An efficient and simple higher order shear and normal deformation theory for functionally graded material (FGM) plates

Composites Part B: Engineering

Volumn 60, Issue , 2014, Pages 274-283

  Belabed, Zakaria ^a   Ahmed Houari, Mohammed Sid ^a   Tounsi, Abdelouahed ^a   Mahmoud, S R ^b,c   Anwar Beg O ^d  

^a UNIVERSITY OF SIDI BEL ABBES   (Algeria)

^b KING ABDULAZIZ UNIVERSITY   (Saudi Arabia)

^c SOHAG UNIVERSITY   (Egypt)

^d Gort Engovation Research (Propulsion and Biomechanics)   (United Kingdom)

Author keywords

A. Plate; C. Computational modeling; Functionally graded materials

Indexed keywords

COMPUTATIONAL MODEL; FREE-VIBRATION ANALYSIS; FUNCTIONALLY GRADED MATERIAL (FGM); FUNCTIONALLY GRADED PLATES; SHEAR CORRECTION FACTORS; SIMPLY SUPPORTED PLATES; STRESS-FREE BOUNDARY CONDITIONS; TRANSVERSE DISPLACEMENTS;

BEAMS AND GIRDERS; DEFORMATION; EQUATIONS OF MOTION; EQUIVALENT CIRCUITS; SHEAR FLOW; VIBRATION ANALYSIS;

FUNCTIONALLY GRADED MATERIALS;

EID: 84892765410     PISSN: 13598368     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.compositesb.2013.12.057     Document Type: Article

References (78)

