Spectral stochastic isogeometric analysis for linear stability analysis of plate

Abstract

A spectral stochastic isogeometric analysis (SSIGA) scheme is proposed for the stochastic linear stability analysis of plate with uncertain material properties. Within the proposed SSIGA scheme, the first-order shear deformation theory of plate is adopted for modelling the kinematic relationship. Both homogeneous and functionally graded material (FGM) models can be incorporated. The considered spatially dependent uncertainties (i.e., Young’s modulus and Poisson’s ratio) are modelled as random fields with Gaussian and lognormal distributions, and the spatially independent uncertainty (i.e., gradient index of FGM) is modelled as random variable. The generalized isogeometric basis function is adopted for both the random field geometry representation and random field discretization through the Karhunen–Loève (K–L) expansion. An extended support vector regression (X-SVR) with a new generalized Gegenbauer polynomial kernel is developed to model the nonlinear relationship between the structural uncertainties and the buckling load. By further implementing various nonparametric statistical inference methods, the mean, standard deviation, probability density function (PDF), and cumulative distribution function (CDF) of the buckling load can be effectively established to determine the strength limit of the plate. The accuracy, efficiency, and applicability of the proposed approach are illustrated through two numerical examples.