Static, free vibration and buckling analysis of isotropic and sandwich functionally graded plates using a quasi-3D higher-order shear deformation theory and a meshless technique

Composites Part B: Engineering

Volumn 44, Issue 1, 2013, Pages 657-674

  Neves, A M A ^a   Ferreira, A J M ^a   Carrera, E ^b   Cinefra, M ^b   Roque, C M C ^c   Jorge, R M N ^a   Soares, C M M ^d  

^a UNIVERSITY OF PORTO   (Portugal)

^b POLITECNICO DI TORINO   (Italy)

^c UNIVERSITY OF PORTO   (Portugal)

^d INSTITUTO SUPERIOR TÉCNICO   (Portugal)

Author keywords

A. Plates; B. Buckling; B. Vibration; C. Computational modeling; Functionally graded materials

Indexed keywords

A. PLATES; B. VIBRATION; BUCKLING ANALYSIS; CARRERA'S UNIFIED FORMULATION; COMPUTATIONAL MODELING; EIGEN-PROBLEMS; FREE VIBRATION; FUNCTIONALLY GRADED; FUNCTIONALLY GRADED PLATES; GOVERNING EQUATIONS; HIGHER ORDER SHEAR DEFORMATION THEORY; ISOTROPIC PLATES; MESHLESS TECHNIQUES; NUMERICAL RESULTS; PRINCIPLE OF VIRTUAL DISPLACEMENTS; QUASI-3D; RADIAL BASIS FUNCTIONS; SANDWICH PLATES; THICKNESS DIRECTION;

FUNCTIONALLY GRADED MATERIALS; PLATES (STRUCTURAL COMPONENTS); RADIAL BASIS FUNCTION NETWORKS;

VIBRATIONS (MECHANICAL);

EID: 84867498539     PISSN: 13598368     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.compositesb.2012.01.089     Document Type: Article

References (99)

