Analysis of laminated doubly-curved shells by a layerwise theory and radial basis functions collocation, accounting for through-the-thickness deformations

Computational Mechanics

Volumn 48, Issue 1, 2011, Pages 13-25

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

^a UNIVERSITY OF PORTO   (Portugal)

^b POLITECNICO DI TORINO   (Italy)

^c UNIVERSITY OF PORTO   (Portugal)

Author keywords

Bending; Modeling; Numerical methods

Indexed keywords

BENDING (FORMING); DEFORMATION; EQUATIONS OF MOTION; FUNCTIONS; LAMINATING; MODELS; NUMERICAL METHODS; RADIAL BASIS FUNCTION NETWORKS;

CARRERA'S UNIFIED FORMULATION; DOUBLY CURVED SHELLS; LAMINATED SHELL; LAYER-WISE THEORY; LAYERWISE DEFORMATION THEORY; MINDLIN; RADIAL BASIS FUNCTIONS; STATIC AND FREE VIBRATION ANALYSIS;

VIBRATION ANALYSIS;

EID: 79959340527     PISSN: 01787675     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00466-011-0579-4     Document Type: Article

References (62)

1. WT Koiter 1970 On the foundations of the linear theory of thin elastic shell Proc Kon Nederl Akad Wetensch 73 169 195
2. PM Naghdi 1956 A survey of recent progress in the theory of elastic shells Appl Mech Rev 9 365 368
3. JG Ren 1987 Exact solutions for laminated cylindrical shells in cylindrical bending Compos Sci Technol 29 169 187 10.1016/0266-3538(87)90069-8 (Pubitemid 17657995)
4. TK Varadan K Bhaskar 1991 Bending of laminated orthotropic cylindrical shells-an elasticity approach Compos Struct 17 141 156 10.1016/0263-8223(91) 90067-9
5. AK Noor PL Rarig 1974 Three-dimensional solutions of laminated cylinders Comput Methods Appl Mech Eng 3 319 334 0278.73061 10.1016/0045-7825(74)90017-6
6. AK Noor WS Peters 1989 Stress, vibration and buckling of multilayered cylinders J Struct Eng ASCE 115 69 89 10.1061/(ASCE)0733-9445(1989)115:1(69)
7. AK Noor WS Peters 1989 A posteriori estimates for shear correction factors in multilayered composite cylinders J Eng Mech ASCE 115 1225 1245 10.1061/(ASCE)0733-9399(1989)115:6(1225)
8. JQ Ye KP Soldatos 1994 Three-dimensional vibration of laminated cylinders and cylindrical panels with symmetric or antisymmetric cross-ply lay-up Compos Eng 4 429 444 10.1016/S0961-9526(09)80016-6
9. EI Grigolyuk GM Kulikov 1988 General direction of the development of the theory of shells Mekhanica Kompozitnykh Materialov 2 287 298
10. RK Kapania S Raciti 1989 Recent advances in analysis of laminated beams and plates AIAA J 27 923 946 0674.73047 10.2514/3.10202
11. RK Kapania 1989 A review on the analysis of laminated shells J Press Vessel Technol 111 88 96
12. AK Noor WS Burton 1989 Assessment of shear deformation theories for multilayered composite plates Appl Mech Rev 41 1 18 10.1115/1.3152418
13. AK Noor WS Burton 1990 Assessment of computational models for multilayered composite shells Appl Mech Rev 43 67 97
14. AK Noor WS Burton CW Bert 1996 Computational model for sandwich panels and shells Appl Mech Rev 49 155 199 10.1115/1.3101923 (Pubitemid 126635956)
15. KP Soldatos T Timarci 1993 A unified formulation of laminated composites, shear deformable, five-degrees-of-freedom cylindrical shell theories Compos Struct 25 165 171 10.1016/0263-8223(93)90162-J (Pubitemid 23714755)
16. Reddy JN (1997) Mechanics of laminated composite plates, theory and analysis. CRC Press, Boca Raton
17. T Hsu JT Wang 1970 A theory of laminated cylindrical shells consisting of layers of orthotropic laminae AIAA J 8 2141 2146 0222.73096 10.2514/3.6077
18. YK Cheung CI Wu 1972 Free vibrations of thick, layered cylinders having finite length with various boundary conditions J Sound Vib 24 189 200 0241.73092 10.1016/0022-460X(72)90948-0
19. S Srinivas 1973 A refined analysis of composite laminates J Sound Vib 30 495 550 0267.73050 10.1016/S0022-460X(73)80170-1
20. CT Sun JM Whitney 1973 On the theories for the dynamic response of laminated plates AIAA J 11 372 398 10.2514/3.50448
21. EJ Barbero JN Reddy JL Teply 1990 General two-dimensional theory of laminated cylindrical shells AIAA J 28 544 553 0699.73042 10.2514/3.10426 (Pubitemid 20649238)
