68
Views
5
CrossRef citations to date
0
Altmetric
Original Articles

An RBF-Pseudospectral Approach for the Static and Vibration Analysis of Composite Plates Using a Higher-Order Theory

&
Pages 323-339 | Received 18 Jan 2006, Accepted 26 Apr 2007, Published online: 27 Jul 2007

REFERENCES

  • Akhras , G. , Cheung , M. S. and Li , W. 1993 . Static and Vibrations Analysis of Anisotropic Laminated Plates by Finite Strip Method . Int. J.Solids Struct. , vol. 30 ( 22 ) : 3129 – 3137 .
  • Akhras , G. , Cheung , M. S. and Li , W. 1994 . Finite Strip Analysis for Anisotropic Laminated Composite Plates Using Higher-order Deformation Theory . Computers & Structures , vol. 52 ( 3 ) : 471 – 477 .
  • Bathe , K. 1982 . Finite Element Procedures in Engineering Analysis , Englewood Cliffs, New Jersey : Prentice-Hall .
  • Bert , C. W. and Malik , M. 1996 . Differential Quadrature Method in Computational Mechanics: A Review . Applied Mechanics Review , vol. 49 ( 1 ) : 1 – 28 .
  • de Boor , C. 2006 . On Interpolation by Radial Polynomials . Adv. Comput. Math. , vol. 24 : 143 – 153 .
  • Driscoll , T. A. and Fornberg , B. 2002 . Interpolation in the Limit of Increasingly Flat Radial Basis Functions . Comput. Math. Appl. , vol. 43 : 413 – 422 .
  • Fasshauer , G. E. 2004 . RBF Collocation Methods and Pseudospectral Methods , Illinois Institute of Technology . Technical Report
  • Fasshauer , G. E. 2005 . “ RBF Collocation Methods as Pseudospectral Methods ” . In Boundary Elements XXVII , Edited by: Kassab , A. , Brebbia , C. A. , Divo , E. and Poljak , D. 47 – 56 . Southampton : WIT Press .
  • Fasshauer , G. E. 2007 . Meshfree Approximation Methods with Matlab, Interdisciplinary Mathematical Sciences , vol. 6 , Singapore : World Scientific Publishers .
  • Ferreira , A. J. M. 2003 . A Formulation of the Multiquadric Radial Basis Function Method for the Analysis of Laminated Composite Plates . Composite Structures , vol. 59 : 385 – 392 .
  • Ferreira , A. J. M. 2003 . Thick Composite Beam Analysis Using a Global Meshless Approximation Based on Radial Basis Functions . Mechanics of Advanced Materials and Structures , vol. 10 : 271 – 284 .
  • Ferreira , A. J. M. 2005 . Free Vibration Analysis of Timoshenko Beams and Mindlin Plates by Radial Basis Functions . International Journal of Computational Methods , Vol. 2 ( 2 ) : 15 – 31 .
  • Ferreira , A. J. M. 2005 . Polyharmonic (Thin-Plate) Splines in the Analysis of Composite Plates . International Journal of Mechanical Sciences , 46 : 1549 – 1569 .
  • Ferreira , A. J. M. 2005 . Analysis of Composite Plates Using a Layerwise Deformation Theory and Multiquadrics Discretization . Mech. Adv. Mater. Struct. , vol. 12 ( 2 ) : 99 – U112 .
  • Ferreira , A. J. M. and Barbosa , J. T. 2000 . Buckling Behaviour of Composite Shells . Composite Structures , vol. 50 : 93 – 98 .
  • Ferreira , A. J. M. , Batra , R. C. , Roque , C. M. C. , Qian , L. F. and Martins , P. A. L. S. 2005 . Static Analysis of Functionally Graded Plates Using Third-order Shear Deformation Theory and a Meshless Method . Composite Structures , vol. 69 : 449 – 457 .
  • Ferreira , A. J. M. and Fasshauer , G. E. 2006 . Natural Frequencies of Shear Deformable Beams and Plates by a RBF-Pseudospectral Method . Computer Methods in Applied Mechanics and Engineering , vol. 196 : 134 – 146 .
  • Ferreira , A. J. M. , Roque , C. M. C. and Martins , P. A. L. S. 2003 . 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 , vol. 34 : 627 – 636 .
  • Ferreira , A. J. M. , Roque , C. M. C. and Martins , P. A. L. S. 2004 . Radial Basis Functions and Higher-order Theories in the Analysis of Laminated Composite Beams and Plates . Composite Structures , vol. 66 : 287 – 293 .
  • Rahman , S. and Xu , H. 2005 . A Meshless Method for Computational Stochastic Mechanics . International Journal for Computational Methods in Engineering Science and Mechanics , vol. 6 : 41 – 58 .
  • Fornberg , B. 1998 . A Practical Guide to Pseudospectral Methods , New York : Cambridge University Press .
  • Kansa , E. J. and Multiquadrics- , A . 1990 . Scattered Data Approximation Scheme with Applications to Computational Fluid Dynamics. I: Surface Approximations and Partial Derivative Estimates . Comput. Math. Appl. , vol. 19 ( 8/9 ) : 127 – 145 .
