Stochastic low-velocity impact on functionally graded plates: Probabilistic and non-probabilistic uncertainty quantification

Abstract

This paper quantifies the compound effect of source-uncertainties on low-velocity impact of functionally graded material (FGM) plates following a coupled surrogate based finite element simulation approach. The power law is employed to evaluate the material properties of FGM plate at different points, while the modified Hertzian contact law is implemented to determine the contact force and other parameters in a stochastic framework. The time dependent equations are solved by Newmark's time integration scheme. Insightful results are presented by investigating the effects of degree of stochasticity, oblique impact angle, thickness of plate, temperature, power law index, and initial velocity of impactor following both probabilistic and non-probabilistic approaches along with in-depth deterministic analyses. A detail probabilistic analysis leading to complete probabilistic characterization of the structural responses can be carried out when the statistical distribution of the stochastic input parameters are available. However, in many cases concerning FGM, these statistical distributions may remain unavailable due to the restriction of performing large number of experiments. In such situations, a fuzzy-based non-probabilistic approach could be appropriate to characterize the effect of uncertainty. A surrogate based approach based on artificial neural network coupled with the finite element model for low-velocity impact analysis of FGM plates is developed for achieving computational efficiency. The numerical results reveal that the low-velocity impact on FGM plates is significantly influenced by the effect of inevitable source-uncertainty associated with the stochastic system parameters, whereby the importance of adopting an inclusive design paradigm considering the effect of source-uncertainties in the impact analysis is established.