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

Journal of Composite Materials

Volumn 45, Issue 24, 2011, Pages 2523-2536

  Ferreira, A J M ^a   Roque, C M C ^b   Carrera, E ^c   Cinefra, M ^c   Polit, O ^d  

^a UNIVERSITY OF PORTO   (Portugal)

^b UNIVERSITY OF PORTO   (Portugal)

^c POLITECNICO DI TORINO   (Italy)

^d UNIVERSITÉ PARIS OUEST NANTERRE LA DÉFENSE   (France)

Author keywords

collocation; composites; laminated plates; plates and shells; radial basis functions; unified formulation

Indexed keywords

COLLOCATION; LAMINATED PLATE; PLATES AND SHELLS; RADIAL BASIS FUNCTIONS; UNIFIED FORMULATION;

BUCKLING; DEFORMATION; IMAGE SEGMENTATION; LAMINATING; NUMERICAL ANALYSIS; PLATES (STRUCTURAL COMPONENTS); RADIAL BASIS FUNCTION NETWORKS;

VIBRATION ANALYSIS;

EID: 80955166487     PISSN: 00219983     EISSN: 1530793X     Source Type: Journal    
DOI: 10.1177/0021998311401103     Document Type: Article

References (66)

1. Kirchhoff G. Uber das gleichgewicht und die bewegung einer elastischen scheibe. J Angew Math. 1850 ; 40: 51-88
2. Reissner E. The effect of transverse shear deformations on the bending of elastic plates. J Appl Mech. 1945 ; 12: A69 - A77
3. Mindlin RD. Influence of rotary inertia and shear in flexural motions of isotropic elastic plates. J Appl Mech. 1951 ; 18: 31-38
4. Zenkert D An introduction to sandwich structures. Oxford: Chamelon Press ; 1995
5. Vinson JR The behavior of sandwich structures of isotropic and composite materials. Lancaster PA: Technomic Publishing Co ; 1999
6. Lekhnitskii SG. Strength calculation of composite beams. Vestnik Inzhen i Tekhnikov. 1935 ; 9
7. Carrera E. Theories and finite elements for multilayered anisotropic, composite plates and shells. Arch Comput Methods Eng. 2002 ; 9: 87-140
8. Carrera E. Historical review of zig-zag theories for multilayered plates and shells. Appl Mech Rev. 2003 ; (56). 287-308 (Pubitemid 40205918)
9. Murakami H. Laminated composite plate theory with improved in-plane responses. J Appl Mech. 1986 ; 53: 661-666 (Pubitemid 16630969)
10. Carrera E. Developments, ideas, and evaluations based upon reissners mixed variational theorem in the modelling of multilayered plates and shells. Appl Mech Rev. 2001 ; 54: 301-329
11. Carrera E. A study of transverse normal stress effects on vibration of multilayered plates and shells. J Sound Vib. 1999 ; 225: 803-829 (Pubitemid 129536976)
12. Carrera E. Theories and finite elements for multilayered plates and shells: A unified compact formulation with numerical assessment and benchmarking. Arch Comput Meth Eng. 2003 ; 10: 215-297
13. Meyer-Piening HR, Rao KM. Analysis of thick laminated anisotropic composites plates by the finite element method. Comp Struct. 1990 ; 15: 185-213
14. Carrera E, Demasi L. Multilayered finite plate element based on reissner mixed variational theorem. part i: Theory. and part ii: Numerical analysis. Int J Numer Methods Eng. 2002 ; 55: 191-231
15. Varadan TK, Bhaskar K. A higher-order theory for bending analysis of laminated shells of revolution. Compos Struct. 1991 ; 40: 815-819 (Pubitemid 21707515)
16. Carrera E. The use of murakamis zig-zag function in the modeling of layered plates and shells. Compos Struct. 2004 ; 82: 541-554
17. Carrera E, Brischetto S. A comparison of various kinematic models for sandwich shell panels with soft core. J Compos Mater. 2009 ; 43: 2201-2221
18. Carrera E, Brischetto S. A survey with numerical assessment of classical and refined theories for the analysis of sandwich plate. Appl Mech Rev. 2009 ; 62 (1). 1-17
19. Carrera E, Brischetto S, Demasi L. Improved bending analysis of sandwich plate by using zig-zag function. Compos Struct. 2009 ; 89: 408-415
20. Carrera E, Brischetto S, Demasi L. Improved response of unsymmetrically laminated sandwich plates by using zig-zag functions. J Sand Struct Mater. 2009 ; 11 (2-3). 257-267
