change material into corrugated cores. [PERSON] et al. [15] explored the use of space partitioning in the optimization problem of the ITPS to avoid local optima. Uncertainties in thermal loads [16; 17] and geometric and material properties [18; 19; 20] were characterized and analyzed. By incorporating uncertainty analysis into the optimization, the reliability and robustness of the ITPS could be improved. A study carried out by [PERSON] et al. [21] showed that different core options have a significant influence on the structural responses of the ITPS. Various core topologies, such as the open-cell foam [22], pin-reinforced cores [23], honeycomb cores [24; 25], lattice cores [26; 27; 28], folded cores [29] and corrugated cores [30], have been applied and show great thermal and mechanical performance. Multi-layer insulation structures [31; 32; 33; 34] were proposed, and optimization results show they are superior to one-layer core ITPSs. However, optimization based on a specific core configuration might not result in the optimum design due to the initial layout limitation. Since the core is the design driver for the ITPS, there is credible evidence to suggest that by solely focusing on the design of the core layout, the ITPS design could be refined. The objective of this paper is to obtain the best core design for the ITPS that can balance thermal and mechanical performance as far as possible.