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

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Abstract

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).

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Authors and Affiliations

  1. State Key Laboratory of Advanced Design and Manufacturing for Vehicle Body, Hunan University, Changsha, 410082, People’s Republic of China

    Chensen Ding, Xiangyang Cui, Guangyao Li & Yong Cai

  2. Collaborative Innovation Center of Intelligent New Energy Vehicle, Shanghai, 200092, People’s Republic of China

    Chensen Ding, Xiangyang Cui, Guangyao Li & Yong Cai

  3. Department of Mechanical Engineering, University of Minnesota-Twin Cities, Minneapolis, MN, 55455, USA

    Chensen Ding, Rohit R. Deokar & Kumar K. Tamma

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  1. Chensen Ding
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  2. Rohit R. Deokar
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Correspondence to Xiangyang Cui or Kumar K. Tamma.

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Ding, C., Deokar, R.R., Cui, X. et al. Proper orthogonal decomposition and Monte Carlo based isogeometric stochastic method for material, geometric and force multi-dimensional uncertainties. Comput Mech 63, 521–533 (2019). https://doi.org/10.1007/s00466-018-1607-4

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  • DOI: https://doi.org/10.1007/s00466-018-1607-4

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