Buckling and vibration analysis of isotropic and laminated plates by radial basis functions

Composites Part B: Engineering

Volumn 42, Issue 3, 2011, Pages 592-606

  Ferreira, A J M ^a   Roque, C M C ^b   Neves, A M A ^a   Jorge, R M N ^a   Soares, C M M ^c   Liew, K M ^d  

^a UNIVERSITY OF PORTO   (Portugal)

^b UNIVERSITY OF PORTO   (Portugal)

^c INSTITUTO SUPERIOR TÉCNICO   (Portugal)

^d CITY UNIVERSITY OF HONG KONG   (Hong Kong)

Author keywords

A. Plates; C. Computational modelling; C. Laminate mechanics

Indexed keywords

A. PLATES; ARBITRARY BOUNDARY CONDITIONS; C. COMPUTATIONAL MODELLING; C. LAMINATE MECHANICS; CRITICAL LOAD; FIRST-ORDER SHEAR DEFORMATION THEORY; IRREGULAR GEOMETRIES; LAMINATED PLATE; NUMERICAL APPROACHES; RADIAL BASIS FUNCTIONS;

LAMINATING; MECHANICS; PLATES (STRUCTURAL COMPONENTS); RADIAL BASIS FUNCTION NETWORKS; SHEAR DEFORMATION;

VIBRATION ANALYSIS;

EID: 79951558624     PISSN: 13598368     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.compositesb.2010.08.001     Document Type: Article

References (47)

