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Analysis of thick plates by radial basis functions

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Abstract

In this paper, we use a higher-order shear deformation theory and a radial basis function collocation technique for predicting the static deformations and free vibration behavior of thick plates. Through numerical experiments, the capability and efficiency of this collocation technique for static and vibration problems are demonstrated, and the numerical accuracy and convergence are thoughtfully examined.

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References

  1. Lo K.H., Christensen R.M., Wu E.M.: A high-order theory of plate deformation, part 1: Homogeneous plates. J. Appl. Mech. 44, 663–668 (1977)

    Article  MATH  Google Scholar 

  2. Lo K.H., Christensen R.M., Wu E.M.: A high-order theory of plate deformation, part 2: laminated plates. J. Appl. Mech. 44, 669–676 (1977)

    Article  MATH  Google Scholar 

  3. Kant T.: Numerical analysis of thick plates. Comput. Methods Appl. Mech. Eng. 31, 1–18 (1982)

    Article  MATH  Google Scholar 

  4. Kant T., Owen D.R.J., Zienkiewicz O.C.: A refined higher-order co plate element. Comput. Struct. 15, 177–183 (1982)

    Article  MATH  MathSciNet  Google Scholar 

  5. Pandya B.N., Kant T.: Higher-order shear deformable theories for flexure of sandwich plates-finite element evaluations. Int. J. Solids Struct. 24, 419–451 (1988)

    Article  Google Scholar 

  6. Batra R.C., Vidoli S.: Higher order piezoelectric plate theory derived from a three-dimensional variational principle. AIAA J. 40, 91–104 (2002)

    Article  Google Scholar 

  7. Carrera E.: C0 Reissner-Mindlin multilayered plate elements including zig–zag and interlaminar stress continuity. Int. J. Numer. Methods Eng. 39, 1797–1820 (1996)

    Article  MATH  Google Scholar 

  8. Carrera E., Kroplin B.: Zig-zag and interlaminar equilibria effects in large deflection and post-buckling analysis of multilayered plates. Mech. Compos. Mater. Struct. 4, 69–94 (1997)

    Google Scholar 

  9. Carrera E.: Evaluation of layer-wise mixed theories for laminated plate analysis. AIAA J. 36, 830–839 (1998)

    Article  Google Scholar 

  10. Librescu L., Khdeir A.A., Reddy J.N.: A comprehensive analysis of the state of stress of elastic anisotropic flat plates using refined theories. Acta Mech. 70, 57–81 (1987)

    Article  MATH  Google Scholar 

  11. Reddy J.N.: Mechanics of laminated composite plates. CRC Press, New York (1997)

    MATH  Google Scholar 

  12. Fiedler L., Vestroni F., Lacarbonara W.: A generalized higher-order theory for multi-layered, shear-deformable composite plates. Acta Mech. 209, 85–98 (2010)

    Article  MATH  Google Scholar 

  13. Kansa E.J.: Multiquadrics- a scattered data approximation scheme with applications to computational fluid dynamics. i: Surface approximations and partial derivative estimates. Comput. Math. Appl. 19, 127–145 (1990)

    Article  MATH  MathSciNet  Google Scholar 

  14. Hon Y.C., Lu M.W., Xue W.M., Zhu Y.M.: Multiquadric method for the numerical solution of byphasic mixture model. Appl. Math. Comput. 88, 153–175 (1997)

    Article  MATH  MathSciNet  Google Scholar 

  15. Hon Y.C., Cheung K.F., Mao X.Z., Kansa E.J.: A multiquadric solution for the shallow water equation. ASCE J. Hydraul. Eng. 125, 524–533 (1999)

    Article  Google Scholar 

  16. Wang J.G., Liu G.R., Lin P.: Numerical analysis of Biot’s consolidation process by radial point interpolation method. Int. J. Solids Struct. 39, 1557–1573 (2002)

    Article  MATH  Google Scholar 

  17. Liu G.R., Gu Y.T.: A local radial point interpolation method (lrpim) for free vibration analyses of 2-d solids. J. Sound Vib. 246, 29–46 (2001)

    Article  Google Scholar 

  18. Liu G.R., Wang J.G.: A point interpolation meshless method based on radial basis functions. Int. J. Numer. Meth. Eng. 54, 1623–1648 (2002)

    Article  MATH  Google Scholar 

  19. Wang J.G., Liu G.R.: On the optimal shape parameters of radial basis functions used for 2-d meshless methods. Comp. Meth. Appl. Mech. Eng. 191, 2611–2630 (2002)

