Design optimization of domes against instability considering joint stiffness

Abstract

Stability is the determining factor in the design of domes. The member section designation and joint stiffness are two important factors that significantly affect the global stability. However, the current design method, which determines member sections and joints in two separate stages, assumes that joints are ideally rigid. This design method neglects the interactions among members and joints. In this paper, the theory of form vulnerability is further extended with the introduction of joint flexibility. The relative gradient of the well-formedness of flexible joints, denoted as gra_r, is defined to reflect the instability mechanism from the perspectives of members and joints. Then, a single-layer dome is taken as an example to illustrate the effect of joint stiffness on the stability of the dome. This case study is quantitatively analyzed from the perspectives of the stability of the dome and the gra_r values of the dome. In addition, a reasonable range of joint stiffness values is determined according to the analysis. Next, topology optimization is adopted to develop joints of different sizes with stiffness values within the given range. A set of optimal joints is composed of novel joints with reasonable configurations. Subsequently, the optimization scheme of domes against instability considering the joint stiffness is proposed. The member sections and joint stiffness values are simultaneously taken as the optimization variables to consider the interactive effects of members and joints on dome stability. Maximizing of the lowest gra_r (gra_rmin) is the optimization objective. The steel consumption and design requirements are taken as constraints. The corresponding algorithm is developed, and two domes with different spans are employed to verify the proposed design method. The two illustrative domes demonstrate that the proposed optimization method against instability accounting for joint stiffness can simultaneously optimize the member sections and joint flexibilities. The stability capacities of the optimal domes with flexible joints are as high as those of the optimal domes with rigid joints, but the steel consumption is remarkably reduced compared with that for domes designed using the traditional method.