1. M. Koizumi The concept of FGM, functionally gradient materials Ceram Trans 34 1993 3 10
2. E. Feldman, and J. Aboudi Buckling analysis of functionally graded plates subjected to uniaxial loading Compos Struct 38 1-4 1997 29 36
3. S. Abrate Functionally graded plates behave like homogeneous plates Composites Part B 39 1 2008 151 158
4. M. Mahdavian Buckling analysis of simply-supported functionally graded rectangular plates under non-uniform in-plane compressive loading J Solid Mech 1 3 2009 213 225
5. M. Mohammadi, A.R. Saidi, and E. Jomehzadeh Levy solution for buckling analysis of functionally graded rectangular plates Appl Compos Mater 17 2 2010 81 93
6. J.N. Reddy Mechanics of laminated composite plates and shells: theory and analysis 2004 CRC Press Baton Rouge, Florida, USA
7. E. Reissner Reflection on the theory of elastic plates ASME J Appl Mech 38 1945 1453 1464
8. R.D. Mindlin Influence of rotary inertia and shear on flexural motions of isotropic elastic plates ASME J Appl Mech 18 1951 31 38
9. L. Della Croce, and P. Venini Finite elements for functionally graded Reissner-Mindlin plates Comput Meth Appl Mech Eng 193 2004 705 725
10. J. Yang, K.M. Liew, and S. Kitipornchai Second-order statistics of the elastic buckling of functionally graded rectangular plates Compos Sci Technol 65 2005 1165 1175
11. X. Zhao, Y.Y. Lee, and K.M. Liew Mechanical and thermal buckling analysis of functionally graded plates Compos Struct 90 2 2009 161 171
12. S. Moradi, and M.H. Mansouri Thermal buckling analysis of shear deformable laminated orthotropic plates by differential quadrature Steel Compos Struct 12 2012 129 147
13. R. Menaa, A. Tounsi, F. Mouaici, I. Mechab, M. Zidi, and E.A. Adda Bedia Analytical solutions for static shear correction factor of functionally graded rectangular beams Mech Advan Mater Struct 19 2012 641 652
14. H. Yaghoobi, and P. Yaghoobi Buckling analysis of sandwich plates with FGM face sheets resting on elastic foundation with various boundary conditions: an analytical approach Meccanica 48 2013 2019 2035
15. M.M. Rashidi, A. Shooshtari, and O. Anwar Bég Homotopy perturbation study of nonlinear vibration of Von Kármán rectangular plates Comput Struct 106/107 2012 46 55
16. R.B. Nelson, and D.R. Lorch A refined theory for laminated orthotropic plates ASME J Appl Mech 41 1974 177 184
17. K.H. Lo, R.M. Christensen, and E.M. Wu A high-order theory of plate deformation-part 2: laminated plates ASME J Appl Mech 44 1977 669 674
18. A. Bhimaraddi, and L. Stevens A higher order theory for free vibration of orthotropic, homogeneous, and laminated rectangular plates ASME J Appl Mech 51 1984 195 198
19. J.N. Reddy A simple higher-order theory for laminated composite plates ASME J Appl Mech 51 1984 745 752
20. T. Kant, and B. Pandya A simple finite element formulation of a higher-order theory for unsymmetrically laminated composite plates Compos Struct 9 1988 215 246
21. T. Kant, and R.K. Khare A higher-order facet quadrilateral composite shell element Int J Numer Meth Eng 40 1997 4477 4499
22. M. Talha, and B.N. Singh Static response and free vibration analysis of FGM plates using higher order shear deformation theory Appl Math Modell 34 2010 3991 4011
23. F. Tornabene Free vibration analysis of functionally graded conical, cylindrical shell and annular plate structures with a four-parameter power-law distribution Comput Meth Appl Mech Eng 198 2009 2911 2935
24. A.M.A. Neves, A.J.M. Ferreira, E. Carrera, C.M.C. Roque, M. Cinefra, and R.M.N. Jorge et al. 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
25. A.M.A. Neves, A.J.M. Ferreira, E. Carrera, C.M.C. Roque, M. Cinefra, and R.M.N. Jorge et al. A quasi-3D hyperbolic shear deformation theory for the static and free vibration analysis of functionally graded plates Compos Struct 94 2012 1814 1825
26. A.M.A. Neves, A.J.M. Ferreira, E. Carrera, M. Cinefra, C.M.C. Roque, and R.M.N. Jorge et al. 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 Compos Part B: Eng 44 2013 657 674
27. F. Tornabene, N. Fantuzzi, E. Viola, and A.J.M. Ferreira Radial basis function method applied to doubly-curved laminated composite shells and panels with a general higher-order equivalent single layer formulation Compos Part B: Eng 55 2013 642 659
28. E. Viola, F. Tornabene, and N. Fantuzzi General higher-order shear deformation theories for the free vibration analysis of completely doubly-curved laminated shells and panels Compos Struct 95 2013 639 666
