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, the traditional deterministic analysis methods are hard to quantify the stochastic influence. The Radial Basis Function (RBF)-enhanced Direct Probability Integral Method (DPIM) is proposed to efficiently determine the probabilistic characteristics of buckling critical loads in plate and shell structures under multiple random variables, which provides 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 method effectively reduces the computational cost for implementing the time-consuming buckling finite element analysis in the original direct probability integral 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.

This paper proposes a robust structural layout optimization method for stiffened plate structures under load uncertainty, enabling the simultaneous optimization of stiffener layout and size. Based on the ground structure method, a robust optimization model is established in which the radii of circular beam sections representing the stiffener are selected as design variables, the total structural mass is imposed as a constraint, and a weighted combination of the expectation and variance of structural compliance under uncertain loading is taken as the objective function. The analytical sensitivity formulations of the expectation and variance of structural compliance, as well as the mass constraint with respect to the design variables, are deduced in detail. The method of moving asymptotes (MMA) is adopted to solve the proposed robust layout optimization problem. Finally, two numerical examples are performed to verify the effectiveness and applicability of the proposed method.