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A new wavelet-based thin plate element using B-spline wavelet on the interval

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Abstract

By interacting and synchronizing wavelet theory in mathematics and variational principle in finite element method, a class of wavelet-based plate element is constructed. In the construction of wavelet-based plate element, the element displacement field represented by the coefficients of wavelet expansions in wavelet space is transformed into the physical degree of freedoms in finite element space via the corresponding two-dimensional C1 type transformation matrix. Then, based on the associated generalized function of potential energy of thin plate bending and vibration problems, the scaling functions of B-spline wavelet on the interval (BSWI) at different scale are employed directly to form the multi-scale finite element approximation basis so as to construct BSWI plate element via variational principle. BSWI plate element combines the accuracy of B-spline functions approximation and various wavelet-based elements for structural analysis. Some static and dynamic numerical examples are studied to demonstrate the performances of the present element.

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Authors and Affiliations

  1. School of Mechantronic Engineering, Guilin University of Electronic Technology, Guilin, 541004, People’s Republic of China

    Xiang Jiawei & Zhang Yinghong

  2. School of Mechanical Engineering, The State Key Laboratory for Manufacturing Systems Engineering, Xi’an Jiaotong University, Xi’an, 710049, People’s Republic of China

    Chen Xuefeng & He Zhengjia

Authors
  1. Xiang Jiawei
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  2. Chen Xuefeng
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  3. He Zhengjia
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  4. Zhang Yinghong
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Correspondence to Xiang Jiawei.

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Jiawei, X., Xuefeng, C., Zhengjia, H. et al. A new wavelet-based thin plate element using B-spline wavelet on the interval. Comput Mech 41, 243–255 (2008). https://doi.org/10.1007/s00466-007-0182-x

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  • DOI: https://doi.org/10.1007/s00466-007-0182-x

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