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Structural Engineering and Mechanics Volume 82, Number 1, April10 2022 , pages 31-40 DOI: https://doi.org/10.12989/sem.2022.82.1.031 |
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A stochastic finite element method for dynamic analysis of bridge structures under moving loads |
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Xiang Liu, Lizhong Jiang, Ping Xiang, Zhipeng Lai, Yuntai Zhang and Lili Liu
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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. | ||
| Key Words | ||
| finite element method; point estimate method; railway bridge; random dynamics; stochastic field | ||
| Address | ||
| Xiang Liu: School of Civil Engineering, Fujian University of Technology, Fuzhou 350118, China Lizhong Jiang: School of Civil Engineering, Central South University, Changsha 410075, China; National Engineering Research Center of High-speed Railway Construction Technology, Changsha 410075, China Ping Xiang: School of Civil Engineering, Central South University, Changsha 410075, China; Engineering Research Center for Seismic Disaster Prevention and Engineering, Geological Disaster Detection of Jiangxi Province, East China University of Technology, China Zhipeng Lai: School of Civil Engineering, Central South University, Changsha 410075, China; National Engineering Research Center of High-speed Railway Construction Technology, Changsha 410075, China Yuntai Zhang: School of Civil Engineering, Central South University, Changsha 410075, China Lili Liu: School of Civil Engineering, Central South University, Changsha 410075, China | ||