Structural Engineering and Mechanics

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A stochastic finite element method for dynamic analysis of bridge structures under moving loads

  • Liu, Xiang (School of Civil Engineering, Fujian University of Technology) ;
  • Jiang, Lizhong (School of Civil Engineering, Central South University) ;
  • Xiang, Ping (School of Civil Engineering, Central South University) ;
  • Lai, Zhipeng (School of Civil Engineering, Central South University) ;
  • Zhang, Yuntai (School of Civil Engineering, Central South University) ;
  • Liu, Lili (School of Civil Engineering, Central South University)
  • Received : 2021.01.05
  • Accepted : 2021.12.29
  • Published : 2022.04.10
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Abstract

In structural engineering, the material properties of the structures such as elastic modulus, shear modulus, density, and size may not be deterministic and may vary at different locations. The dynamic response analysis of such structures may need to consider these properties as stochastic. This paper introduces a stochastic finite element method (SFEM) approach to analyze moving loads problems. Firstly, Karhunen-Loéve expansion (KLE) is applied for expressing the stochastic field of material properties. Then the mathematical expression of the random field is substituted into the finite element model to formulate the corresponding random matrix. Finally, the statistical moment of the dynamic response is calculated by the point estimation method (PEM). The accuracy and efficiency of the dynamic response obtained from the KLE-PEM are demonstrated by the example of a moving load passing through a simply supported Euler-Bernoulli beam, in which the material properties (including elastic modulus and density) are considered as random fields. The results from the KLE-PEM are compared with those from the Monte Carlo simulation. The results demonstrate that the proposed method of KLE-PEM has high accuracy and efficiency. By using the proposed SFEM, the random vertical deflection of a high-speed railway (HSR) bridge is analyzed by considering the random fields of material properties under the moving load of a train.

Keywords

Acknowledgement

The work described in this paper is supported by grants from the National Natural Science Foundation of China (U1934207 and 11972379), Fujian University of Technology (GY-Z21181), the science and technology innovation Program of Hunan Province (2021RC2011), the China Postdoctoral Science Foundation (2021M703648), Fund of Engineering Research Center for Seismic Disaster Prevention and Engineering Geological Disaster Detection of Jiangxi Province (SDGD202001), the Key R&D Program of Hunan Province (2020SK2060), and Central South University (Grant Nos. 502045006, 502390001 and innovation-driven project 502501006).

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