1. E. Reissner, and Y. Stavsky Bending and stretching of certain types of aelotropic elastic plates J Appl Mech 28 1961 402 408
2. R.D. Mindlin Influence of rotary inertia and shear in flexural motions of isotropic elastic plates J Appl Mech 18 1951 31 38
3. E. Reissner The effect of transverse shear deformations on the bending of elastic plates J Appl Mech 12 1945 A69 A77
4. T. Kant Numerical analysis of thick plates Comput Methods Appl Mech Eng 31 1982 1 18
5. SIMPLE HIGHER-ORDER THEORY FOR LAMINATED COMPOSITE PLATES J.N. Red (Pubitemid 15422865)
6. E.J. Kansa Multiquadrics - a scattered data approximation scheme with applications to computational fluid dynamics. I: surface approximations and partial derivative estimates Comput Math Appl 19 8/9 1990 127 145 (Pubitemid 20668364)
7. Y.C. Hon, M.W. Lu, W.M. Xue, and Y.M. Zhu Multiquadric method for the numerical solution of byphasic mixture model Appl Math Comput 88 1997 153 175 (Pubitemid 127683562)
8. Y.C. Hon, K.F. Cheung, X.Z. Mao, and E.J. Kansa A multiquadric solution for the shallow water equation ASCE J Hydraul Eng 125 5 1999 524 533 (Pubitemid 29400985)
9. J.G. Wang, G.R. Liu, and P. Lin Numerical analysis of biots consolidation process by radial point interpolation method Int J Solids Struct 39 6 2002 1557 1573 (Pubitemid 34306039)
10. G.R. Liu, and Y.T. Gu A local radial point interpolation method (lrpim) for free vibration analyses of 2-d solids J Sound Vib 246 1 2001 29 46 (Pubitemid 32866245)
11. G.R. Liu, and J.G. Wang A point interpolation meshless method based on radial basis functions Int J Num Methods Eng 54 2002 1623 1648 (Pubitemid 34842350)
12. J.G. Wang, and G.R. Liu On the optimal shape parameters of radial basis functions used for 2-d meshless methods Comput Meth Appl Mech Eng 191 2002 2611 2630 (Pubitemid 34452176)
13. X.L. Chen, G.R. Liu, and S.P. Lim An element free galerkin method for the free vibration analysis of composite laminates of complicated shape Compos Struct 59 2003 279 289 (Pubitemid 36011091)
14. K.Y. Dai, G.R. Liu, S.P. Lim, and X.L. Chen An element free galerkin method for static and free vibration analysis of shear-deformable laminated composite plates J Sound Vib 269 2004 633 652
15. G.R. Liu, and X.L. Chen Buckling of symmetrically laminated composite plates using the element-free galerkin method Int J Struct Stabil Dyn 2 2002 281 294
16. K.M. Liew, X.L. Chen, and J.N. Reddy Mesh-free radial basis function method for buckling analysis of non-uniformity loaded arbitrarily shaped shear deformable plates Comput Methods Appl Mech Eng 193 2004 205 225
17. Y.Q. Huang, and Q.S. Li Bending and buckling analysis of antisymmetric laminates using the moving least square differential quadrature method Comput Methods Appl Mech Eng 193 2004 3471 3492 (Pubitemid 38921161)
18. L. Liu, G.R. Liu, and V.C.B. Tan Element free method for static and free vibration analysis of spatial thin shell structures Comput Methods Appl Mech Eng 191 2002 5923 5942 (Pubitemid 36036254)
19. A.J.M. Ferreira A formulation of the multiquadric radial basis function method for the analysis of laminated composite plates Compos Struct 59 2003 385 392 (Pubitemid 41167838)
20. A.J.M. Ferreira Thick composite beam analysis using a global meshless approximation based on radial basis functions Mech Adv Mater Struct 10 2003 271 284
21. A.J.M. Ferreira, C.M.C. Roque, and P.A.L.S. Martins 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 2003 627 636
22. C.M. Wang, K.M. Liew, Y. Xiang, and S. Kipornchai Buckling of rectangular Mindlin plates with internal line supports Int J Solid Struct 30 1 1993 1 17
23. A.A. Khdeir, and L. Librescu Analysis of symmetric cross-ply elastic plates using a higher-order theory. Part ii: buckling and free vibration Compos Struct 9 1988 259 277 (Pubitemid 18623963)
24. A. Bhimaraddi Free vibration analysis of doubly curved shallow shells on rectangular planform using three-dimensional elasticity theory Int J Solids Struct 27 7 1991 897 913
25. S. Kitipornchai, Y. Xiang, C.M. Wang, and K.M. Liew Buckling of thick skew plates Int J Num Meth Eng 36 1993 1299 1310
26. K.M. Liew, J. Wang, T.Y. Ng, and M.J. Tan Free vibration and buckling analyses of shear-deformable plates based on fsdt meshfree method J Sound Vib 276 2004 997 1017
27. K.M. Liew, and Y.Q. Huang Bending and buckling of thick symmetric rectangular laminates using the moving least-squeares differential quadrature method Int J Mech Sci 45 2003 95 114
28. K.M. Liew, Y.Q. Huang, and J.N. Reddy Vibration analysis of symmetrically laminated plates based on fsdt using the moving least squares differential quadrature method Comput Methods Appl Mech Eng 192 19 2003 2203 2222 (Pubitemid 36669470)
29. N.S. Putcha, and J.N. Reddy Stability and natural vibration analysis of laminated plates by using a mixed element based on a refined plate theory J. Sound Vib 104 2 1986 285 300 (Pubitemid 16474109)
30. J.N. Reddy, and N.D. Phan Stability and vibration of isotropic, orthotropic and laminated plates according to a higher-order shear deformation theory J. Sound Vib 98 2 1985 157 170 (Pubitemid 15491877)
31. E. Carrera Historical review of zig-zag theories for multilayered plates and shells Appl Mech Rev 56 2003 287 308 (Pubitemid 40205918)
32. W.R. Madich, and S.A. Nelson Multivariate interpolation and conditionally positive definite functions. ii Math Comp 54 189 1990 211 230
33. J. Yoon Spectral approximation orders of radial basis function interpolation on the sobolev space SIAM J Math Anal 33 4 2001 946 958
34. R.L. Hardy Multiquadric equations of topography and other irregular surfaces Geophys Res 176 1971 1905 1915
35. M.D. Buhmann Radial basis functions Acta Numer 9 2000 1 38
36. J.N. Reddy Mechanics of laminated composite plates: theory and analysis 1997 CRC Press Boca Raton
37. K.M. Liew, and T.M. Teo Differential cubature method for analysis of shear deformable rectangular plates on pasternak foundations Int J Mech Sci 44 2002 1179 1194 (Pubitemid 34715776)
38. K.M. Liew, J.B. Han, Z.M. Xiao, and H. Du Differential quadrature method for Mindlin plates on winkler foundations Int J Mech Sci 38 1996 405 421 (Pubitemid 126349567)
39. J.B. Han, and K.M. Liew Numerical differential quadrature method for Reissner-Mindlin plates on two-parameter foundations Int J Mech Sci 39 1997 977 989 (Pubitemid 127382128)
40. K.M. Liew, Y.Q. Huang, and J.N. Reddy Vibration analysis of symmetrically laminated plates based on fsdt using the moving least squares differential quadrature method Comput Meth Appl Mech Eng 192 2003 2203 2222 (Pubitemid 36669470)
41. A.J.M. Ferreira, and G.E. Fasshauer Computation of natural frequencies of shear deformable beams and plates by a rbf-pseudospectral method Comput Methods Appl Mech Eng 196 2006 134 146 (Pubitemid 46158175)
42. D.J. Dawe, and O.L. Roufaeil Rayleigh-Ritz vibration analysis of Mindlin plates J Sound Vib 69 3 1980 345 359 (Pubitemid 11436200)
43. E. Hinton Numerical methods and software for dynamic analysis of plates and shells 1988 Pineridge Press
44. K.M. Liew, C.M. Wang, Y. Xiang, and S. Kitipornchai Vibration of Mindlin plates 1998 Elsevier Amsterdam
45. A.J.M. Ferreira MATLAB codes for finite element analysis: solids and structures 2008 Springer
46. A.A. Khdeir, and L. Librescu Analysis of symmetric cross-ply elastic plates using a higher-order theory, part ii: buckling and free vibration Compos Struct 9 1988 259 277 (Pubitemid 18623963)
47. A.K. Noor Free vibration of multilayered plates AIAA J 11 1973 1038 1039