    Article  MATH  Google Scholar 

  20. Chen X.L., Liu G.R., Lim S.P.: An element free Galerkin method for the free vibration analysis of composite laminates of complicated shape. Compos. Struct. 59, 279–289 (2003)

    Article  Google Scholar 

  21. Dai K.Y., Liu G.R., Lim S.P., Chen X.L.: An element free Galerkin method for static and free vibration analysis of shear-deformable laminated composite plates. J. Sound Vib. 269, 633–652 (2004)

    Article  Google Scholar 

  22. Liu G.R., Chen X.L.: Buckling of symmetrically laminated composite plates using the element-free Galerkin method. Int. J. Struct. Stab. Dyn. 2, 281–294 (2002)

    Article  MATH  Google Scholar 

  23. Liew K.M., Chen X.L., Reddy J.N.: Mesh-free radial basis function method for buckling analysis of non-uniformity loaded arbitrarily shaped shear deformable plates. Comput. Methods Appl. Mech. Eng. 193, 205–225 (2004)

    Article  MATH  Google Scholar 

  24. Huang Y.Q., Li Q.S.: Bending and buckling analysis of antisymmetric laminates using the moving least square differential quadrature method. Comput. Methods Appl. Mech. Eng. 193, 3471–3492 (2004)

    Article  MATH  Google Scholar 

  25. Liu L., Liu G.R., Tan V.C.B.: Element free method for static and free vibration analysis of spatial thin shell structures. Comput. Methods Appl. Mech. Eng. 191, 5923–5942 (2002)

    Article  MATH  Google Scholar 

  26. Ferreira A.J.M.: A formulation of the multiquadric radial basis function method for the analysis of laminated composite plates. Compos. Struct. 59, 385–392 (2003)

    Article  Google Scholar 

  27. Ferreira A.J.M.: Thick composite beam analysis using a global meshless approximation based on radial basis functions. Mech. Adv. Mater. Struct. 10, 271–284 (2003)

    Article  Google Scholar 

  28. Ferreira A.J.M., Roque C.M.C., Martins P.A.L.S.: Analysis of composite plates using higher-order shear deformation theory and a finite point formulation based on the multiquadric radial basis function method. Composites: Part B 34, 627–636 (2003)

    Article  Google Scholar 

  29. Mindlin R.D.: Influence of rotary inertia and shear in flexural motions of isotropic elastic plates. J. Appl. Mech. 18, 31–38 (1951)

    MATH  Google Scholar 

  30. Hardy R.L.: Multiquadric equations of topography and other irregular surfaces. Geophys. Res. 176, 1905–1915 (1971)

    Article  Google Scholar 

  31. Buhmann M.D.: Radial basis functions. Acta Numer. 9, 1–38 (2000)

    Article  MathSciNet  Google Scholar 

  32. Ferreira A.J.M., Fasshauer G.E.: Computation of natural frequencies of shear deformable beams and plates by a rbf-pseudospectral method. Comput. Methods Appl. Mech. Eng. 196, 134–146 (2006)

    Article  MATH  Google Scholar 

  33. Ferreira A.J.M.: MATLAB Codes for Finite Element Analysis: Solids and Structures. Springer, New York (2008)

    Google Scholar 

  34. Dawe D.J., Roufaeil O.L.: Rayleigh-Ritz vibration analysis of Mindlin plates. J. Sound Vib. 69, 345–359 (1980)

    Article  MATH  Google Scholar 

  35. Liew K.M., Wang J., Ng T.Y., Tan M.J.: Free vibration and buckling analyses of shear-deformable plates based on fsdt meshfree method. J. Sound Vib. 276, 997–1017 (2004)

    Article  Google Scholar 

  36. Hinton E.: Numerical Methods and Software for Dynamic Analysis of Plates and Shells. Pineridge Press, Swansea (1988)

    Google Scholar 

  37. Kant T., Swaminathan K.: Free vibration of isotropic, orthotropic, and multilayer plates based on higher order refined theories. J. Sound Vib. 241, 319–327 (2001)

    Article  Google Scholar 

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Authors and Affiliations

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

    A. J. M. Ferreira

  2. INEGI, Faculdade de Engenharia da Universidade do Porto, Rua Dr. Roberto Frias, 4200-465, Porto, Portugal

    C. M. C. Roque

Authors
  1. A. J. M. Ferreira
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  2. C. M. C. Roque
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Correspondence to A. J. M. Ferreira.

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Ferreira, A.J.M., Roque, C.M.C. Analysis of thick plates by radial basis functions. Acta Mech 217, 177–190 (2011). https://doi.org/10.1007/s00707-010-0395-5

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  • DOI: https://doi.org/10.1007/s00707-010-0395-5

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