Static, free vibration, and buckling analysis of laminated composite Reissner-Mindlin plates using NURBS-based isogeometric approach

International Journal for Numerical Methods in Engineering

Volumn 91, Issue 6, 2012, Pages 571-603

  Thai, Chien H ^a   Nguyen Xuan, H ^a,b   Nguyen Thanh, N ^c   Le, T H ^d   Nguyen Thoi, T ^a,b   Rabczuk, T ^c  

^a TON DUC THANG UNIVERSITY   (Viet Nam)

^b UNIVERSITY OF NATURAL SCIENCES   (Viet Nam)

^c University Bauhaus   (Germany)

^d VIETNAM NATIONAL UNIVERSITY   (Viet Nam)

Author keywords

Isogeometric analysis; Laminated composite Reissner Mindlin plates; Stabilization technique

Indexed keywords

BUCKLING ANALYSIS; FIRST-ORDER SHEAR DEFORMATION THEORY; FREE VIBRATION; ISOGEOMETRIC ANALYSIS; LAMINATED COMPOSITE PLATES; NON-UNIFORM RATIONAL B-SPLINES; NUMERICAL EXAMPLE; NUMERICAL PROCEDURES; SHEAR-LOCKING; STABILIZATION TECHNIQUES;

LAMINATED COMPOSITES; MINDLIN PLATES; STABILIZATION; VIBRATIONS (MECHANICAL);

INTERPOLATION;

EID: 84864006149     PISSN: 00295981     EISSN: 10970207     Source Type: Journal    
DOI: 10.1002/nme.4282     Document Type: Article

References (92)

