# Structural Design and Optimization of Separated Air-Rib Tents Based on Response Surface Methodology
## 1 Introduction  
As simple and foldable building structures, inflatable tents are lightweight and site adaptable. Along with the development of generalization, integration, and facilitation [1; 2], inflatable tents are widely used in tourism, military, disaster relief, and construction fields. Air-rib tents, which are one kind of inflatable tent, are widely used. These tents are supported by air ribs which are filled with high-pressure air and based on the shape of the ribs, and they include two main types: arched rib tents and broken-line rib tents. They can also be divided into vertical types and curved types by the arrangement of ribs, as shown in Figure 1.  
Compared with a tent supported by a metal frame, the displacement of an air-rib tent under external load is larger [5; 6]. The main evaluation indexes for the stability of an air-rib tent are stress and displacement. The bearing capacity of an arched-rib tent is better than that of a tent with broken-line ribs in the same arrangement. Tents with curved type ribs can resist more loads than tents with the vertical type [3]; however, a tent of the vertical type has more effective space. The large deformation of the tent reduces the effective space, so it is important to reduce the displacement of air-rib tents by parameter optimization. To analyze the mechanical properties of structures, there are, mainly, test and finite element simulation methods. Because of the large size of separated air-rib tents, the testing cost is high. Using the finite element method, the calculation time is short, the applicability is strong, and the testing cost is low [7; 8]. Therefore, finite element analysis is more suitable for tent mechanical property analysis. The influence of the structural parameters of an air-rib tent on its load bearing capacity has been studied by many scholars. [PERSON] et al. [9] established a finite element model of a long-span skeleton membrane structure by tension-only bar elements. A prestressed cable was added to the membrane structure to meet the strength requirements. [PERSON] et al. [10] set up cables to enhance the stability of a dry coal shed with a long span. The dry coal shed was composed of cable-arch trusses, and the prestressed cable was represented by a bar element in the simulation model. [PERSON] et al. [11] established a finite element model of an air-tight inflatable tent, and the rod element Link10 was used to simulate the wind ropes. The effects of parameters such as the internal pressure of the tent, the internal pressure of the ribs, and the structural parameters on the stability were studied. [PERSON] et al. [12; 13] explored the wind pressure distribution of a large stadium by wind tunnel tests and finite element simulation methods. They proposed that a cable can reduce the displacement of the membrane, and showed that the cross-sectional area of the cable has no significant effect on the displacement. To date, most researchers have improved the stability of structures by adding wind ropes, but less research has investigated the influence of wind rope parameters on the parapulin displacement. Therefore, it is necessary to optimize the structure of wind ropes by exploring the influence of wind rope parameters on the tent. Currently, the main optimization methods are the response surface methodology [14; 15; 16; 17], the linear weighting method [18], the coupled genetic algorithm [19], the chaotic water stricter algorithm [20], and the primary objective method [21]. The response surface method  
Figure 1: The shape and arrangement of the tents [3; 4]: (**a**) the arched-rib tent; (**b**) the broken-line rib tent; reprinted with permission from Ref. [3]. 2021, [PERSON]. (**c**) The vertical type tent; (**d**) the curved type tent. Adapted with permission from Ref. [4]. 2008, [PERSON]. ology transforms the implicit function relation in the actual model into a direct function relation by mathematical statistics; then, the optimal solution is determined [22; 23].