Optimization of domes against instability

Static stability is a decisive factor in the design of domes. Stability-related external factors, such as load and supports, are incorporated into structural vulnerability theory by the definition of a relative rate of joint well-formedness ($r_r$). Hence, the instability mechanism of domes can be revealed. To improve stability, an optimization model against instability, which takes the maximization of the lowest $r_r$ ($r_{r,min}$) as the objective and the discrete member sections as the variables, is established with constraints on the design requirements and steel consumption. Optimizations are performed on two real-life Kiewitt-6 model domes with a span of 23.4 m and rise of 11.7 m, which are initially constructed for shaking table collapse test. Well-formedness analyses and stability calculation (via arc-length method) of the models throughout the optimization history demonstrate that this proposed method can effectively enhance $r_{r,min}$ and optimize the static stability of shell-like structures. Additionally, seismic performance of the optimum models subjected to the same earthquake as in the shaking table test is checked. The supplemental simulations prove that the optimum models are superior to the original models under earthquake load as well.