Sparse Polynomial Chaos Expansion for Uncertainty Quantification of Composite Cylindrical Shell with Geometrical and Material Uncertainty

Abstract

The geometrical dimensions and mechanical properties of composite materials exhibit inherent variation and uncertainty in practical engineering. Uncertainties in geometrical dimensions and mechanical properties propagate to the structural performance of composite cylindrical shells under hydrostatic pressure. However, traditional methods for quantification of uncertainty, such as Monte Carlo simulation and the response surface method, are either time consuming with low convergence rates or unable to deal with high-dimensional problems. In this study, the quantification of the high-dimensional uncertainty of the critical buckling pressure of a composite cylindrical shell with geometrical and material uncertainties was investigated by means of sparse polynomial chaos expansion (PCE). With limited design samples, sparse PCE was built and validated for predictive accuracy. Statistical moments (mean and standard deviation) and global sensitivity analysis results were obtained based on the sparse PCE. The mean and standard deviation of critical buckling pressure were 3.5777 MPa and 0.3149 MPa, with a coefficient of variation of 8.801%. Global sensitivity analysis results from Sobol’ indices and the Morris method showed that the uncertainty of longitudinal modulus has a massive influence on the critical buckling pressure of composite cylindrical shell, whereas the uncertainties of transverse modulus, shear modulus, and Poisson’s ratio have a weak influence. When the coefficient of variation of ply thickness and orientation angle does not surpass 2%, the uncertainties of ply thickness and orientation angle have a weak influence on the critical buckling pressure. The study shows that the sparse PCE is effective at resolving the problem of high-dimensional uncertainty quantification of composite cylindrical shell with geometrical and material uncertainty.