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Analysis of plates on Winkler foundation by wavelet collocation

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References

  1. Winkler E (1867) Die Lehre von der Elasticitaet und Festigkeit. Dominicus, Prag

    MATH  Google Scholar 

  2. Leissa AW (1973) The free vibration of plates. J Sound Vibr 31:257–293

    Article  ADS  MATH  Google Scholar 

  3. Lam KY, Wang CM, He XQ (2000) Canonical exact solutions for levy-plates on two-parameter foundation using green’s functions. Eng Struct 22:364–378

    Article  Google Scholar 

  4. Xiang Y, Wang CM, Kitipornchai S (1994) Exact vibration solution for initially stressed Mindlin plates on Pasternak foundation. Int J Mech Sci 36:311–316

    Article  MATH  Google Scholar 

  5. Omurtag MH, Ozutok A, Akoz AY (1997) Free vibration analysis of Kirchhoff plates resting on elastic foundation by mixed finite element formulation based on gateaux differential. Int J Numer Methods Eng 40:295–317

    Article  MathSciNet  Google Scholar 

  6. Matsunaga H (2000) Vibration and stability of thick plates on elastic foundations. J Eng Mech (ASCE) 126:27–34

    Article  Google Scholar 

  7. Shen HS, Yang J, Zhang L (2001) Free and forced vibration of Reissner-Mindlin plates with free edges resting on elastic foundations. J Sound Vibr 244:299–320

    Article  ADS  Google Scholar 

  8. Ayvaz Y, Daloglu A, Dogangun A (1998) Application of a modified Vlasov model to earthquake analysis of plates resting on elastic foundations. J Sound Vibr 212:499–509

    Article  ADS  Google Scholar 

  9. Liew KM, Teo TM (2002) Differential cubature method for analysis of shear deformable rectangular plates on Pasternak foundations. Int J Mech Sci 44:1179–1194

    Article  MATH  Google Scholar 

  10. Liew KM, Han JB, Xiao ZM, Du H (1996) Differential quadrature method for Mindlin plates on Winkler foundations. Int J Mech Sci 38:405–421

    Article  MATH  Google Scholar 

  11. Han JB, Liew KM (1997) Numerical differential quadrature method for Reissner-Mindlin plates on two-parameter foundations. Int J Mech Sci 39:977–989

    Article  MATH  Google Scholar 

  12. Zhou D, Cheung YK, Lo SH, Au FTK (2004) Three-dimensional vibration analysis of rectangular thick plates on Pasternak foundation. Int J Numer Meth Eng 59:1313–1334

    Article  MATH  Google Scholar 

  13. Civalek O, Acar MH (2007) Discrete singular convolution method for the analysis of Mindlin plates on elastic foundations. Int J Press Vessels Piping 84:527–535

    Article  Google Scholar 

  14. Chucheepsakul S, Chinnaboom B (2002) An alternative domain boundary element technique for analyzing plates on two-parameter elastic foundations. Eng Anal Bound Elem 26:547–555

    Article  MATH  Google Scholar 

  15. Ma J, Chen JX, Yang S, He Z (2004) The construction of wavelet-finite element and its application. Finite Elem Anal Des 40:541–554

    Article  Google Scholar 

  16. Civalek O (2007) Nonlinear analysis of thin rectangular plates on Winkler-Pasternak elastic foundations by dsc-hdq methods. Appl Math Mod 31:606–624

    Article  MATH  Google Scholar 

  17. Liu FL (2000) Rectangular thick plates on Winkler foundation: differential quadrature element solution. Int J Solids Struct 37(12):1743–1763

    Article  MATH  Google Scholar 

  18. Gupta DC, Tomar JS, Kumar V (1984) Natural frequencies of a non homogeneous isotropic elastic infinite plate of variable thickness resting on elastic foundation. Meccanica 19(4):320–324

    Article  MATH  Google Scholar 

  19. Bertoluzza S, Castro LM Adaptive wavelet collocation for elasticity: first results. Preprint, IAN-CNR, IAN-CNR (Pavia, Italy) (2001)

  20. Bertoluzza S, Naldi G (1996) A wavelet collocation method for the numerical solution of partial differential equations. Appl Comput Harm Anal 3:1–9

    Article  MATH  MathSciNet  Google Scholar 

  21. Castro LMS, Bertoluzza S, Ferreira AJM (2009) A high order collocation method for the static and vibration analysis of composite plates using a first-order theory. Compos Struct 89:424–432

    Article  Google Scholar 

  22. Bertoluzza S (1997) An adaptive collocation method based on interpolating wavelets. In: Kurdila A, Dahmen W, Oswald P (eds) Multiscale wavelet methods for partial differential equations. Academic Press, San Diego

    Google Scholar 

  23. Dahmen W, Michelli C (1993) Using the refinement equation for evaluating integrals of wavelets. SIAM J Numer Anal 30:507–533

    Article  MATH  MathSciNet  Google Scholar 

  24. Kobayashi H, Sonoda K (1989) Rectangular Mindlin plates on elastic foundation. Int J Mech Sci 31(9):679–692

    Article  MATH  Google Scholar 

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Authors and Affiliations

  1. Departamento de Engenharia Mecânica, Faculdade de Engenharia, Universidade do Porto, Rua Dr. Roberto Frias, 4200-465, Porto, Portugal

    A. J. M. Ferreira

  2. Departamento de Engenharia Civil e Arquitectura, IST-UTL, Avenida Rovisco Pais, 1049-001, Lisbon, Portugal

    Luís M. S. Castro

  3. Istituto di Analisi Numerica, C.N.R., via Ferrata, 1, 27100, Pavia, Italy

    Silvia Bertoluzza

Authors
  1. A. J. M. Ferreira
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  2. Luís M. S. Castro
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  3. Silvia Bertoluzza
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Correspondence to A. J. M. Ferreira.

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Ferreira, A.J.M., Castro, L.M.S. & Bertoluzza, S. Analysis of plates on Winkler foundation by wavelet collocation. Meccanica 46, 865–873 (2011). https://doi.org/10.1007/s11012-010-9341-9

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  • DOI: https://doi.org/10.1007/s11012-010-9341-9

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