Spectral stochastic isogeometric analysis for static response of FGM plate with material uncertainty

In this study, the nondeterministic structural responses of functionally graded material (FGM) plates under static loads with uncertain material property is investigated. The considered spatially dependent uncertainties are modelled as random fields with Gaussian distribution. A novel spectral stochastic isogeometric analysis (SSIGA) framework is proposed for such uncertainty quantification through the first-order shear deformation theory. Within the SSIGA framework, the non-uniform rational B-spline (NURBS) is adopted for both the geometry modelling of the random fields of the uncertain material properties and random field discretization through the Karhunen-Loeve (K-L) expansion. Such new feature provides an effective and practically applicable random field modelling technique, especially for uncertain parameters over complex physical domains. The polynomial chaos expansion (PCE) is employed for estimating the statistical characteristics (e.g., mean and standard deviation) of any concerned structural responses (e.g., displacement and stress). By further implementing various statistical inference techniques, the probability density functions (PDF) and cumulative distribution functions (CDF) of structural responses can be established to determine both serviceability and strength limits of FGM plate. Two numerical examples are thoroughly investigated to illustrate the applicability, effectiveness and efficiency of the proposed computational approach.