Proper orthogonal decomposition and Monte Carlo based isogeometric stochastic method for material, geometric and force multi-dimensional uncertainties

This paper develops a proper orthogonal decomposition (POD) and Monte Carlo simulation (MCS) based isogeometric stochastic method for multi-dimensional uncertainties. The geometry of the structure is exactly represented and more accurate deterministic solutions are provided via isogeometric analysis (IGA). Secondly, we innovatively tackle multi-dimensional uncertainties, including separate material, geometric and force randomness, and their combined cases. Thirdly, MCS is employed to solve the multi-dimensional uncertainty problem. However, we significantly decrease its huge computational burden whilst keeping its universality and accuracy at the same time. This is accomplished by coupling POD with MCS in the IGA stochastic analysis. Namely, we reduce the full order system whose DOFs is N to a much smaller DOF s. Several examples validate that the proposed scheme is general, effective and efficient; and the larger the scale and/or the number of the samples of the problem, the more advantageous the method will inherit.