Analysis of laminated shells by a sinusoidal shear deformation theory and radial basis functions collocation, accounting for through-the-thickness deformations

Composites Part B: Engineering

Volumn 42, Issue 5, 2011, Pages 1276-1284

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

A. Laminates; B. Vibration; C. Numerical analysis

Indexed keywords

A. LAMINATES; B. VIBRATION; C. NUMERICAL ANALYSIS; CARRERA'S UNIFIED FORMULATION; FREE-VIBRATION ANALYSIS; LAMINATED SHELL; RADIAL BASIS FUNCTIONS; SHEAR DEFORMATION THEORY;

EQUATIONS OF MOTION; LAMINATING; NUMERICAL ANALYSIS; RADIAL BASIS FUNCTION NETWORKS; SHEAR DEFORMATION;

VIBRATION ANALYSIS;

EID: 79956100488     PISSN: 13598368     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.compositesb.2011.01.031     Document Type: Article

References (47)

1. W.T. Koiter On the foundations of the linear theory of thin elastic shell Proc Kon Ned Akad Wetensch 73 1970 169 195
2. P.M. Naghdi A survey of recent progress in the theory of elastic shells Appl Mech Rev 9 1956 365 368
3. 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
4. E. 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
5. E. Carrera On the use of the Murakami's zig-zag function in the modeling of layered plates and shells Comput Struct 82 2004 541 554
6. E. Carrera, and S. Brischetto Analysis of thickness locking in classical, refined and mixed theories for layered shells Compos Struct 85 2008 83 90 (Pubitemid 351598109)
7. M. Cinefra, S. Belouettar, M. Soave, and E. Carrera Variable kinematic models applied to free-vibration analysis of functionally graded material shells Eur J Mech A/Solids 29 2010 1078 1087
8. M. D'Ottavio, D. Ballhause, B. Kröplin, and E. Carrera Closed-form solutions for the free-vibration problem of multilayered piezoelectric shells Comput Struct 84 2006 1506 1518 (Pubitemid 43947154)
9. M. Touratier A generalization of shear deformation theories for axisymmetric multilayered shells Int J Solids Struct 29 1992 1379 1399
10. M. Touratier An efficient standard plate theory Int J Eng Sci 29 1991 901 916
11. M. Touratier A refined theory of laminated shallow shells Int J Solids Struct 29 1992 1401 1415
12. P. Vidal, and O. Polit A family of sinus finite elements for the analysis of rectangular laminated beams Compos Struct 84 2008 56 72 (Pubitemid 351201873)
13. S. Cheng Elasticity theory of plates and a refined theory J Appl Mech 46 1979 644 650
14. O. Polit, and M. Touratier High order triangular sandwich plate finite element for linear and nonlinear analyses Comput Methods Appl Mech Eng 185 2000 305 324
15. D. Chapelle, and K.-J. Bathe The finite element analysis of shells: fundamentals 2003 Springer Berlin
16. W. Flügge Stresses in shells 2nd ed. 1960 Springer Berlin
17. A. Scordelis, and K.S. Lo Computer analysis in cylindrical shells J Am Concr Inst 61 1964 561 593
18. J.N. Reddy Mechanics of laminated composite plates and shells 2nd ed. Theory and analysis 2003 CRC Press FL
19. E. 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
20. J. Pitkäranta The problem of membrane locking in finite element analysis of cylindrical shells Numer Math 61 1992 523 542
21. C. Chinosi, L. Della Croce, and T. Scapolla Numerical results on the locking for cylindrical shells Comput-Assist Mech Eng Sci J 5 1 1998 31 44 (Pubitemid 128570311)
22. O.C. Zienkiewicz, R.L. Taylor, and J.M. Too Reduced integration techniques in general analysis of plates and shells Int J Numer Methods Eng 3 1971 275 290
23. K.-J. Bathe, and E. Dvorkin A formulation of general shell elements - the use of mixed interpolation of tensorial components Int J Numer Methods Eng 22 1986 697 722 (Pubitemid 16538309)
24. D.N. Arnold, and F. Brezzi Locking free finite element methods for shells Math Comput 66 1997 1 14
25. H.-C. Huang Membrane locking and assumed strain shell elements Comput Struct 27 5 1987 671 677
26. 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)
27. Y.C. Hon, M.W. Lu, W.M. Xue, and Y.M. Zhu Multiquadric method for the numerical solution of biphasic mixture model Appl Math Comput 88 1997 153 175 (Pubitemid 127683562)
28. 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)
29. J.G. Wang, G.R. Liu, and P. Lin Numerical analysis of Biot's consolidation process by radial point interpolation method Int J Solids Struct 39 6 2002 1557 1573 (Pubitemid 34306039)
30. 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)
31. G.R. Liu, and J.G. Wang A point interpolation meshless method based on radial basis functions Int J Numer Methods Eng 54 2002 1623 1648 (Pubitemid 34842350)
32. J.G. Wang, and G.R. Liu On the optimal shape parameters of radial basis functions used for 2-d meshless methods Comput Methods Appl Mech Eng 191 2002 2611 2630 (Pubitemid 34452176)
33. 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)
34. 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
35. G.R. Liu, and X.L. Chen Buckling of symmetrically laminated composite plates using the element-free Galerkin method Int J Struct Stab Dyn 2 2002 281 294
36. 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
37. 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)
38. 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)
39. S. Xiang, K.M. Wang, Y.T. Ai, Y.D. Sha, and H. Shi Analysis of isotropic, sandwich and laminated plates by a meshless method and various shear deformation theories Compos Struct 91 1 2009 31 37
40. S. Xiang, H. Shi, K.M. Wang, Y.T. Ai, and Y.D. Sha Thin plate spline radial basis functions for vibration analysis of clamped laminated composite plates Eur J Mech A/Solids 29 2010 844 850
41. A.J.A. Ferreira, C.M.C. Roque, and R.M.N. Jorge Analysis of composite and sandwich plate by trigonometric layer-wise deformation theory and radial basis function J Sandwich Struct Mater 8 2006 497 515 (Pubitemid 44582303)
42. 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)
43. 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
44. 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
45. R.L. Hardy Multiquadric equations of topography and other irregular surfaces Geophys Res 176 1971 1905 1915
46. 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)
47. J.N. Reddy, and C.F. Liu A higher-order shear deformation theory of laminated elastic shells Int J Eng Sci 23 1985 319 330 (Pubitemid 15494942)