21. Carrera E, Brischetto S, Demasi L. Free vibration of sandwich plates and shells by using zig-zag function. Shock Vib. 2009 ; 16: 495-503
22. Kansa EJ. Multiquadrics- a scattered data approximation scheme with applications to computational fluid dynamics. i: Surface approximations and partial derivative estimates. Comput Math Appl. 1990 ; 19 (8/9). 127-145 (Pubitemid 20668364)
23. Hon YC, Lu MW, Xue WM, Zhu YM. Multiquadric method for the numerical solution of byphasic mixture model. Appl Math Comput. 1997 ; 88: 153-175 (Pubitemid 127683562)
24. Hon YC, Cheung KF, Mao XZ, Kansa EJ. A multiquadric solution for the shallow water equation. ASCE J Hydraul Eng. 1999 ; 125 (5). 524-533 (Pubitemid 29400985)
25. Wang JG, Liu GR, Lin P. Numerical analysis of biots consolidation process by radial point interpolation method. Int J Solids Struct. 2002 ; 39 (6). 1557-1573 (Pubitemid 34306039)
26. Liu GR, Gu YT. A local radial point interpolation method (lrpim) for free vibration analyses of 2-d solids. J Sound Vib. 2001 ; 246 (1). 29-46 (Pubitemid 32866245)
27. Liu GR, Wang JG. A point interpolation meshless method based on radial basis functions. International j Numer Meth Eng. 2002 ; 54: 1623-1648 (Pubitemid 34842350)
28. Wang JG, Liu GR. On the optimal shape parameters of radial basis functions used for 2-d meshless methods. Comput Methods Appl Mech Eng. 2002 ; 191: 2611-2630 (Pubitemid 34452176)
29. Chen XL, Liu GR, Lim SP. An element free galerkin method for the free vibration analysis of composite laminates of complicated shape. Compos Struct. 2003 ; 59: 279-289 (Pubitemid 36011091)
30. Dai KY, Liu GR, Lim SP, Chen XL. An element free galerkin method for static and free vibration analysis of shear-deformable laminated composite plates. J Sound Vib. 2004 ; 269: 633-652
31. Liu GR, Chen XL. Buckling of symmetrically laminated composite plates using the element-free galerkin method. Int J Struct Stab Dyn. 2002 ; 2: 281-294
32. Liew KM, Chen XL, Reddy JN. Mesh-free radial basis function method for buckling analysis of non-uniformity loaded arbitrarily shaped shear deformable plates. Comput Meth Appl Mech Eng. 2004 ; 193: 205-225
33. Huang YQ, Li QS. Bending and buckling analysis of antisymmetric laminates using the moving least square differential quadrature method. Comput Meth Appl Mech Eng. 2004 ; 193: 3471-3492 (Pubitemid 38921161)
34. Liu L, Liu GR, Tan VCB. Element free method for static and free vibration analysis of spatial thin shell structures. Comput Meth Appl Mech Eng. 2002 ; 191: 5923-5942 (Pubitemid 36036254)
35. Xiang S, Wang KM, Ai YT, Sha YD, Shi H. Analysis of isotropic, sandwich and laminated plates by a meshless method and various shear deformation theories. Compos Struct. 2009 ; 91 (1). 31-37
36. Xiang S, Shi H, Wang KM, Ai YT, Sha YD. Thin plate spline radial basis functions for vibration analysis of clamped laminated composite plates. Eur J Mech A/Solids. 2010 ; 29: 844-850
37. Liu GR, Nguyen-Thoi T Smoothed finite element Method. Boca Raton, FL: CRC Press ; 2010
38. Liu GR, Nguyen-Thoi T, Lam KY. An edge-based smoothed finite element method (es-fem) for static, free and forced vibration analyses in solids. J Sound Vib. 2009 ; 320: 1100-1130
39. Nguyen-Xuan H, Liu GR, Thai-Hoang C, Nguyen-Thoi T. An edge-based smoothed finite element method with stabilized discrete shear gap technique for analysis of reissner-mindlin plates. Comput Meth Appl Mech Eng. 2009 ; 199: 471-489
40. Nguyen-Xuan H, Liu GR, Nguyen-Thoi T, Nguyen-Tran C. An edge-based smoothed finite element method for analysis of two-dimensional piezoelectric structures. Smart Mater Struct. 2009 ; 18 (6). 065015-065015
41. Nguyen-Thoi T, Liu GR, Vu-Do HC, Nguyen-Xuan H. An edge-based smoothed finite element method (es-fem) for visco-elastoplastic analyses of 2d solids using triangular mesh. Comput Mech. 2009 ; 45: 23-44
42. Nguyen-Thoi T, Liu GR, Nguyen-Xuan H. An n-sided polygonal edge-based smoothed finite element method (nes-fem) for solid mechanics. Int J Numer Methods Biomed Eng. 2010 ;:
43. Ferreira AJM. A formulation of the multiquadric radial basis function method for the analysis of laminated composite plates. Compos Struct. 2003 ; 59: 385-392 (Pubitemid 41167838)
44. Ferreira AJM. Thick composite beam analysis using a global meshless approximation based on radial basis functions. Mech Adv Mater Struct. 2003 ; 10: 271-284
45. Ferreira AJM, Roque CMC, Martins PALS. 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. 2003 ; 34: 627-636
46. Ferreira AJM, Roque CMC, Carrera E, Cinefra M. Analysis of thick isotropic and cross-ply laminated plates by radial basis functions and unified formulation. J Sound Vib. 2011 ; 330 (4). 771-787
47. Touratier M. An efficient standard plate theory. Int J Eng Sci. 1991 ; 29: 901-916
48. Vidal P, Polit O. A family of sinus finite elements for the analysis of rectangular laminated beams. Compos Struct. 2008 ; 84: 56-72 (Pubitemid 351201873)
49. Demasi L. 3 hierarchy plate theories for thick and thin composite plates: the generalized unified formulation. Compos Struct. 2008 ; 84: 256-270 (Pubitemid 351396261)
50. Touratier M. A generalization of shear deformation theories for axisymmetric multilayered shells. Int J Solids Struct. 1992 ; 29: 1379-1399
51. Touratier M. A refined theory of laminated shallow shells. Int J Solids Struct. 1992 ; 29 (11). 1401-1415
52. Carrera E. C0 reissner-mindlin multilayered plate elements including zig-zag and interlaminar stress continuity. Int J Numer Meth Eng. 1996 ; 39: 1797-1820 (Pubitemid 126648002)
53. Carrera E, Kroplin B. Zig-zag and interlaminar equilibria effects in large deflection and post-buckling analysis of multilayered plates. Mech Compos Mater Struct. 1997 ; 4: 69-94
54. Carrera E. Evaluation of layer-wise mixed theories for laminated plate analysis. AIAA J. 1998 ; 36: 830-839 (Pubitemid 128585677)
55. Hardy RL. Multiquadric equations of topography and other irregular surfaces. Geophys Res. 1971 ; 176: 1905-1915
56. Ferreira AJM, Fasshauer GE. Computation of natural frequencies of shear deformable beams and plates by a rbf-pseudospectral method. Comput Methods Appl Mech Eng. 2006 ; 196: 134-146 (Pubitemid 46158175)
57. Akhras G, Cheung MS, Li W. Finite strip analysis for anisotropic laminated composite plates using higher-order deformation theory. Comput Struct. 1994 ; 52 (3). 471-477
58. Reddy JN. A simple higher-order theory for laminated composite plates. J Appl Mech. 1984 ; 51: 745-752 (Pubitemid 15422865)
59. Reddy JN, Chao WC. A comparison of closed-form and finite-element solutions of thick laminated anisotropic rectangular plates. Nucl Eng Des. 1981 ; 64: 153-167 (Pubitemid 12521425)
60. Pagano NJ. Exact solutions for rectangular bidirectional composites and sandwich plates. J Compos Mater. 1970 ; 4: 20-34
61. Ferreira AJM. Analysis of composite plates using a layerwise deformation theory and multiquadrics discretization. Mech Adv Mater Struct. 2005 ; 12 (2). 99-112 (Pubitemid 41673172)
62. Reddy JN Mechanics of laminated composite plates: theory and analysis. Boca Raton, FL: CRC Press ; 1997
63. Khdeir AA, Librescu L. Analysis of symmetric cross-ply elastic plates using a higher-order theory,part ii: buckling and free vibration. Compos Struct. 1988 ; 9: 259-277 (Pubitemid 18623963)
64. Liew KM, Huang YQ, Reddy JN. Vibration analysis of symmetrically laminated plates based on fsdt using the moving least squares differential quadrature method. Comput Meth Appl Mech Eng. 2003 ; 192: 2203-2222 (Pubitemid 36669470)
65. Khdeir AA, Librescu L. Analysis of symmetric cross-ply elastic plates using a higher-order theory. part ii: buckling and free vibration. Compos Struct. 1988 ; 9: 259-277 (Pubitemid 18623963)
66. Liew KM, Huang YQ. Bending and buckling of thick symmetric rectangular laminates using the moving least-squeares differential quadrature method. Int J Mech Sci. 2003 ; 45: 95-114