# Optimisation of Cable Dome Structure Design for Progressive Collapse Resistance
## 1 Introduction  
According to [PERSON]'s idea of tensegrity, cable dome structures are a type of flexible structure formed through tension with tension cables and struts as the basic elements [1]. Given the high tensile strength of these cables and the application of prestress for structure stiffness adjustment, these structures are widely used in construction and the commonly used types are the Geiger cable dome [2] and Levy cable dome [3]. Economic development and technological advancements have contributed to the development of cable dome structures towards longer spans, more complex forms, and more novel materials. Meanwhile, the fact that numerous incidents of building collapse have been reported as a result of extreme loading environments, such as explosions and extreme weather conditions [4; 5; 6], has merited research into the analysis and evaluation of the performance (e.g., resistance to progressive collapse) of cable dome structures and the optimisation of their design. Current studies on cable dome optimisation have focussed on the optimisation of prestress, element cross-sectional area, structural shape, and structural topology. [PERSON] [7]; [PERSON] and [PERSON] [8]; [PERSON] [9]; and [PERSON], [PERSON], and [PERSON] [10] proposed prestress optimisation design models with the optimisation goals of minimising the level of global prestress applied to the cable dome structure, minimising the maximum initial internal force of members (typically the initial internal force of the outer hoop cable), minimising the initial strainof the structure, minimising the mass of the structure, and minimising the reaction force of the support. [PERSON] and [PERSON] [11]; [PERSON] [7]; [PERSON] [12]; and [PERSON] [13] optimised the element cross-sectional areas of various cable dome structure components by minimising the cost of construction, minimising the weight, and optimising the stiffness. [PERSON] [14] increased the evenness of internal force distribution in the net structure of the main cables of the Five-hundred-meter Aperture Spherical radio Telescope by optimising the element cross section through the method of constant tensile force replacement. [PERSON] and [PERSON] [15] proposed a progressive structural optimisation approach in which the influence of each component on the global performance of structures is evaluated to eliminate elements with the least contributions, thereby optimising the topology and shape of structures. [PERSON] et al. [16], [PERSON] et al. [17], and [PERSON] [18] developed lattice structure topology optimisation models based on structure robustness and the solid isotropic material with penalisation method, a variable density method. [PERSON] [19] established a shape optimisation model for cable dome structures by using the multipopulation genetic algorithm and particle swarm algorithm by adopting control element length as the independent variable, and by employing minimum structural response in a loaded structure as an optimisation indicator. As for optimisation algorithm, some interesting and novel algorithms have been developed and applied, such as surrogate-assisted stochastic optimisation inversion algorithm [20], shrimp and goby association search algorithm [21], velocity pausing particle swarm optimisation [22], and grey wolf optimiser algorithm [23]. Overall, the current approaches of prestress optimisation for cable dome structures have mostly been focussed on minimising the prestress level or minimising the maximum member prestress in the load case. Optimised designs of element cross section, structural shape, and structural topology have been based on the optimisation objectives of minimising the structure mass and achieving optimal stiffness. In practice, a cable dome structure is lightweight, typically with a steel quantity less than 30 kg/m\({}^{2}\); therefore, the benefit of optimising the mass of a structure is limited.