Multivariate uncertainty analysis of fracture problems through model order reduction accelerated SBFEM

An efficient Monte Carlo simulation (MCS) method that analyses the influences of multivariate uncertain parameters on the response of cracked structures is proposed. The scaled boundary finite element method (SBFEM) is used to solve the static and dynamic crack propagation problems and obtain a full-order snapshot model. The combination of a proper orthogonal decomposition with model order reduction and a radial basis function is used to achieve accelerated stochastic analysis based on MC simulations. The proper orthogonal decomposition-radial basis function (POD-RBF) method is more difficult to use directly for multivariate problems. Thus, we proposed an efficient operation suitable for multiple input variables. In crack propagation simulations, an optimized polygon meshing algorithm is used. Numerical results show that the proposed method can stochastically analyse multidimensional input variables and effectively obtain the responses of cracked structures, which verifies the effectiveness of the POD-RBF method.