1. Reddy JN.Mechanics of Laminated Composite Plates and Shells Theory and Analysis, 2nd edn. CRC Press: New York, 2004.
2. Reissner E, Stavsky Y.Bending and stretching of certain types of aeolotropic elastic plates. Journal of Applied Mechanics 1961; 28:402-408.
3. Stavsky Y.Bending and stretching of laminated aeolotropic plates. Journal of Engineering Mechanics Division 1961; 87:31-56.
4. Dong SB, Pister KS, Taylor RL.On the theory of laminated anisotropic plates and shells. Journal of Aeronautical Science 1962; 29(8):969-975.
5. Yang PC, Norris CH, Stavsky Y.Elastic wave propagation in heterogeneous plates. International Journal of Solids and Structures 1966; 2:665-684.
6. Ambartsumyan SA.Theory of Anisotropic Plates. Technomic: Westport, CT, 1969.
7. Whitney JM, Leissa AW.Analysis of heterogeneous anisotropic plates. Journal of Applied Mechanics 1969; 36(2):261-266.
8. Whitney JM.The effect of transverse shear deformation in the bending of laminated plates. Journal of Composite Materials 1969; 3:534-547.
9. Reissner E.The effect of transverse shear deformations on the bending of elastic plates. Journal of Applied Mechanics 1945; 12:A69-A77.
10. Reddy JN.Energy and Variational Methods in Applied Mechanics. Wiley: New York, 1984.
11. Ferreira AJM, Castro LMS, Bertoluzza S.A high order collocation method for the static and vibration analysis of composite plates using a first-order theory. Composite Structures 2009; 89(3):424-432.
12. Ferreira AJM, Jorge RMN, Roque CMC.Free vibration analysis of symmetric laminated composite plates by FSDT and radial basis functions. Computer Methods in Applied Mechanics and Engineering 2005; 194:4265-4278.
13. Liew KM, Huang YQ, Reddy JN.Vibration analysis of symmetrically laminated plates based on FSDT using the moving least squares differential quadrature method. Computer Methods in Applied Mechanics and Engineering 2003; 192:2203-22.
14. Liew KM.Solving the vibration of thick symmetric laminates by Reissner/Mindlin plate theory and the P-Ritz method. Journal of Sound and Vibration 1996; 198:343-360.
15. Liew KM, Han JB, Xiao ZM.Differential quadrature method for thick symmetric cross-ply laminates with first-order shear flexibility. International Journal of Solids and Structures 1996; 33:2647-2658.
16. Liew KM, Huang YQ, Reddy JN.Moving least square differential quadrature method and its application to the analysis of shear deformable plates. International Journal for Numerical Methods in Engineering 2003; 56:2331-2351.
17. Liew KM, Huang YQ.Bending and buckling of thick symmetric rectangular laminates using the moving least-squares differential quadrature method. International Journal of Mechanical Science 2003; 45:95-114.
18. Ferreira AJM, Roque C, Neves A, Jorge RMN, Soares CMM, Liew KM.Buckling and vibration analysis of isotropic and laminated plates by radial basis functions. Composites-Part B 2011; 42:592-606.
19. Reddy JN, Phan ND.Stability and vibration of isotropic, orthotropic and laminated plates according to a higher order shear deformation theory. Journal of Sound and Vibration 1985; 89:157-170.
20. Phan ND, Reddy JN.Analysis of laminated composite plates using a higher-order shear deformation theory. International Journal for Numerical Methods in Engineering 1985; 21:2201-2219.
21. Reddy JN, Khdeir AA.Buckling and vibration of laminated composite plates using various plate theories. American Institute of Aeronautics and Astronautics Journal 1989; 27(12):1808-1817.
22. Kdheir A.Analysis of symmetric cross-ply elastic plates using a higher-order theory, part II: buckling and free vibration. Composite Structures 1988; 9:259-277.
23. Khdeir AA, Librescu L.Analysis of symmetric cross-ply elastic plates using a higher-order theory: part II: buckling and free vibration. Composite Structures 1988; 9:259-277.
24. Chakrabarti A, Sheikh AH.Buckling of laminated composite plates by a new element based on higher order shear deformation theory. Mechanics of Composite Materials and Structures 2003; 10(4):303-317.
25. Nosier A, Kapania RK, Reddy JN.Free vibration analysis of laminated plates using a layerwise theory. American Institute of Aeronautics and Astronautics Journal 1993; 31(12):2335-2346.
26. Ferreira AJM.Analysis of composite plates using a layerwise deformation theory and multiquadrics discretization. Mechanics of Advanced Materials and Structures 2005; 12(2):99-112.
27. Pagano NJ.Exact solutions for rectangular bidirectional composites and sandwich plates. Journal of Composite Materials 1970; 4:20-34.
28. Noor AK, Mathers. Shear-flexible finite element method of laminated composite plate. Technical report, NASA, 1975.
29. Pagano NJ, Soni RS.Global-local laminate variational model. International Journal of Solids and Structures 1983; 19:207-228.
30. Zhen W, Wanji C.Free vibration of laminated composite and sandwich plates using global-local higher-order theory. Journal of Sound and Vibration 2006; 298:333-349.
31. Touratier M.An efficient standard plate theory. International Journal of Engineering Science 1991; 29(8):901-916.
32. Karama M, Afaq KS, Mistou S.Mechanical behaviour of laminated composite beam by new multi-layered laminated composite structures model with transverse shear stress continuity. International Journal of Solids and Structures 2003; 40:1525-1546.