  • Kansa , E. J. 1990 . Multiquadrics—A Scattered Data Approximation Scheme with Applications to Computational Fluid Dynamics. II: Solutions to Parabolic, Hyperbolic and Elliptic Partial Differential Equations . Comput. Math. Appl. , vol. 19 ( 8/9 ) : 147 – 161 .
  • Laura , P. A. A. and Gutierrez , R. H. 1993 . Analysis of Vibrating Timoshenko Beams Using the Method of Differential Quadrature . Shock and Vibration , vol. 1 ( 1 ) : 89 – 93 .
  • Liew , K. M. 1996 . Solving the Vibration of Thick Symmetric Laminates by Reissner/Mindlin Plate Theory and the p-Ritz Method . Journal of Sound and Vibration , vol. 198 : 343 – 360 .
  • Liew , K. M. , Han , J. B. and Xiao , Z. M. 1997 . Vibration Analysis of Circular Mindlin Plates Using Differential Quadrature Method . Journal of Sound and Vibration , vol. 205 ( 5 ) : 617 – 630 .
  • Liew , K. M. , Huang , Y. Q. and Reddy , J. N. 2003 . Vibration Analysis of Symmetrically Laminated Plates Based on FSDT Using the Moving Least Squares Differential Quadrature Method . Comp. Meth. Appl. Mech. Eng. , vol. 192 : 2203 – 2222 .
  • Pagano , N. J. 1970 . Exact Solutions for Rectangular Bidirectional Composites and Sandwich Plates . Compos. J. Mater. , vol. 4 : 20 – 34 .
  • Pandya , B. N. and Kant , T. 1988 . Higher-Order Shear Deformable Theories for Flexure of Sandwich Plates-Finite Element Evaluations . Int. J. Solids and Structures , vol. 24 : 419 – 451 .
  • Platte , R. B. and Driscoll , T. A. 2006 . Eigenvalue Stability of Radial Basis Function Discretizations for Time-dependent Problems . Comput. Math. Appl. , vol. 51 ( 8 ) : 1251 – 1268 .
  • Reddy , J. N. 1984 . A Simple Higher-order Theory for Laminated Composite Plates . Appl. J. Mech. , vol. 51 : 745 – 752 .
  • Reddy , J. N. 2006 . Introduction to the Finite Element Method, , 3rd ed. , New York : McGraw-Hill .
  • Reddy , J. N. 2004 . Mechanics of Laminated Composite Plates and Shells, , 2nd ed. , Boca Raton, FL : CRC Press .
  • Reddy , J. N. 2002 . Energy Principles and Variational Methods in Applied Mechanics, , 2nd ed. , New York : John Wiley .
  • Rippa , S. 1999 . An Algorithm for Selecting a Good Value for the Parameter c in Radial Basis Function Interpolation . Adv. Comput. Math. , vol. 11 : 193 – 210 .
  • Sarra , S. A. 2005 . Adaptive Radial Basis Function Methods for Time Dependent Partial Differential Equations . Appl. Numer. Math. , vol. 54 : 79 – 94 .
  • Schaback , R. 2005 . Multivariate Interpolation by Polynomials and Radial Basis Functions . Constr. Approx. , vol. 21 : 293 – 317 .
  • Schaback , R. Limit Problems for Interpolation by Analytic Radial Basis Functions . Comput. J. Appl. Math. , to appear
  • Srinivas , S. 1973 . A Refined Analysis of Composite Laminates . J. Sound and Vibration , vol. 30 : 495 – 507 .
  • Trefethen , L. N. 2000 . Spectral Methods in Matlab , Philadelphia, PA : SIAM .
  • Weaver , W. and Johnson , P. 1987 . Structural Dynamics by Finite Elements Englewood Cliffs, NJ
  • Wendland , H. 1995 . Piecewise Polynomial, Positive Definite and Compactly Supported Radial Functions of Minimal Degree . Adv. in Comput. Math. , vol. 4 : 389 – 396 .
  • Zhen , W. and Wanji , C. 2006 . Free Vibration of Laminated Composite and Sandwich Plates Using Global-local Higher-order Theory . Journal of Sound and Vibration , vol. 298 : 333 – 349 .
  • Reddy , J. N. 2004 . Mechanics of Laminated Composite Plates and Shells: Theory and Analysis, , 2nd ed. , Boca Raton, FL : CRC Press .
  • Reddy , J. N. and Arciniega , R. A. 2004 . Shear Deformation Plate and Shell Theories: Stavsky to Present . Mechanics of Advanced Materials and Structures , vol. 11 ( 6 ) : 535 – 516 . Part II
  • Ma , Y. Q. , Ang , K. K. and McGuckin , D. 2005 . A Plate Element Based on Relative Displacement Concept . International Journal for Computational Methods in Engineering Science and Mechanics , vol. 6 ( 3 ) : 153 – 159 .
  • Kdheir , A. A. and Librescu , L. 1988 . Analysis of Symmetric Cross-ply Elastic Plates Using a Higher-order Theory, Part II: Buckling and Free Vibration . Composite Structures , vol. 9 : 259 – 277 .

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.