Uncertainty Analysis of a Composite Plate Using Anti-optimization and PCE

Uncertainty propagation has gained increasing attention in the research community in recent years. A better understanding of the uncertainty translates into a more efficient final product. Composite materials are susceptible to the aforementioned uncertainties, for instance by means of variations in material properties, loadings and manufacturing process. In this study, a composite plate uncertainty propagation problem is addressed with three techniques: Anti-optimization Interval Analysis, Polynomial Chaos Expansion (PCE), and the traditional Monte Carlo method. The dynamic mechanical response of the composite plate is analysed in the time domain. The anti-optimization interval analysis approach resulted in wider envelopes in the time histories (lower and upper bounds) when compared to PCE and Monte Carlo, especially in the last and more challenging example. Despite being unable to generate envelopes as broad as the other two approaches, PCE showed to be very attractive due to the small number of function evaluations used, especially in simpler problems. The adopted PCE algorithm is based in a non-intrusive approach: The Multivariate Collocation Method.