33. Soldatos KP.A transverse shear deformation theory for homogeneous monoclinic plates. Acta Mechanica 1992; 94:195-200.
34. Aydogdu M.A new shear deformation theory for laminated composite plates. Composite Structures 2009; 89:94-101.
35. Meiche NE, Tounsi A, Ziane N, Mechab I, Bedia EAA.A new hyperbolic shear deformation theory for buckling and vibration of functionally graded sandwich plate. International Journal of Mechanical Sciences 2011; 53:237-247.
36. Reddy JN.A refined nonlinear theory of plates with transverse shear deformation. International Journal of Solids and Structures 1984; 20(9-10):881-906.
37. Shimpi RP.Refined plate theory and its variants. AIAA Journal 2002; 40(1):137-146.
38. Shimpi RP, Patel HG.A two variable refined plate theory for orthotropic plate analysis. International Journal of Solids and Structures 2006; 43(22):6783-6799.
39. Reddy JN.Introduction to the Finite Element Method. McGraw-Hill: New York, 1993.
40. Reddy JN.Mechanics of Laminated Composite Plates. CRC Press: New York, 1997.
41. Reis AD, Albuquerque EL, Torsani FL, Palermo LJ, Sollero P.Computation of moments and stresses in laminated composite plates by the boundary element method. Engineering Analysis with Boundary Element 2011; 35:105-113.
42. Paiva WP, Sollero P, Albuquerque EL.Modal analysis of anisotropic plates using the boundary element method. Engineering Analysis with Boundary Element 2011; 35:1248-1255.
43. Nguyen-Xuan H, Rabczuk T, Bordas S, Debongnie JF.A smoothed finite element method for plate analysis. Computer Methods in Applied Mechanics and Engineering 2008; 197:1184-1203.
44. Nguyen-Xuan H, Rabczuk T, Nguyen-Thanh N, Nguyen-Thoi T, Bordas S.A node-based smoothed finite element method (NS-FEM) for analysis of Reissner-Mindlin plates. Computational Mechanics 2010; 46:679-701.
45. Nguyen-Thanh N, Rabczuk T, Nguyen-Xuan H, Bordas S.An alternative alpha finite element method free and forced vibration analysis of solids using triangular meshes. Journal of Computational and Applied Mathematics 2010; 233(9):2112-2135.
46. Nguyen-Thanh N, Rabczuk T, Nguyen-Xuan H, Bordas S.An alternative alpha finite element method with stabilized discrete shear gap technique for analysis of Mindlin-Reissner plates. Finite Elements in Analysis and Design 2011; 47:519-535.
47. Nguyen-Thanh N, Rabczuk T, Nguyen-Xuan H, Bordas S.A smoothed finite element method for shell analysis. Computer Methods in Applied Mechanics and Engineering 2008; 198(2):165-177.
48. Thai-Hoang C, Nguyen-Thanh N, Nguyen-Xuan H, Rabczuk T, Bordas S.A smoothed finite element method for free vibration and buckling analysis of shells. KSCE Journal of Civil Engineering 2011; 15(2):347-361.
49. Thai-Hoang C, Nguyen-Thanh N, Nguyen-Xuan H, Rabczuk T.An alternative alpha finite element method with discrete shear gap technique for analysis of laminated composite plates. Applied Mathematics and Computation 2011; 217(17):7324-7348.
50. Rabczuk T, Belytschko T.Cracking particles: a simplified meshfree methods for arbitrary evolving cracks. International Journal for Numerical Methods in Engineering 2004; 61:2316-2343.
51. Rabczuk T, Xiao SP, Sauer M.Coupling of meshfree methods with finite elements: basic concepts and test results. Communications in Numerical Methods in Engineering 2006; 22:1031-1065.
52. Rabczuk T, Areias PMA.A meshfree thin shell for arbitrary evolving cracks based on an external enrichment. Computer Methods in Applied Mechanics and Engineering 2006; 16(2):115-130.
53. Rabczuk T, Belytschko T.A three dimensional large deformation meshfree method for arbitrary evolving cracks. Computer Methods in Applied Mechanics and Engineering 2007; 196:2777-2799.
54. Rabczuk T, Areias PMA, Belytschko T.A meshfree thin shell method for non-linear dynamic fracture. International Journal for Numerical Methods in Engineering 2007; 72:524-548.
55. Rabczuk T, Samaniego E.Discontinuous modelling of shear bands with adaptive meshfree methods. Computer Methods in Applied Mechanics and Engineering 2008; 197:641-658.
56. Liu L, Chua LP, Ghista DN.Mesh-free radial basis function method for static, free vibration and buckling analysis of shear deformable composite laminates. Composite Structures 2007; 78:58-69.
57. Hughes TJR, Cottrell JA, Bazilevs Y.Isogeometric analysis: CAD, finite elements, NURBS, exact geometry and mesh refinement. Computer Methods in Applied Mechanics and Engineering 2005; 194(39-41):4135-4195.
58. Elguedj T, Bazilevs Y, Calo V, Hughes T.B and F projection methods for nearly incompressible linear and non-linear elasticity and plasticity using higher-order NURBS elements. Computer Methods in Applied Mechanics and Engineering 2008; 197:2732-2762.
59. Cottrell JA, Reali A, Bazilevs Y, Hughes TJR.Isogeometric analysis of structural vibrations. Computer Methods in Applied Mechanics and Engineering 2006; 195(41-43):5257-5296.
60. Benson DJ, Bazilevs Y, Hsu MC, Hughes TJR.Isogeometric shell analysis: the Reissner-Mindlin shell. Computer Methods in Applied Mechanics and Engineering 2010; 199(5-8):276-289.
61. Kiendl J, Bletzinger KU, Linhard J, Wchner R.Isogeometric shell analysis with Kirchhoff-Love elements. Computer Methods in Applied Mechanics and Engineering 2009; 198(49-52):3902-3914.
62. Kiendl J, Bazilevs Y, Hsu MC, Wchner R, Bletzinger KU.The bending strip method for isogeometric analysis of Kirchhoff-Love shell structures comprised of multiple patches. Computer Methods in Applied Mechanics and Engineering 2010; 199(37-40):2403-2416.
