Snap-Through Buckling Reliability Analysis Under Spatiotemporal Variability and Epistemic Uncertainty

Abstract

Surrogate models often provide an effective tradeoff between accuracy and efficiency during reliability analysis with expensive physics models. In snap-through buckling reliability analysis, a surrogate model could be built for the critical buckling load, as a function of loading, material properties, geometry, and boundary conditions. However, in the presence of spatiotemporal variability, the response surface of the critical buckling load is often highly nonlinear and irregular, thus rendering commonly used response surface-type surrogate modeling strategies ineffective. This paper proposes a new buckling reliability analysis method based on support vector machines for structures subjected to spatiotemporal variability and in the presence of epistemic uncertainty regarding model inputs and parameters. Bayesian calibration is first used to quantify the epistemic uncertainty in the modeling of spatiotemporal variability under limited data. Upon the modeling of spatiotemporal variability and epistemic uncertainty, a time-dependent reliability analysis method is developed for the snap-through buckling failure by constructing a nonlinear support vector machine classifier. Considering that the computer simulation is computationally expensive and the support vector machine classifier may not be well trained due to limited computational resources, a method is also developed to quantify the uncertainty in the reliability estimate due to classification uncertainty. A curved beam with an uncertain boundary condition, spatially varying cross-section geometry, and spatiotemporally varying loading is used to demonstrate the effectiveness of the proposed method.