DOI QR코드

DOI QR Code

Static and vibration analysis of thin plates by using finite element method of B-spline wavelet on the interval

  • Xiang, Jiawei (School of Mechantronic Engineering, Guilin University of Electronic Technology) ;
  • He, Zhengjia (School of Mechanical Engineering, Xi'an Jiaotong University) ;
  • He, Yumin (School of Mechanical Engineering, Xi'an Jiaotong University) ;
  • Chen, Xuefeng (School of Mechanical Engineering, Xi'an Jiaotong University)
  • Received : 2005.08.02
  • Accepted : 2006.09.19
  • Published : 2007.03.30

Abstract

A finite element method (FEM) of B-spline wavelet on the interval (BSWI) is used in this paper to solve the static and vibration problems of thin plate. Instead of traditional polynomial interpolation, the scaling functions of two-dimensional tensor product BSWI are employed to construct the transverse displacements field. The method combines the accuracy of B-spline functions approximation and various basis functions for structural analysis. Some numerical examples are studied to demonstrate the proposed method and the numerical results presented are in good agreement with the solutions of other methods.

Keywords

References

  1. Basu, P.K., Jorge, A.B., Badri, S. and Lin, J. (2003), 'Higher-order modeling of continua by finite-element, boundary-element, Meshless, and wavelet methods', Comput. Math. Appl., 46, 15-33 https://doi.org/10.1016/S0898-1221(03)90078-2
  2. Bertoluzza, S., Naldi, G. and Ravel, J.C. (1994), 'Wavelet methods for the numerical solution of boundary value problems on the interval', Wavelets: Theory, Algorithms, and Applications. Chui, C.K., Montefusco, L. and Puccio, L. (eds.), Academic Press, London. 425-448
  3. Blevins, R.D. (1979), Formulas for Natural Frequency and Mode Shape, Van Nostrand Reinhold Co., New York
  4. Canuto, C., Tabacco, A. and Urban, K. (1999), 'The wavelet element method Part 1: Construction and analysis', Appl. Comput. Harmon. A., 6, 1-52 https://doi.org/10.1006/acha.1997.0242
  5. Canuto, C., Tabacco, A. and Urban, K. (2000), 'The wavelet element method Part II: Realization and additional feature in 2D and 3D', Appl. Comput. Harmon. A., 8, 123-165 https://doi.org/10.1006/acha.2000.0282
  6. Chen, W.H. and Wu, C.W. (1995), 'A spline wavelets element method for frame structures vibration', Comput. Mech., 16(1), 11-21 https://doi.org/10.1007/BF00369881
  7. Chen, W.H. and Wu, C.W. (1996), 'Extension of spline wavelets element method to membrane vibration analysis', Comput. Mech., 18(1),46-54 https://doi.org/10.1007/BF00384175
  8. Chen, X.F., Yang, S.J., Ma, J.X. and He, Z.J. (2004), 'The construction of wavelet finite element and, its application', Finite Elem. Anal. Des., 40(5-6), 541-554 https://doi.org/10.1016/S0168-874X(03)00077-5
  9. Chui, C.K. and Quak, E. (1992), 'Wavelets on a bounded interval', Numer. Math. Approx. Theory, 1, 53-57
  10. Cohen, A. (2003), Numerical Analysis of Wavelet Method, Elsevier Press, Amsterdam
  11. GangaRao, Hota Y.S. and Chaudhary, V.K. (1988), 'Analysis of skew and triangular plates in bending', Comput. Struct., 28(2), 223-235 https://doi.org/10.1016/0045-7949(88)90043-0
  12. Goswami, J.C., Chan, A.K. and Chui, C.K. (1995), 'On solving first-kind integral equations using wavelets on a bounded interval', IEEE T Antenn. Propag., 43, 614-622 https://doi.org/10.1109/8.387178
  13. Ko, J., Kurdila, A.J. and Pilant, M.S. (1997), 'Triangular wavelet based finite elements via multivalued scaling equations', Comput. Meth. Appl. Mech. Eng., 146(1-2), 1-17 https://doi.org/10.1016/S0045-7825(96)01209-1
  14. Liew, K.M., Xiang, Y., Kitlipomchai, S. and Wang, C.M. (1993), 'Vibration of thick skew plates based on Mindlin shear deformation plate theory', J. Sound Vib., 168(1), 39-69 https://doi.org/10.1006/jsvi.1993.1361
  15. 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
  16. Mallat, S.G (1999), A Wavelet Tour of Signal Processing, Academic Press, London
  17. Morley, L.S.D. (1963), Skew Plates and Structures, Pergamon Press, New York
  18. Quak, E. and Weyrich, N. (1994), 'Decomposition and Reconstruction algorithms for spline wavelets on a Bounded interval', Appl. Comput. Harmon. A., 3, 217-231
  19. Raju, K.K. and Hinton, E. (1980), 'Natural frequencies and modes of rhombic Mindlin plates', Earthq. Eng. Struct. Dyn., 8, 55-62 https://doi.org/10.1002/eqe.4290080106
  20. Shen, P.C. (1991), Spline Finite Methods in Structural Analysis, Hydraulic and Electric Press, Beijin (In Chinese)
  21. Shen, P.C. and He, P.X, (1995), 'Bending analysis of rectangular moderately thick plates using spline finite element method', Comput. Struct., 54(6), 1023-1029 https://doi.org/10.1016/0045-7949(94)00401-N
  22. Timoshenko, S.P. and Goodier, J.N. (1970), Theory of Elasticity, McGraw-Hill Press, New York
  23. Warburton, G.B. (1954), 'The vibration of rectangular plates', Proc. of Institution of Mechanical Engineering, London, 371-385
  24. Xiang, J.W., Chen, X.F., He, Y.M. and He, Z.J. (2006), 'The construction of plane elastomechanics and mindlin plate elements of B-spline wavelet on the interval', Finite Elem. Anal. Des., 42(14-15),1269-1280 https://doi.org/10.1016/j.finel.2006.06.006
  25. Xiang, J.W., Chen, X.F., Li, B., He, Y.M. and He, Z.J. (2006), 'Identification of crack in a beam based on finite element method of B-spline wavelet on the interval', J. Sound Vib., 296(4-5),1046-1052 https://doi.org/10.1016/j.jsv.2006.02.019
  26. Zhou, Y.H., Wang, J.Z. and Zheng, X.J. (1998), 'Application of wavelet Galerkin FEM to bending of beam and plate structures', Appl. Math. Mech., 19(8), 697-706
  27. Zienkiewicz, O.C. (1988), The Finite Element Method, McGRAW-Hill Book Company Limited, London
  28. Zienkiewicz, O.C. and Lefebvre, D. (1988), 'A robust triangular plate bending element of the Reissener-Mindlin type', Int. J. Numer. Methods Eng., 26,1169-1184 https://doi.org/10.1002/nme.1620260511