22. KN Cho CW Bert AG Striz 1991 Free vibrations of laminated rectangular plates analyzed by higher order individual-layer theory J Sound Vib 145 429 442 10.1016/0022-460X(91)90112-W (Pubitemid 21654269)
23. A Nosier RK Kapania JN Reddy 1993 Free vibration analysis of laminated plates using a layer-wise theory AIAA J 31 2335 2346 0793.73052 10.2514/3.11933
24. P Gaudenzi R Barboni A Mannini 1995 A finite element evaluation of single-layer and multi-layer theories for the analysis of laminated plates Compos Struct 30 427 440 10.1016/0263-8223(94)00065-4
25. E Carrera 1998 Evaluation of layer-wise mixed theories for laminated plates analysis AIAA J 36 830 839 10.2514/2.444 (Pubitemid 128585677)
26. E Carrera 1998 Layer-wise mixed models for accurate vibration analysis of multilayered plates J Appl Mech 65 820 828 10.1115/1.2791917
27. E Carrera 2003 Theories and finite elements for multilayered plates and shells: a unified compact formulation with numerical assessment and benchmarking Arch Comput Methods Eng 97 10 215
28. E Carrera 1999 Multilayered shell theories accounting for layerwise mixed description. Part 1: governing equations AIAA J 37 9 1107 1116 10.2514/2.821
29. E Carrera 1999 Multilayered shell theories accounting for layerwise mixed description. Part 2: numerical evaluations AIAA J 37 9 1117 1124 10.2514/2.822
30. E Carrera 1999 A study of transverse normal stress effect on vibration of multilayered plates and shells J Sound Vib 225 5 803 829 10.1006/jsvi.1999.2271 (Pubitemid 129536976)
31. E Carrera 1998 A Reissner's mixed variational theorem applied to vibrational analysis of multilayered shell J Appl Mech 66 63 78
32. ST Dennis AN Palazotto 1989 Transverse shear deformation in orthotropic cylindrical pressure vessels using a higher-order shear theory AIAA J 27 10 1441 1447 0684.73019 10.2514/3.10283
33. Merk J (1995) Hierarchische, Kontinuumbasiert Shalenelemente höhere Ordnung. PhD Dissertation, Institute for Statics and Dynamics, Universität Stuttgart, Stuttgart, Germany
34. S Di E Ramm 1993 Hybrid stress formulation for higher-order theory of laminated shell analysis Comput Method Appl Mech Eng 109 359 376 0847.73060 10.1016/0045-7825(93)90087-E
35. EJ Kansa 1990 Multiquadrics: a scattered data approximation scheme with applications to computational fluid dynamics. I: Surface approximations and partial derivative estimates Comput Math Appl 19 8/9 127 145 0692.76003 10.1016/0898-1221(90)90270-T (Pubitemid 20668364)
36. YC Hon MW Lu WM Xue YM Zhu 1997 Multiquadric method for the numerical solution of byphasic mixture model Appl Math Comput 88 153 175 0910.76059 10.1016/S0096-3003(96)00309-8 (Pubitemid 127683562)
37. YC Hon KF Cheung XZ Mao EJ Kansa 1999 A multiquadric solution for the shallow water equation ASCE J Hydraul Eng 125 5 524 533 10.1061/(ASCE)0733- 9429(1999)125:5(524) (Pubitemid 29400985)
38. JG Wang GR Liu P Lin 2002 Numerical analysis of biot's consolidation process by radial point interpolation method Int J Solids Struct 39 6 1557 1573 1061.74014 10.1016/S0020-7683(02)00005-7 (Pubitemid 34306039)
39. GR Liu YT Gu 2001 A local radial point interpolation method (LRPIM) for free vibration analyses of 2-d solids J Sound Vib 246 1 29 46 10.1006/jsvi.2000.3626 (Pubitemid 32866245)
40. GR Liu JG Wang 2002 A point interpolation meshless method based on radial basis functions Int J Numer Methods Eng 54 1623 1648 1098.74741 10.1002/nme.489 (Pubitemid 34842350)
41. JG Wang GR Liu 2002 On the optimal shape parameters of radial basis functions used for 2-d meshless methods Comput Methods Appl Mech Eng 191 2611 2630 1065.74074 10.1016/S0045-7825(01)00419-4 (Pubitemid 34452176)
42. XL Chen GR Liu SP Lim 2003 An element free galerkin method for the free vibration analysis of composite laminates of complicated shape Compos Struct 59 279 289 10.1016/S0263-8223(02)00034-X (Pubitemid 36011091)
