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Construction and Application of Multivariable Wavelet Finite Element for Flat Shell Analysis

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A Correction to this article was published on 22 November 2018

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Abstract

Based on B-spline wavelet on the interval (BSWI) and the multivariable generalized variational principle, the multivariable wavelet finite element for flat shell is constructed by combining the elastic plate element and the Mindlin plate element together. First, the elastic plate element formulation is derived from the generalized potential energy function. Due to its excellent numerical approximation property, BSWI is used as the interpolation function to separate the solving field variables. Second, the multivariable wavelet Mindlin plate element is deduced and constructed according to the multivariable generalized variational principle and BSWI. Third, by following the displacement compatibility requirement and the coordinate transformation method, the multivariable wavelet finite element for flat shell is constructed. The novel advantage of the constructed element is that the solving precision and efficiency can be improved because the generalized displacement field variables and stress field variables are interpolated and solved independently. Finally, several numerical examples including bending and vibration analyses are given to verify the constructed element and method.

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  • 22 November 2018

    In all the articles in Acta Mechanica Solida Sinica, Volume 31, Issues 1–4, the copyright is incorrectly displayed as “The Chinese Society of Theoretical and Applied Mechanics and Technology ” where it should be “The Chinese Society of Theoretical and Applied Mechanics”.

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Acknowledgements

This work was supported by the National Natural Science Foundation of China (No. 51775408), the Project funded by the Key Laboratory of Product Quality Assurance & Diagnosis (No. 2014SZS14-P05) and the open foundation of Zhejiang Provincial Key Laboratory of Laser Processing Robot/Key Laboratory of Laser Precision Processing & Detection (lzsy-12).

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Authors and Affiliations

  1. State Key Laboratory for Manufacturing Systems Engineering, Xi’an Jiaotong University, Xi’an, 710049, China

    Xingwu Zhang, Yanfei He, Jia Geng & Xuefeng Chen

  2. School of Mechanical Engineering, Xi’an Jiaotong University, Xi’an, 710049, China

    Xingwu Zhang, Yanfei He, Jia Geng & Xuefeng Chen

  3. Department of Mechanical Engineering, Case Western Reserve University, Cleveland, OH, 44106, USA

    Robert X. Gao

  4. Zhejiang Provincial Key Laboratory of Laser Processing Robot/Key Laboratory of Laser Precision Processing & Detection, Wenzhou University, Wenzhou, 325035, China

    Jiawei Xiang

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  1. Xingwu Zhang
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  2. Yanfei He
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  4. Jia Geng
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  5. Xuefeng Chen
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Correspondence to Xuefeng Chen.

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Zhang, X., He, Y., Gao, R.X. et al. Construction and Application of Multivariable Wavelet Finite Element for Flat Shell Analysis. Acta Mech. Solida Sin. 31, 391–404 (2018). https://doi.org/10.1007/s10338-018-0038-2

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  • DOI: https://doi.org/10.1007/s10338-018-0038-2

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