Stochastic vibration and buckling analysis of functionally graded sandwich thin-walled beams

Stochastic vibration and buckling analysis of functionally graded sandwich thin-walled beams with I-section based on the first-order shear deformation theory is for the first time proposed in this paper. The material properties of beams in both web and two flanges are assumed to be continuously varied in its thickness. Additionally, the constituent material properties are randomly changed according to the lognormal distributions. These stochastic variabilities are then propagated to the stochastic responses of the thin-walled beam through a beam solver with hybrid series-type approximation functions. To achieve efficient evaluations for stochastic responses including natural frequencies and critical buckling loads, polynomial chaos expansion (PCE) based surrogate model is developed. The efficiency and accuracy of PCE's results are assessed by comparing with those of crude Monte Carlo simulation. Sensitivity analysis is carried out to compare the importance of the uncertainty in material properties to stochastic responses. New results reported in this paper can be interesting benchmarks for scientific and engineering community in the future.