29. E. Viola, F. Tornabene, and N. Fantuzzi Static analysis of completely doubly-curved laminated shells and panels using general higher-order shear deformation theories Compos Struct 101 2013 59 93
30. F.A. Fazzolari, and E. Carrera Free vibration analysis of sandwich plates with anisotropic face sheets in thermal environment by using the hierarchical trigonometric Ritz formulation Compos Part B Eng 50 2013 67 81
31. F. Tornabene, N. Fantuzzi, E. Viola, and E. Carrera Static analysis of doubly-curved anisotropic shells and panels using CUF approach, differential geometry and differential quadrature method Compos Struct 107 2014 675 697
32. J.N. Reddy Analysis of functionally graded plates Int J Num Meth Eng 47 2000 663 684
33. A.M. Zenkour Generalized shear deformation theory for bending analysis of functionally graded plates Appl Math Modell 30 2006 67 84
34. H. Ait Atmane, A. Tounsi, I. Mechab, and E.A. Adda Bedia Free vibration analysis of functionally graded plates resting on Winkler-Pasternak elastic foundations using a new shear deformation theory Int J Mech Mat Des 6 2010 113 121
35. S. Benyoucef, I. Mechab, A. Tounsi, A. Fekrar, H. Ait Atmane, and E.A. Adda Bedia Bending of thick functionally graded plates resting on Winkler-Pasternak elastic foundations Mech Comp Mat 46 2010 425 434
36. L.F. Qian, R.C. Batra, and L.M. Chen Static and dynamic deformations of thick functionally graded elastic plates by using higher-order shear and normal deformable plate theory and meshless local Petrov-Galerkin method Comp Part B: Eng 35 2004 685 697
37. E. Carrera, S. Brischetto, M. Cinefra, and M. Soave Effects of thickness stretching in functionally graded plates and shells Comp Part B: Eng 42 2011 23 133
38. E. Carrera Developments, ideas and evaluations based upon Reissner's mixed variational theorem in the modeling of multilayered plates and shells Appl Mech Rev 54 2001 301 329
39. E. Carrera Theories and finite elements for multilayered plates and shells: a unified compact formulation with numerical assessment and benchmarking Arch Comp Meth Eng 10 2003 215 296
40. E. Carrera, and A. Ciuffreda A unified formulation to assess theories of multilayered plates for various bending problems Compos Struct 69 2005 271 293
41. L. Demasi 6 Mixed plate theories based on the generalized unified formulation. Part I: governing equations Compos Struct 87 2009 1 11
42. L. Demasi 6 Mixed plate theories based on the generalized unified formulation. Part III: advanced mixed high order shear deformation theories Compos Struct 87 2009 183 194
43. L. Demasi 6 Mixed plate theories based on the generalized unified formulation. Part IV: zig-zag theories Compos Struct 87 2009 95 205
44. L. Demasi 6 Mixed plate theories based on the generalized unified formulation. Part V: results Compos Struct 88 2009 1 16
45. Demasi L 6 Mixed plate theories based on the generalized unified formulation.: Part II: layerwise theories Compos Struct 87 2009 12 22
46. E. Carrera, S. Brischetto, and P. Nali Plates and shells for smart structures: classical and advanced theories for modeling and analysis 2011 Wiley New York, USA
47. E. Carrera, G. Giunta, and M. Petrolo Beam structures: classical and advanced theories 2011 Wiley New York, USA
48. H. Matsunaga Stress analysis of functionally graded plates subjected to thermal and mechanical loadings Compos Struct 87 2009 344 357
49. M. Talha, and B.N. Singh Static response and free vibration analysis of FGM plates using higher order shear deformation theory Appl Math Modell 34 2010 3991 4011
50. J.N. Reddy A general nonlinear third-order theory of functionally graded plates Int J Aerosp Lightweight Struct 1 2011 1 21
51. A. Zenkour, and Benchmark trigonometric Benchmark trigonometric and 3-D elasticity solutions for an exponentially graded thick rectangular plate Arch Appl Mech 77 2007 197 214
52. J.L. Mantari, and C. Guedes Soares Generalized hybrid quasi-3D shear deformation theory for the static analysis of advanced composite plates Compos Struct 94 2012 2561 2575
53. J.L. Mantari, and C. Guedes Soares A novel higher-order shear deformation theory with stretching effect for functionally graded plates Compos Part B: Eng 45 2013 268 281
54. H.T. Thai, and S.E. Kim A simple quasi-3D sinusoidal shear deformation theory for functionally graded plates Compos Struct 99 2013 172 180
