Spectral stochastic isogeometric analysis of linear elasticity

Abstract

The stochastic isogeometric analysis of linear elasticity problem is investigated in this study. The spectral stochastic analysis is introduced into isogeometric analysis (IGA), and a novel, yet robust, stochastic analysis framework, namely the spectral stochastic isogeometric analysis (SSIGA), is freshly proposed. Unlike traditional numerical solutions of the Karhunen–Loève (K-L) expansion, the non-uniform rational B-spline (NURBS) and T-spline basis functions are employed within the proposed framework of SSIGA, so the random fields acting on a continuous physical medium with complex geometry can be handled in an appropriate, physically feasible and efficient fashion. The polynomials chaos expansion (PCE) is implemented to represent the stochastic structural response (e.g., displacement, strain and stress), such that all corresponding statistical characteristics (e.g., mean and standard deviation) can be robustly acquired. Furthermore, by utilizing the nonparametric statistical analysis, both probability density functions (PDFs) and cumulative distribution functions (CDFs) of concerned structural displacements and stresses can be effectively established. Within the framework of IGA, by meticulously implementing the concept of the higher-order k-refinement, the proposed SSIGA provides a more legitimate and efficient stochastic computational approach for modern engineering structures which are complicated by both spatially dependent uncertainties and complex geometries.