43. KY Dai GR Liu SP Lim XL Chen 2004 An element free galerkin method for static and free vibration analysis of shear-deformable laminated composite plates J Sound Vib 269 633 652 10.1016/S0022-460X(03)00089-0
44. GR Liu XL Chen 2002 Buckling of symmetrically laminated composite plates using the element-free galerkin method Int J Struct Stab Dyn 2 281 294 1205.74162 10.1142/S0219455402000634
45. KM Liew XL Chen JN Reddy 2004 Mesh-free radial basis function method for buckling analysis of non-uniformity loaded arbitrarily shaped shear deformable plates Comput Methods Appl Mech Eng 193 205 225 1075.74700 10.1016/j.cma.2003. 10.002 (Pubitemid 38086750)
46. YQ Huang QS Li 2004 Bending and buckling analysis of antisymmetric laminates using the moving least square differential quadrature method Comput Methods Appl Mech Eng 193 3471 3492 1068.74090 10.1016/j.cma.2003.12.039 (Pubitemid 38921161)
47. L Liu GR Liu VCB Tan 2002 Element free method for static and free vibration analysis of spatial thin shell structures Comput Methods Appl Mech Eng 191 5923 5942 1083.74610 10.1016/S0045-7825(02)00504-2 (Pubitemid 36036254)
48. S Xiang KM Wang YT Ai YD Sha H Shi 2009 Analysis of isotropic, sandwich and laminated plates by a meshless method and various shear deformation theories Compos Struct 91 1 31 37 10.1016/j.compstruct.2009.04.029
49. S Xiang H Shi KM Wang YT Ai YD Sha 2010 Thin plate spline radial basis functions for vibration analysis of clamped laminated composite plates Eur J Mech A Solids 29 844 850 10.1016/j.euromechsol.2010.02.012
50. AJM Ferreira CMC Roque RMN Jorge 2006 Analysis of composite and sandwich plate by trigonometric layer-wise deformation theory and radial basis function J Sandwich Struct Mater 8 497 515 10.1177/1099636206065873 (Pubitemid 44582303)
51. AJM Ferreira 2003 A formulation of the multiquadric radial basis function method for the analysis of laminated composite plates Compos Struct 59 385 392 10.1016/S0263-8223(02)00239-8 (Pubitemid 41167838)
52. AJM Ferreira 2003 Thick composite beam analysis using a global meshless approximation based on radial basis functions Mech Adv Mater Struct 10 271 284 10.1080/15376490306743
53. AJM Ferreira CMC Roque PALS Martins 2003 Analysis of composite plates using higher-order shear deformation theory and a finite point formulation based on the multiquadric radial basis function method Compos B 34 627 636 10.1016/S1359-8368(03)00083-0
54. E Carrera 2001 Developments, ideas, and evaluations based upon reissner's mixed variational theorem in the modelling of multilayered plates and shells Appl Mech Rev 54 301 329 10.1115/1.1385512
55. 0 Reissner-Mindlin multilayered plate elements including zig-zag and interlaminar stress continuity Int J Numer Methods Eng 39 1797 1820 0885.73076 10.1002/(SICI)1097-0207(19960615)39:11<1797::AID- NME928>3.0.CO;2-W (Pubitemid 126648002)
56. E Carrera B Kroplin 1997 Zig-zag and interlaminar equilibria effects in large deflection and post-buckling analysis of multilayered plates Mech Compos Mater Struct 4 69 94
57. E Carrera 1998 Evaluation of layer-wise mixed theories for laminated plate analysis AIAA J 36 830 839 10.2514/2.444 (Pubitemid 128585677)
58. RL Hardy 1971 Multiquadric equations of topography and other irregular surfaces Geophys Res 176 1905 1915 10.1029/JB076i008p01905
59. AJM Ferreira GE Fasshauer 2006 Computation of natural frequencies of shear deformable beams and plates by a rbf-pseudospectral method Comput Methods Appl Mech Eng 196 134 146 1120.74528 10.1016/j.cma.2006.02.009 (Pubitemid 46158175)
60. JN Reddy CF Liu 1985 A higher-order shear deformation theory of laminated elastic shells Int J Eng Sci 23 319 330 0559.73072 10.1016/0020-7225(85)90051-5 (Pubitemid 15494942)
61. M Cinefra E Carrera P Nali 2010 MITC technique extended to variable kinematic multilayered plate elements Compos Struct 92 1888 1895 10.1016/j.compstruct.2010.01.009
62. Cinefra M, Chinosi C, Della Croce L (2011) MITC9 shell elements based on refined theories for the analysis of isotropic cylindrical structures. Mech Adv Mater Struct (in press)