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Structural Engineering and Mechanics Volume 50, Number 5, June10 2014 , pages 679-695 DOI: https://doi.org/10.12989/sem.2014.50.5.679 |
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The construction of second generation wavelet-based multivariable finite elements for multiscale analysis of beam problems |
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Youming Wang, Qing Wu and Wenqing Wang
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| Abstract | ||
| A design method of second generation wavelet (SGW)-based multivariable finite elements is proposed for static and vibration beam analysis. An important property of SGWs is that they can be custom designed by selecting appropriate lifting coefficients depending on the application. The SGW-based multivariable finite element equations of static and vibration analysis of beam problems with two and three kinds of variables are derived based on the generalized variational principles. Compared to classical finite element method (FEM), the second generation wavelet-based multivariable finite element method (SGWMFEM) combines the advantages of high approximation performance of the SGW method and independent solution of field functions of the MFEM. A multiscale algorithm for SGW-MFEM is presented to solve structural engineering problems. Numerical examples demonstrate the proposed method is a flexible and accurate method in static and vibration beam analysis. | ||
| Key Words | ||
| second generation wavelet; multivariable finite element method; generalized variational principles; multiscale structural analysis | ||
| Address | ||
| Youming Wang, Qing Wu and Wenqing Wang : School of Automation, Xi | ||