Probability model evolution laws and mechanisms of non-linear buckling capacity of single-layer spherical gridshells with topology-constrained initial imperfections

•New paradigm of buckling capacity probability model for single-layer gridshells.•Probability model evolution laws under various parameters.•Joint well-formedness is strongly tied to structural buckling modes.•Evolution mechanism of probability model of non-linear buckling capacity.•New guidelines for construction and acceptance of single-layer gridshells. This research offers a detailed probability analysis of the non-linear buckling capacity (NBC) of single-layer gridshells (SLGs), impacted significantly by stochastic initial geometric imperfections during construction. Employing the constrained stochastic imperfection modal method, which adeptly incorporates topology constraints of actual initial imperfection scenarios. The key factors, such as the imperfection simulation method, imperfection amplitude, number of rings, and the rise-to-span ratio, are evaluated through systematic numerical analysis. The results reveal that the traditional random imperfection method cannot obtain the actual bimodal distribution of the NBC, and it can overestimate the maximum and minimum NBCs by 5.16 % and 52.49 %. Furthermore, the joint well-formedness is introduced to quantify the joint local stiffness, and it is found to have a highly intertwined correlation with the structural non-linear buckling mode. The evolution mechanism of probability models can be elucidated through the joint initial deviations leading to changes in joint well-formedness (i.e., local stiffness), based on which it is concluded that an imperfection amplitude of 1/1500 of the structural span should be recommended to be the imperfection amplitude acceptance limit to fully utilize the structural global buckling capacity; significant deviations in primary rib joints and inner ring joints markedly affect the NBC more than those in non-primary rib joints and outer ring joints. The aforementioned conclusions are essential for revising guidelines for permissible joint deviations and assessment methodologies for critical joints throughout the construction.