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High-precision solution to the moving load problem using an improved spectral element method

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In this paper, the spectral element method (SEM) is improved to solve the moving load problem. In this method, a structure with uniform geometry and material properties is considered as a spectral element, which means that the element number and the degree of freedom can be reduced significantly. Based on the variational method and the Laplace transform theory, the spectral stiffness matrix and the equivalent nodal force of the beam-column element are established. The static Green function is employed to deduce the improved function. The proposed method is applied to two typical engineering practices—the one-span bridge and the horizontal jib of the tower crane. The results have revealed the following. First, the new method can yield extremely high-precision results of the dynamic deflection, the bending moment and the shear force in the moving load problem. In most cases, the relative errors are smaller than 1%. Second, by comparing with the finite element method, one can obtain the highly accurate results using the improved SEM with smaller element numbers. Moreover, the method can be widely used for statically determinate as well as statically indeterminate structures. Third, the dynamic deflection of the twin-lift jib decreases with the increase in the moving load speed, whereas the curvature of the deflection increases. Finally, the dynamic deflection, the bending moment and the shear force of the jib will all increase as the magnitude of the moving load increases.

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Acknowledgements

The project was supported by the National Key Technology R&D Program (Grant 2011BAJ02B01-02) and the National Natural Science Foundation of China (Grant 11602065).

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Authors and Affiliations

  1. College of Shipbuilding Engineering, Harbin Engineering University, Harbin, 150001, China

    Shu-Rui Wen

  2. School of Mechatronics Engineering, Harbin Institute of Technology, Harbin, 150001, China

    Shu-Rui Wen & Nian-Li Lu

  3. College of Aerospace and Civil Engineering, Harbin Engineering University, Harbin, 150001, China

    Zhi-Jing Wu

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  1. Shu-Rui Wen
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Correspondence to Shu-Rui Wen.

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Wen, SR., Wu, ZJ. & Lu, NL. High-precision solution to the moving load problem using an improved spectral element method. Acta Mech. Sin. 34, 68–81 (2018). https://doi.org/10.1007/s10409-017-0678-3

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  • DOI: https://doi.org/10.1007/s10409-017-0678-3

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