1. M.B. Bever, and P.E. Duwez Gradients in composite materials Mater Sci Eng 10 0 1972 1 8
2. Y. Miyamoto, W.A. Kaysser, B.H. Rabin, A. Kawasaki, and R.G. Ford Functionally graded materials: design, processing and applications 1999 Kluwer Academic Publishers
3. F.J. Ferrante, and L.L. Graham-Brady Stochastic simulation of non-gaussian/non-stationary properties in a functionally graded plate Comput Methods Appl Mech Eng 194 12-16 2005 1675 1692
4. H. M Yin, L. Z Sun, and G. H Paulino Micromechanics-based elastic model for functionally graded materials with particle interactions Acta Mater 52 12 2004 3535 3543
5. Zheng Zhong, and Ertao Shang Closed-form solutions of three-dimensional functionally graded plates Mech Adv Mater Struct 15 5 2008 355 363
6. T.K. Nguyen, K. Sab, and G. Bonnet Shear correction factors for functionally graded plates Mech Adv Mater Struct 14 8 2007 567 575
7. Victor Birman, and Larry W. Byrd Modeling and analysis of functionally graded materials and structures Appl Mech Rev 60 5 2007 195 216
8. M. Koizumi Fgm activities in Japan Compos Part B: Eng 28 1-2 1997 1 4 Use of composites multi-phased and functionally graded materials
9. J.N. Reddy, and C.D. Chin Thermomechanical analysis of functionally graded cylinders and plates J Therm Stress 21 6 1998 593 626
10. J.N. Reddy Analysis of functionally graded plates Int J Numer Methods Eng 47 2000 663 684
11. S.S. Vel, and R.C. Batra Three-dimensional analysis of transient thermal stresses in functionally-graded plates Int J Solids Struct 40 25 2003 7181 7196
12. S.S. Vel, and R.C. Batra Exact solution for thermoelastic deformations of functionally graded thick rectangular plates AIAA J 40 2002 1421 1433
13. Z.Q. Cheng, and R.C. Batra Three-dimensional thermoelastic deformations of a functionally graded-elliptic plate Composites: Part B 31 2000 97 106
14. R. Javaheri, and M.R. Eslami Thermal buckling of functionally graded plates based on higher order theory J Therm Stress 25 7 2002 603 625
15. M. Kashtalyan Three-dimensional elasticity solution for bending of functionally graded rectangular plates Eur J Mech - A/Solids 23 5 2004 853 864
16. M. Kashtalyan, and M. Menshykova Three-dimensional elasticity solution for sandwich panels with a functionally graded core Compos Struct 87 1 2009 36 43
17. L.F. Qian, R.C. Batra, and L.M. Chen Static and dynamic deformations of thick functionally graded elastic plate by using higher-order shear and normal deformable plate theory and meshless local Petrov-Galerkin method Composites: Part B 35 2004 685 697
18. A.M. Zenkour A comprehensive analysis of functionally graded sandwich plates: Part 1 - deflection and stresses Int J Solids Struct 42 18-19 2005 5224 5242
19. A.M. Zenkour Generalized shear deformation theory for bending analysis of functionally graded plates Appl Math Modell 30 2006 67 84
20. Fernando Ramirez, Paul R. Heyliger, and Ernian Pan Static analysis of functionally graded elastic anisotropic plates using a discrete layer approach Compos Part B: Eng 37 1 2006 10 20
21. A.J.M. Ferreira, R.C. Batra, C.M.C. Roque, L.F. Qian, and P.A.L.S. Martins Static analysis of functionally graded plates using third-order shear deformation theory and a meshless method Compos Struct 69 4 2005 449 457
22. A.J.M. Ferreira, C.M.C. Roque, R.M.N. Jorge, G.E. Fasshauer, and R.C. Batra Analysis of functionally graded plates by a robust meshless method Mech Adv Mater Struct 14 8 2007 577 587
23. Shyang-Ho Chi, and Yen-Ling Chung Mechanical behavior of functionally graded material plates under transverse load - part i: analysis Int J Solids Struct 43 13 2006 3657 3674
24. Shyang-Ho Chi, and Yen-Ling Chung Mechanical behavior of functionally graded material plates under transverse load - part ii: numerical results Int J Solids Struct 43 13 2006 3675 3691
25. Z.Q. Cheng, and R.C. Batra Deflection relationships between the homogeneous kirchhoff plate theory and different functionally graded plate theories Arch Mech 52 2000 143 158
26. R.C. Batra, and J. Jin Natural frequencies of a functionally graded anisotropic rectangular plate J Sound Vib 282 1-2 2005 509 516
27. A.J.M. Ferreira, R.C. Batra, C.M.C. Roque, L.F. Qian, and R.M.N. Jorge Natural frequencies of functionally graded plates by a meshless method Compos Struct 75 1-4 2006 593 600
