Wind loads in most random vibration studies are assumed to follow Gaussian processes, and reliability-based design is generally conducted based on moment methods to ensure structural survivability. However, membrane roofs under typhoon attacks are loaded by strong non-Gaussian random excitations. The contributions of the third-order moment (skewness) and fourth-order moment (kurtosis) to the structural reliability become more significant. This study investigated the stochastic dynamic response and reliability of hyperbolic parabolic membrane structures excited by non-Gaussian wind loads. Firstly, the Fokker-Planck-Kolmogorov (FPK) governing equation of membrane structures is established, with considerations of both geometric nonlinear stiffness and nonlinear motion-induced aerodynamic force. Then, the steady-state displacement response is analyzed in the slow-varying process of the system. Consequently, a series of analytical solutions, including probability density function (PDF), root mean square (RMS) value, skewness, and kurtosis, can be obtained. The accuracy of the proposed theoretical model is validated throughout a number of wind tunnel tests including various wind velocities and directions. The effects of geometric nonlinear stiffness term, nonlinear motion-induced aerodynamic force, reduced wind velocity and rise-span ratio on structural reliability are thoroughly discussed. The findings reveal that the structural extreme response shows strong non-Gaussian behavior, featured with skewness of -1.5 similar to 1.2 and kurtosis of 3.82 similar to 6.89. The influence of geometric nonlinear stiffness and nonlinear motion-induced aerodynamic force on structural reliability can reach up to 28.42 % and 29.84 %, respectively. Among various design parameters, the reduced wind velocity shows the most significant influence on structural reliability. In the probability-based design framework, the critical reduced wind velocity is identified as 1.2, and the critical rise-span ratio is recommended as 1/10. The research proposed in this paper provides an accurate analytical model for predicting the dynamic behavior of such flexible structures under typhoons.
