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Stochastic finite element method based on point estimate and Karhunen–Loéve expansion

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Abstract

The present study proposes a new stochastic finite element method. The Karhunen–Loéve expansion is utilized to discretize the stochastic field, while the point estimate method is applied for calculating the random response of the structure. Two illustrative examples, including finite element models with one-dimensional and two-dimensional stochastic fields, are investigated to demonstrate the accuracy and efficiency of the proposed method. Furthermore, two classical finite element analysis methods are used to validate the results. It is proved that the proposed method can model both the one-dimensional and the two-dimensional stochastic finite element problems accurately and efficiently.

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  • 12 January 2021

    Journal abbreviated title on top of the page has been corrected to “Arch Appl Mech”

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Acknowledgements

The work described in this paper is supported by grants from the National Natural Science Foundation of China (Grant Nos. U1934207, 51778630, and 11972379), the Fundamental Research Funds for the Central Universities of Central South University (Grant No. 2020zzts148), Jiangsu Key Laboratory of Environmental Impact and Structural Safety in Engineering, China University of Mining & Technology and Engineering Research Center for Seismic Disaster Prevention and Engineering Geological Disaster Detection of Jiangxi Province (SDGD202001).

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Authors and Affiliations

  1. School of Civil Engineering, Central South University, Changsha, 410075, Hunan, China

    Xiang Liu, Lizhong Jiang, Ping Xiang, Wangbao Zhou & Zhipeng Lai

  2. National Engineering Laboratory for High-speed Railway Construction, Changsha, China

    Lizhong Jiang, Ping Xiang, Wangbao Zhou & Zhipeng Lai

  3. School of Civil Engineering and Architecture, East China Jiaotong University, Nanchang, 330013, China

    Yulin Feng

  4. Jiangsu Key Laboratory of Environmental Impact and Structural Safety in Engineering, China University of Mining and Technology, Xuzhou, China

    Ping Xiang

  5. Engineering Research Center for Seismic Disaster Prevention and Engineering Geological Disaster Detection of Jiangxi Province, Nanchang, China

    Ping Xiang

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  1. Xiang Liu
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Correspondence to Ping Xiang.

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Liu, X., Jiang, L., Xiang, P. et al. Stochastic finite element method based on point estimate and Karhunen–Loéve expansion. Arch Appl Mech 91, 1257–1271 (2021). https://doi.org/10.1007/s00419-020-01819-8

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