28. S.S. Vel, and R.C. Batra Three-dimensional exact solution for the vibration of functionally graded rectangular plates J Sound Vib 272 2004 703 730
29. A.M. Zenkour A comprehensive analysis of functionally graded sandwich plates: part 2 - buckling and free vibration Int J Solids Struct 42 18-19 2005 5243 5258
30. C.M.C. Roque, A.J.M. Ferreira, and R.M.N. Jorge A radial basis function approach for the free vibration analysis of functionally graded plates using a refined theory J Sound Vib 300 3-5 2007 1048 1070
31. Z.Q. Cheng, and R.C. Batra Exact correspondence between eigenvalues of membranes and functionally graded simply supported polygonal plates J Sound Vib 229 2000 879 895
32. M.M. Najafizadeh, and M.R. Eslami Buckling analysis of circular plates of functionally graded materials under uniform radial compression Int J Mech Sci 44 12 2002 2479 2493
33. Birman V. Buckling of functionally graded hybrid composite plates. In: Proceedings of the 10th conference on engineering mechanics; 1995. p. 1199-202.
34. R. Javaheri, and M.R. Eslami Buckling of functionally graded plates under in-plane compressive loading ZAMM - J Appl Math Mech/Zeitschrift f++r Angewandte Mathematik und Mechanik 82 4 2002 277 283
35. o plate element Comput Struct 15 2 1982 177 183
36. B.N. Pandya, and T. Kant Higher-order shear deformable theories for flexure of sandwich plates-finite element evaluations Int J Solids Struct 24 12 1988 1267 1286
37. B.N. Pandya, and T. Kant Finite element analysis of laminated composite plates using a higher-order displacement model Compos Sci Technol 32 2 1988 137 155
38. T. Kant, and K. Swaminathan Analytical solutions for the static analysis of laminated composite and sandwich plates based on a higher order refined theory Compos Struct 56 4 2002 329 344
39. T. Kant, and K. Swaminathan Analytical solutions for free vibration of laminated composite and sandwich plates based on a higher-order refined theory Compos Struct 53 1 2001 73 85
40. Ajay Kumar Garg, Rakesh Kumar Khare, and Tarun Kant Higher-order closed-form solutions for free vibration of laminated composite and sandwich shells J Sandwich Struct Mater 8 3 2006 205 235
41. R.C. Batra, and S. Vidoli Higher-order piezoelectric plate theory derived from a three-dimensional variational principle AIAA J 40 2002 91 104
42. R.C. Batra, S. Vidoli, and F. Vestroni Plane wave solutions and modal analysis in higher order shear and normal deformable plate theories J Sound Vib 257 1 2002 63 88
43. L.F. Qian, R.C. Batra, and L.M. Chen Analysis of cylindrical bending thermoelastic deformations of functionally graded plates by a meshless local petrovâAŞgalerkin method Comput Mech 33 2004 263 273 10.1007/s00466-003-0527-z
44. L.F. Qian, and R.C. Batra Transient thermoelastic deformations of a thick functionally graded plate J Therm Stress 27 8 2004 705 740
45. L.F. Qian, and R.C. Batra Three-dimensional transient heat conduction in a functionally graded thick plate with a higher-order plate theory and a meshless local Petrov-Galerkin method Comput Mech 35 2005 214 226 10.1007/s00466-004-0617-6
46. L.F. Qian, R.C. Batra, and L.M. Chen Free and forced vibrations of thick rectangular plates using higher-order shear and normal deformable plate theory and meshless Petrov-Galerkin (mlpg) method Comput Model Eng Sci 4 2003 519 534
47. L.F. Qian, R.C. Batra, and L.M. Chen Elastostatic deformations of a thick plate by using a higher-order shear and normal deformable plate theory and two meshless local Petrov-Galerkin (mlpg) methods Comput Model Eng Sci 4 2003 161 175
48. L.F. Qian, and R.C. Batra Design of bidirectional functionally graded plate for optimal natural frequencies J Sound Vib 280 1-2 2005 415 424
49. R.C. Batra, L.F. Qian, and L.M. Chen Natural frequencies of thick square plates made of orthotropic, trigonal, monoclinic, hexagonal and triclinic materials J Sound Vib 270 4-5 2004 1074 1086
50. R.C. Batra, and S. Aimmanee Vibrations of thick isotropic plates with higher order shear and normal deformable plate theories Comput Struct 83 12-13 2005 934 955