55. L. Hadji, H.A. Atmane, A. Tounsi, I. Mechab, and E.A. Adda Bedia Free vibration of functionally graded sandwich plates using four variable refined plate theory Appl Math Mech 32 2011 925 942
56. N. El Meiche, A. Tounsi, N. Ziane, I. Mechab, and E.A. Adda Bedia A new hyperbolic shear deformation theory for buckling and vibration of functionally graded sandwich plate Int J Mech Sci 53 2011 237 247
57. M.S.A. Houari, S. Benyoucef, I. Mechab, A. Tounsi, and E.A. Adda Bedia Two variable refined plate theory for thermoelastic bending analysis of functionally graded sandwich plates J Therm Stress 34 2011 315 334
58. H.H. Abdelaziz, H.A. Atmane, I. Mechab, L. Boumia, A. Tounsi, and E.A. Adda Bedia Static analysis of functionally graded sandwich plates using an efficient and simple refined theory Chin J Aerosp 24 2011 434 448
59. S. Merdaci, A. Tounsi, M.S.A. Houari, I. Mechab, H. Hebali, and S. Benyoucef Two new refined shear displacement models for functionally graded sandwich plates Arch Appl Mech 81 2011 1507 1522
60. M. Bourada, A. Tounsi, M.S.A. Houari, and E.A. Adda Bedia A new four-variable refined plate theory for thermal buckling analysis of functionally graded sandwich plates J Sandwich Struct Mat 14 2012 5 33
61. A. Tounsi, M.S.A. Houari, S. Benyoucef, and E.A. Adda Bedia A refined trigonometric shear deformation theory for thermoelastic bending of functionally graded sandwich plates Aerosp Sci Tech 24 2013 209 220
62. Hamidi A, Zidi M, Houari MSA, Tounsi A. A new four variable refined plate theory for bending response of functionally graded sandwich plates under thermomechanical loading. Comp: Part B; in press.
63. B. Bouderba, M.S.A. Houari, and A. Tounsi Thermomechanical bending response of FGM thick plates resting on Winkler-Pasternak elastic foundations Steel Comp Struct 14 2013 85 104
64. J.L. Mantari, and C. Guedes Soares Finite element formulation of a generalized higher order shear deformation theory for advanced composite plates Compos Struct 96 2013 545 553
65. Y. Benveniste A new approach to the application of Mori-Tanaka's theory in composite materials Mech Mat 6 1987 147 157
66. T. Mori, and K. Tanaka Average stress in matrix and average elastic energy of materials with misfitting inclusions Acta Metall 21 1973 571 574
67. J. Yang, K.M. Liew, and S. Kitipornchai Stochastic analysis of compositionally graded plates with system randomness under static loading Int J Mech Sci 47 2005 1519 1541
68. S. Kitipornchai, J. Yang, and K.M. Liew Random vibration of the functionally graded laminates in thermal environments Comp Meth Appl Mech Eng 195 2006 1075 1095
69. S. Hosseini-Hashemi, M. Fadaee, and S.R. Atashipour Study on the free vibration of thick functionally graded rectangular plates according to a new exact closed-form procedure Compos Struct 93 2011 722 735
70. S. Hosseini-Hashemi, M. Fadaee, and S.R. Atashipour A new exact analytical approach for free vibration of Reissner-Mindlin functionally graded rectangular plates Int J Mech Sci 53 1 2011 11 22
71. H.T. Thai, and S.E. Kim A simple higher-order shear deformation theory for bending and free vibration analysis of functionally graded plates Compos Struct 96 2013 165 173
72. E. Carrera, S. Brischetto, and A. Robaldo Variable kinematic model for the analysis of functionally graded material plates AIAA J 46 2008 194 203
73. J.L. Mantari, and C. Guedes Soares Bending analysis of thick exponentially graded plates using a new trigonometric higher order shear deformation theory Compos Struct 94 2012 1991 2000
74. 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
75. H. Matsunaga Free vibration and stability of functionally graded plates according to a 2-D higher-order deformation theory Compos Struct 82 2008 499 512
76. J.L. Curiel Sosa, O. Anwar Bég, and J. M Liebana Murillo Finite element analysis of structural instability using a switching implicit-explicit technique Int J Comp Meth Eng Sci Mech 14 2013 452 464
77. Curiel Sosa JL, Munoz JJ, Pinho ST, Anwar Bég O. (XFEM) Simulation of damage in laminates. In: Eberhardsteiner J, et al., editors. Applied sciences and engineering (ECCOMAS 2012). Vienna, Austria, September 10-14 2012. p. 1940-6.
78. M.M. Rashidi, A. Shooshtari, and O. Anwar Bég Homotopy perturbation study of nonlinear vibration of Von Kármán rectangular plates Comput Struct 106/107 2012 46 55