Stochastic isogeometric buckling analysis of composite shell considering multiple uncertainties

An efficient stochastic isogeometric analysis (SIGA) framework considering multiple uncertainties is proposed for the stochastic buckling analysis of composite shells. The framework develops a seamless pipeline enabling uncertainty quantification and uncertainty analysis with the same building blocks of Non-Uniform Rational B-Splines (NURBS). The Gaussian random fields with spatial variability of random parameters are represented by Karhunen-Loève expansion, which is a linear combination of a set of independent random variables and orthogonal functions. The orthogonal functions and corresponding eigenvalues are obtained by solving the Fredholm integral equation of the second kind by the Galerkin isogeometric method. This method exploits the regularity of NURBS basis functions delivering globally smooth eigensolutions and the total mean squared error of the random field is minimized simultaneously. In addition, perturbation technique is developed to solve the stochastic linear buckling equation and predict the second-moment statistics of the buckling load and the probability of failure of structures. The accuracy of the proposed method is assessed by independent Monte Carlo simulation (MCS) based on isogeometric analysis (IGA). Moreover, from the point of view of convergence and computational time, it is evident that the proposed SIGA framework can effectively obtain probabilistic characteristics compared with stochastic finite element method (SFEM).