51. D.F. Gilhooley, R.C. Batra, J.R. Xiao, M.A. McCarthy, and J.W. Gillespie Jr. Analysis of thick functionally graded plates by using higher-order shear and normal deformable plate theory and mlpg method with radial basis functions Compos Struct 80 4 2007 539 552
52. J.R. Xiao, D.F. Gilhooley, R.C. Batra, J.W. Gillespie Jr., and M.A. McCarthy Analysis of thick composite laminates using a higher-order shear and normal deformable plate theory (hosndpt) and a meshless method Compos Part B: Eng 39 2 2008 414 427
53. E. Carrera, S. Brischetto, M. Cinefra, and M. Soave Effects of thickness stretching in functionally graded plates and shells Compos Part B: Eng 42 2011 123 133
54. E. Carrera Evaluation of layer-wise mixed theories for laminated plate analysis AIAA J 36 1998 830 839
55. E. Carrera Developments, ideas, and evaluations based upon reissner's mixed variational theorem in the modelling of multilayered plates and shells Appl Mech Rev 54 2001 301 329
56. Erasmo Carrera Theories and finite elements for multilayered plates and shells: a unified compact formulation with numerical assessment and benchmarking Arch Comput Methods Eng 10 2003 215 296
57. S. Brischetto, and E. Carrera Advanced mixed theories for bending analysis of functionally graded plates Comput Struct 88 23-24 2010 1474 1483
58. S. Brischetto Classical and mixed advanced models for sandwich plates embedding functionally graded cores J Mech Mater Struct 4 2009 13 33
59. E. Carrera, S. Brischetto, and A. Robaldo Variable kinematic model for the analysis of functionally graded material plates AIAA J 46 2008 194 203
60. 3 hierarchy plate theories for thick and thin composite plates: the generalized unified formulation Compos Struct 84 2008 256 270
61. Luciano, and Demasi Mixed plate theories based on the generalized unified formulation. Part i: governing equations Compos Struct 87 1 2009 1 11
62. Luciano, and Demasi Mixed plate theories based on the generalized unified formulation. Part ii: layerwise theories Compos Struct 87 1 2009 12 22
63. Luciano, and Demasi Mixed plate theories based on the generalized unified formulation. Part iii: advanced mixed high order shear deformation theories Compos Struct 87 3 2009 183 194
64. Luciano, and Demasi Mixed plate theories based on the generalized unified formulation. Part iv: zig-zag theories Compos Struct 87 3 2009 195 205
65. Luciano, and Demasi Mixed plate theories based on the generalized unified formulation. Part v: results Compos Struct 88 1 2009 1 16
66. Luciano, and Demasi Partially zig-zag advanced higher order shear deformation theories based on the generalized unified formulation Compos Struct 94 2 2012 363 375
67. A.M.A. Neves, A.J.M. Ferreira, E. Carrera, C.M.C. Roque, M. Cinefra, and R.M.N. Jorge Bending of fgm plates by a sinusoidal plate formulation and collocation with radial basis functions Mech Res Commun 38 5 2011 368 371
68. A.M.A. Neves, A.J.M. Ferreira, E. Carrera, C.M.C. Roque, M. Cinefra, and R.M.N. Jorge A quasi-3d sinusoidal shear deformation theory for the static and free vibration analysis of functionally graded plates Compos Part B: Eng 43 2012 711 725
69. Neves AMA, Ferreira AJM, Carrera E, Cinefra M, Roque CMC, Jorge RMN, et al. A quasi-3d hyperbolic shear deformation theory for the static and free vibration analysis of functionally graded plates. Compos Struct, in press.
70. Todd O. Williams Efficiency and accuracy considerations in a unified plate theory with delamination Compos Struct 52 1 2001 27 40
71. Todd O. Williams, and Frank L. Addessio A general theory for laminated plates with delaminations Int J Solids Struct 34 16 1997 2003 2024
72. Marek-Jerzy Pindera, Todd O. Williams, and Steven M. Arnold Thermoplstic response of metal-matrix composites with homogenized and functionally graded interfaces Compos Eng 4 1 1994 129 145 Use of composites in functionally graded materials
73. Todd O. Williams A generalized, multilength scale framework for thermo-diffusional-mechanically coupled, nonlinear, laminated plate theories with delaminations Int J Solids Struct 42 5-6 2005 1465 1490
74. Todd O. Williams A generalized multilength scale nonlinear composite plate theory with delamination Int J Solids Struct 36 20 1999 3015 3050
