# Optimisation of Cable Dome Structure Design for Progressive Collapse Resistance
## 1 Introduction
In addition, optimised designs based on structure performance, particularly resistance to progressive collapse in an extremely complex load case, are uncommon. The first progressive collapse, a concept proposed in the field of civil engineering, was observed in 1968 at Ronan Point, a 22-storey block of flats in London, UK, which progressively collapsed because of a gas explosion [24]. Following the 9-11 terrorist attack in 2001, the complete collapse of the World Trade Center in the United States drew global research attention towards the concepts of progressive collapse and structural robustness in buildings [25]. [PERSON] et al. [26] analysed the Murrah Federal Building incident and argued that redundant load paths are essential for preventing asymmetric building collapse. According to [PERSON] and [PERSON] [27], [PERSON] [28], [PERSON] and [PERSON] [29], [PERSON] and [PERSON] [30], and [PERSON] and [PERSON] [31], increasing the strength and ductility of key building components is a crucial measure against progressive structure collapse. [PERSON], [PERSON], and [PERSON] [32] introduced the concept of structure alternative defensive ability, which refers to the ability of structures to automatically adjust their internal forces when certain components fail because of unexpected events or excessive local overloading. This ability allows structures to halt the progression of damage, thereby preventing their global damage and progressive collapse. [PERSON] et al. [33], [PERSON] et al. [34], [PERSON] et al. [35], and [PERSON] et al. [36] simulated cable breakage by using the element birth and death technique, instantaneous removal of components, and instantaneous loading to analyse the local failure of various cable dome structures as well as the internal force change in members and nodal displacement response following breakage. [PERSON] [37], [PERSON] et al. [38], and [PERSON] et al. [39] analysed the local failures, dynamic structural response, and collapse of various string structures, such as the beam string structure, the cable-arch structure, and the truss string structure. Countries and regions such as North America [40,41], Europe [42,43], and China [44,45] have incorporated requirements for the prevention of structural collapse and the improvement of structural robustness into their design guidelines, standards, and regulations. In summary, the literature on the progressive collapse of structures has predominantly been focused on frame structure systems and has rarely investigated long-span structures. This is because traditional long-span structures, such as space trusses and grid shells, are generally believed to have a relatively high degree of static indeterminacy, and the failure of a single member does not substantially undermine the bearing-capacity reserve of the global structure. However, unlike traditional long-span space trusses or grid shells, cable dome structures have low redundancy and high sensitivity to accidental disturbances, including construction errors, and are thus prone to collapse when they are overloaded or subjected to accidental disturbances [4; 5; 6]. To address the problems associated with cable dome structures, this study analysed typical models of cable dome structure dynamic response and collapse resulting from local member failure by using Ansys LS-DYNA and the full dynamic equivalent load-based instantaneous unloading method. Structural displacement ratios were also compared before and after the removal of components to define the member importance coefficients in order to determine the importance of each component in the progressive collapse resistance of structures. Finally, to optimise the performance of structures in resisting progressive collapse, a stepwise optimisation design solution based on a combination of global and local optimisation was proposed.