In order to seek a reasonable and efficient prestress optimization method for cable domes, this paper proposed a new strategy for growth diffusion mechanism of large step and screening mechanism of growth points by analyzing the basic principle and algorithm mechanism of plant growth simulation algorithm (PGSA). On this basis, the plant growth simulation algorithm based on stage growth (stage growth PGSA) was established. This algorithm divides the optimization process into multiple stages and introduces the corresponding growth diffusion mechanism or screening mechanism of growth points in different stages. Firstly, the growth diffusion mechanism of large step was introduced to realize the spread of growth points by means of one-time diffusion growth with multiple steps. Then, the fast search was carried out with the medium step and the loose screening mechanism. Finally, the convergence was conducted with the small step for accuracy requirements and the strict screening mechanism. Thus, the prestress optimization of cable domes was done by using the stage growth PGSA and compared with other algorithms. The results show that the stage growth PGSA can effectively improve the global searching ability, reduce the growth space, and avoid growth points becoming saturated compared with the original PGSA. The number of calculation iteration of stage growth PGSA is the smallest and the initial strain energy of the structure after optimization is minimal in comparison with those of the multi-island genetic algorithm, adaptive simulated annealing algorithm, and particle swarm optimization algorithm. With its higher optimization efficiency and better optimization effect, therefore, this algorithm is applicable to the prestress optimization of cable domes.

Currently, there is relatively limited research on the stability analysis of spatial structures considering the initial eccentricity of members. To reveal the influence laws of the initial eccentricity of members on the stability bearing capacity of cable-supported cylindrical reticulated shells, this paper proposed a simulation method of introducing the initial eccentricity of members by the end rigid rod and presented the ratio relationship of the elastic modulus between the rigid rod and the initial eccentric rod. Based on this, the random imperfection mode method was used to sequentially introduce the initial eccentricity of members into the perfect structure and the overall imperfect structure. An elasto-plastic process analysis was then conducted to examine the impact of the initial eccentricity of members and the simultaneous application of two types of imperfections on the nonlinear buckling behavior of cable-supported cylindrical reticulated shells. The results show that when the elastic modulus of the rigid rod is taken to be more than 100 times of that of the initial eccentric rod, the calculation results show minor differences. Therefore, the ratio of the elastic modulus between them is taken as 100. The coefficients of stability bearing capacity of cable-supported cylindrical reticulated shells are not remarkably reduced when introducing the initial eccentricity of members into the perfect structure (the maximum reduction is 8. 27%), indicating that the structure is not very sensitive to the initial eccentricity of members, thus the adverse effects of the initial eccentricity of members can be ignored in engineering practice by balancing the calculation work. Compared with the perfect structure, the coefficients of stability bearing capacity of cable-supported cylindrical reticulated shells are significantly reduced by 27. 64% when introducing the initial eccentricity of members into the overall imperfect structure. However, the reductions are slightly smaller than the sums of reductions when the two kinds of imperfections are introduced separately. The overall imperfection and the initial eccentricity of members introduced simultaneously have a certain extent coupling effect on the structural stability bearing capacity, and the effect of the former is more significant.