75. Hashem M. Mourad, Todd O. Williams, and Francis L. Addessio Finite element analysis of inelastic laminated plates using a global-local formulation with delamination Comput Methods Appl Mech Eng 198 3-4 2008 542 554
76. 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
77. 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
78. 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
79. A.J.M. Ferreira, C.M.C. Roque, R.M.N. Jorge, and E.J. Kansa Static deformations and vibration analysis of composite and sandwich plates using a layerwise theory and multiquadrics discretizations Eng Anal Bound Elem 29 12 2005 1104 1114
80. A.J.M. Ferreira, C.M.C. Roque, and R.M.N. Jorge Analysis of composite plates by trigonometric shear deformation theory and multiquadrics Comput Struct 83 27 2005 2225 2237
81. A.J.M. Ferreira, R.C. Batra, C.M.C. Roque, L.F. Qian, and R.M.N. Jorge Natural frequencies of functionally graded plates by a meshless method Compos Struct 75 1-4 2006 593 600
82. A.J.M. Ferreira, C.M.C. Roque, and R.M.N. Jorge Free vibration analysis of symmetric laminated composite plates by fsdt and radial basis functions Comput Methods Appl Mech Eng 194 39-41 2005 4265 4278
83. A.J.M. Ferreira, C.M.C. Roque, and P.A.L.S. Martins Radial basis functions and higher-order shear deformation theories in the analysis of laminated composite beams and plates Compos Struct 66 1-4 2004 287 293
84. A.J.M. Ferreira, C.M.C. Roque, E. Carrera, M. Cinefra, and O. Polit Radial basis functions collocation and a unified formulation for bending, vibration and buckling analysis of laminated plates, according to a variation of murakamiâAŹs zig-zag theory Eur J Mech - A/Solids 30 4 2011 559 570
85. J.D. Rodrigues, C.M.C. Roque, A.J.M. Ferreira, E. Carrera, and M. Cinefra Radial basis functions-finite differences collocation and a unified formulation for bending, vibration and buckling analysis of laminated plates, according to murakami's zig-zag theory Compos Struct 93 7 2011 1613 1620
86. A.J.M. Ferreira, C.M.C. Roque, E. Carrera, and M. Cinefra Analysis of thick isotropic and cross-ply laminated plates by radial basis functions and a unified formulation J Sound Vib 330 4 2011 771 787
87. A.J.M. Ferreira, C.M.C. Roque, E. Carrera, M. Cinefra, and O. Polit Two higher order zig-zag theories for the accurate analysis of bending, vibration and buckling response of laminated plates by radial basis functions collocation and a unified formulation J Compos Mater 2011
88. 0 Reissner-Mindlin multilayered plate elements including zig-zag and interlaminar stress continuity Int J Numer Methods Eng 39 1996 1797 1820
89. T. Mori, and K. Tanaka Average stress in matrix and average elastic energy of materials with misfitting inclusions Acta Metall 21 5 1973 571 574
90. Y. Benveniste A new approach to the application of Mori-Tanaka's theory in composite materials Mech Mater 6 2 1987 147 157
91. R.L. Hardy Multiquadric equations of topography and other irregular surfaces Geophys Res 176 1971 1905 1915
92. E.J. Kansa Multiquadrics - a scattered data approximation scheme with applications to computational fluid dynamics. Part i: surface approximations and partial derivative estimates Comput Math Appl 19 8/9 1990 127 145
93. E.J. Kansa Multiquadrics - a scattered data approximation scheme with applications to computational fluid dynamics. Part ii: solutions to parabolic, hyperbolic and elliptic partial differential equations Comput Math Appl 19 8/9 1990 147 161
94. E. Larsson, and B. Fornberg A numerical study of some radial basis function based solution methods for elliptic pdes Comput Math Appl 46 5-6 2003 891 902
95. C. Franke, and R. Schaback Solving partial differential equations by collocation using radial basis functions Appl Math Comput 93 1 1998 73 82
96. G.E. Fasshauer Newton iteration with multiquadrics for the solution of nonlinear pdes Comput Math Appl 43 2002 423 438
97. Gregory Fasshauer Solving differential equations with radial basis functions: multilevel methods and smoothing Adv Comput Math 11 1999 139 159 10.1023/A:1018919824891
98. H. Wendland Error estimates for interpolation by compactly supported radial basis functions of minimal degree J Approx Theory 93 1998 258 296
99. 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