Cited by

  1. Multivariable wavelet finite element for flexible skew thin plate analysis vol.57, pp.8, 2014, https://doi.org/10.1007/s11431-014-5573-6
  2. A two-step approach to multi-damage detection for plate structures vol.91, 2012, https://doi.org/10.1016/j.engfracmech.2012.04.028
  3. Identification of damage locations based on operating deflection shape vol.28, pp.2, 2013, https://doi.org/10.1080/10589759.2012.716437
  4. Multivariable finite elements based on B-spline wavelet on the interval for thin plate static and vibration analysis vol.46, pp.5, 2010, https://doi.org/10.1016/j.finel.2010.01.002
  5. 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
  6. Vibration analysis of an elastically restrained microcantilever beam under electrostatic loading using wavelet-based finite element method vol.10, pp.3, 2015, https://doi.org/10.1049/mnl.2014.0306
  7. Band Structures Analysis Method of Two-Dimensional Phononic Crystals Using Wavelet-Based Elements vol.7, pp.11, 2017, https://doi.org/10.3390/cryst7110328
  8. A study of multiscale wavelet-based elements for adaptive finite element analysis vol.41, pp.2, 2010, https://doi.org/10.1016/j.advengsoft.2009.09.008
  9. A new wavelet-based thin plate element using B-spline wavelet on the interval vol.41, pp.2, 2007, https://doi.org/10.1007/s00466-007-0182-x
  10. Quantitative nondestructive evaluation of thin plate structures using the complete frequency information from impact testing vol.28, pp.5, 2007, https://doi.org/10.12989/sem.2008.28.5.525
  11. Crack identification in short shafts using wavelet-based element and neural networks vol.33, pp.5, 2007, https://doi.org/10.12989/sem.2009.33.5.543
  12. New decoupled wavelet bases for multiresolution structural analysis vol.35, pp.2, 2007, https://doi.org/10.12989/sem.2010.35.2.175
  13. The numerical solution of dynamic response of SDOF systems using cubic B-spline polynomial functions vol.38, pp.2, 2007, https://doi.org/10.12989/sem.2011.38.2.211
  14. The construction of multivariable Reissner-Mindlin plate elements based on B-spline wavelet on the interval vol.38, pp.6, 2007, https://doi.org/10.12989/sem.2011.38.6.733
  15. Study on damage detection software of beam-like structures vol.39, pp.1, 2007, https://doi.org/10.12989/sem.2011.39.1.077
  16. NURBS-based isogeometric analysis for thin plate problems vol.41, pp.5, 2007, https://doi.org/10.12989/sem.2012.41.5.617
  17. Method using XFEM and SVR to predict the fatigue life of plate-like structures vol.73, pp.4, 2007, https://doi.org/10.12989/sem.2020.73.4.455