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.
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Acknowledgements This work was supported by the National Key R&D Program of China (2017YFB1002704), National Science Foundation of China (11472101) and China Scholarship Council (201606130079).
This work was supported by the National Key R&D Program of China (2017YFB1002704), National Science Foundation of China (11472101) and China Scholarship Council (201606130079).
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- Geometric and force uncertainties
- Isogeometric stochastic analysis
- Multi-dimension uncertainties
- Proper orthogonal decomposition coupled Monte Carlo method (POD–MC)
- Separate and combined material