Abstract: As critical load-bearing components in aerospace, marine, and construction engineering fields, the buckling stability of plate and shell structures directly determines the safety and reliability of entire systems. However, factors such as material property variability significantly influence the distribution characteristics of critical buckling loads, which traditional deterministic analysis methods struggle to accurately quantify. This paper proposes a Radial Basis Function (RBF)-enhanced Direct Probability Integration Method (DPIM) to efficiently determine the probabilistic characteristics of buckling critical loads in plate-shell structures under multiple random variables, establishing theoretical foundations for stochastic buckling uncertainty quantification. By constructing a high-precision explicit surrogate model between critical buckling loads and random variables using RBF, this approach effectively reduces the computational cost of implementing the time-consuming buckling finite element analysis in the original direct probability integration method. Comparative analyses with traditional DPIM and Monte Carlo simulation methods in numerical examples demonstrate that the proposed RBF-enhanced DPIM achieves remarkable computational efficiency improvements while maintaining controlled accuracy loss.

Key words: Plate and shell structures, Buckling analysis, Direct probability Integral method, Radial basis functions, Stochastic mechanics