Structural Engineering and Mechanics

Techno-Press (테크노프레스)
권호 표지
DOI QR코드

DOI QR Code

New decoupled wavelet bases for multiresolution structural analysis

  • Wang, Youming (State Key Lab for Manufacturing Systems Engineering, Xi'an Jiaotong University) ;
  • Chen, Xuefeng (State Key Lab for Manufacturing Systems Engineering, Xi'an Jiaotong University) ;
  • He, Yumin (State Key Lab for Manufacturing Systems Engineering, Xi'an Jiaotong University) ;
  • He, Zhengjia (State Key Lab for Manufacturing Systems Engineering, Xi'an Jiaotong University)
  • Received : 2008.07.01
  • Accepted : 2010.01.06
  • Published : 2010.05.30
⟨ Previous Next ⟩

Abstract

One of the intractable problems in multiresolution structural analysis is the decoupling computation between scales, which can be realized by the operator-orthogonal wavelets based on the lifting scheme. The multiresolution finite element space is described and the formulation of multiresolution finite element models for structural problems is discussed. Various operator-orthogonal wavelets are constructed by the lifting scheme according to the operators of multiresolution finite element models. A dynamic multiresolution algorithm using operator-orthogonal wavelets is proposed to solve structural problems. Numerical examples demonstrate that the lifting scheme is a flexible and efficient tool to construct operator-orthogonal wavelets for multiresolution structural analysis with high convergence rate.

Keywords

References

  1. Castrillon-Candas, J. and Amaratunga, K. (2003), "Spatially adapted multiwavelets and sparse representation of integral equations on general geometries", SIAM J. Sci. Comput., 24(5), 1530-1566. https://doi.org/10.1137/S1064827501371238
  2. Chen, C.M. and Huang, Y.Q. (1995), High Accuracy Theory of Finite Element Methods, Science and Technology Press, Hunan. (in Chinese)
  3. Chen, X.F., Yang, S.J. and He, Z.J. (2004), "The construction of wavelet finite element and its application", Finite Elem. Anal. Des., 40, 541-554. https://doi.org/10.1016/S0168-874X(03)00077-5
  4. Davis, G.M., Strela, V. and Turcajova, R. (1999), Multiwavelet Construction Via the Lifting Scheme, Wavelet Analysis and Multiresolution Methods, Lecture Notes in Pure and Applied Mathematics (Ed. Marcel Dekker), New York.
  5. D'Heedene, S., Amaratunga, K. and Castrillón-Candás, J. (2005) "Generalized hierarchical bases: a Wavelet- Ritz-Galerkin framework for Lagrangian FEM", Eng. Comput., 22(1), 15-37. https://doi.org/10.1108/02644400510572398
  6. He, Y.M., Chen, X.F., Xiang, J.W. and He, Z.J. (2007), "Adaptive multiresolution finite element method based on second generation wavelets", Finite Elem. Anal. Des., 43, 566-579. https://doi.org/10.1016/j.finel.2006.12.009
  7. Ma, J.X., Xue, J.J., Yang, S.J. and He, Z.J. ( 2003), "A study of the construction and application of a Daubechies wavelet-based beam element", Finite Elem. Anal. Des., 39(10), 965-975. https://doi.org/10.1016/S0168-874X(02)00141-5
  8. Mallat, S.G. (1998), A Wavelet Tour of Signal Processing, Academic Press, Boston.
  9. Pinho, P., Ferreira, P.J.S.G. and Pereira, J.R. (2004), "Multiresolution analysis using biorthogonal and interpolating wavelets", IEEE Antenn. Propag. Soc. Symp., 2, 1483-1486.
  10. Sudarshan, R., Amaratunga, K. and Gratsch, T. (2006), "A combined approach for goal-oriented error estimation and adaptivity using operator-customized finite element wavelets", Int. J. Numer. Meth. Eng., 66, 1002-1035. https://doi.org/10.1002/nme.1578
  11. Sweldens, W. (1997), "The lifting scheme: a construction of second generation wavelets", SIAM J. Math. Anal., 29(2), 511-546.
  12. Vasilyev, O.V. and Bowman, C. (2000), "Second generation wavelet collocation method for the solution of partial differential equations", J. Commun. Phys., 165, 660-693. https://doi.org/10.1006/jcph.2000.6638
  13. Wang, X.C. (2002), The Finite Element Methods, Tsing Hua University Press, Beijing. (in Chinese)
  14. Xiang, J.W., He, Z.J. and Chen, X.F. ( 2007), "Static and vibration analysis of thin plates by using finite element method of B-spline wavelet on the interval", Struct. Eng. Mech., 25(5), 613-629. https://doi.org/10.12989/sem.2007.25.5.613

Cited by

  1. An Improved Method of Parameter Identification and Damage Detection in Beam Structures under Flexural Vibration Using Wavelet Multi-Resolution Analysis vol.15, pp.12, 2015, https://doi.org/10.3390/s150922750
  2. A two-step damage identification approach for beam structures based on wavelet transform and genetic algorithm vol.51, pp.3, 2016, https://doi.org/10.1007/s11012-015-0227-8
  3. Wavelet-based numerical analysis: A review and classification vol.81, 2014, https://doi.org/10.1016/j.finel.2013.11.001
  4. The construction of second generation wavelet-based multivariable finite elements for multiscale analysis of beam problems vol.50, pp.5, 2014, https://doi.org/10.12989/sem.2014.50.5.679
  5. The construction of multivariable Reissner-Mindlin plate elements based on B-spline wavelet on the interval vol.38, pp.6, 2010, https://doi.org/10.12989/sem.2011.38.6.733
  6. Galerkin Meshfree Methods: A Review and Mathematical Implementation Aspects vol.5, pp.4, 2010, https://doi.org/10.1007/s40819-019-0665-4