63. Benson DJ, Bazilevs Y, Hsu MC, Hughes TJR.A large deformation, rotation-free, isogeometric shell. Computer Methods in Applied Mechanics and Engineering 2011; 200(13-16):1367-1378.
64. Wall WA, Frenzel MA, Cyron C.Isogeometric structural shape optimization. Computer Methods in Applied Mechanics and Engineering 2008; 197(33-40):2976-2988.
65. Kouhia R.On stabilized finite element methods for the Reissner-Mindlin plate model. International Journal for Numerical Methods in Engineering 2008; 74(8):1314-1328.
66. Lyly M, Stenberg R, Vihinen T.A stable bilinear element for Reissner-Mindlin plate model. Methods in Applied Mechanics and Engineering 1993; 110:243-353.
67. Veiga LB, Buffa A, Lovadina C, Martinelli M, Sangalli G.An isogeometric method for the Reissner-Mindlin plate bending problem. Computer Methods in Applied Mechanics and Engineering 2012; 209-212:45-53.
68. Taylor RL, Auricchio F.Linked interpolation for Reissner-Mindlin plate elements. Part I- A simple triangle. International Journal for Numerical Methods in Engineering 1993; 36:3056-3066.
69. Ferreira AJM.Matlab Codes for Finite Element Analysis: Solids and Structures. Springer: London, 2008.
70. Ferreira AJM, Batra RC, Roque CMC, Qian LF, Jorge RMN.Natural frequencies of functionally graded plates by a meshless method. Composite Structures 2006; 75(1-4):593-600.
71. Roque CMC, Cunha D, Ferreira AJM.A local radial basis functions - Finite differences technique for the analysis of composite plates. Engineering Analysis with Boundary Elements 2011; 35:363-374.
72. Liew KM, Chen XL.Buckling of rectangular Mindlin plates subjected to partial in-plane edge loads using the radial point interpolation method. International Journal of Solids and Structures 2004; 41:1677-1695.
73. Leissa AW, Ayoub EF.Vibration and buckling of a simply supported rectangular plate subjected to a pair of in-plane concentrated forces. Journal of Sound and Vibration 1988; 127(1):155-171.
74. Timoshenko SP, James MG.Theory of Elastic Stability. McGraw-Hill: Singapore, 1985.
75. Srinivasm S.A refined analysis of composite laminates. Journal of Sound and Vibration 1973; 30:495-507.
76. Pandya BN, Kant T.Higher-order shear deformable theories for flexure of sandwich plates-finite element evaluations. International Journal of Solids and Structures 1988; 24:419-451.
77. Ferreira AJM, Fasshauer GE.Natural frequencies of shear deformable beams and plates by a RBF-Pseudospectral method. Computer Methods in Applied Mechanics and Engineering 2006; 196:134-146.
78. Reddy JN.A simple higher-order theory for laminated composite plates. Journal of Applied Mechanics 1984; 51:742-752.
79. Akhras G, Cheung MS, Li W.Static and vibrations analysis of anisotropic laminated plates by finite strip method. International Journal of Solids and Structures 1993; 30(22):3129-3137.
80. Akhras G, Cheung MS, Li W.Finite strip analysis for anisotropic laminated composite plates using higher-order deformation theory. Computers and Structures 1994; 52(3):471-477.
81. 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. Composite Structures 2003; 34:627-636.
82. Ferreira AJM.A formulation of the multiquadric radial basis function method for the analysis of laminated composite plates. Composite Structures 2003; 59(3):385-392.
83. Nguyen-Van H, Mai-Duy N, Tran-Cong T.Free vibration analysis of laminated plate/shell structures based on FSDT with a stabilized nodal-integrated quadrilateral element. Journal of Sound and Vibration 2008; 313(1-2):205-223.
84. Wang S.Free vibration analysis of skew fiber-reinforced composite laminates based on first-order shear deformation plate theory. Journal of Sound and Vibration 1997; 63:525-538.
85. Haldar S, Sengupta D.Free vibration analysis of composite right angle triangular plate using a shear flexible element. Journal of Reinforced Plastics and Composites 2003; 22(3):229-255.
86. Nguyen-Van H, Mai-Duy N, Karunasena W, Tran-Cong T.Buckling and vibration analysis of laminated composite plate/shell structures via a smoothed quadrilateral flat shell element with in-plane rotations. Computers and Structures 2011; 89:612-625.
87. Huang YQ, Li QS.Bending and buckling analysis of antisymmetric laminates using the moving least square differential quadrature method. Computer Methods in Applied Mechanics and Engineering 2004; 193(33-35):3471-3492.
88. Wang J, Liew KM, Tan MJ, Rajendran S.Analysis of rectangular laminated composite plates via FSDT meshless method. International Journal of Mechanical Sciences 2002; 44(7):1275-1293.
89. Fares ME, Zenkour AM.Buckling and free vibration of non-homogeneous composite cross-ply laminated plates with various plate theories. Composite Structures 1999; 44:279-287.
90. Bazilevs Y, Calo VM, Cottrell JA, Evans JA, Hughes TJR, Lipton S, Scott MA, Sederberg TW.Isogeometric analysis using T-splines. Computer Methods in Applied Mechanics and Engineering 2010; 199(5-8):229-263.
91. Nguyen-Thanh N, Nguyen-Xuan H, Bordas S, Rabczuk T.Isogeometric analysis using polynomial splines over hierarchical T-meshes for two-dimensional elastic solids. Computer Methods in Applied Mechanics and Engineering 2011; 200(21-22):1892-1908.
92. Nguyen-Thanh N, Kiendl J, Nguyen-Xuan H, Wuchner R, Bletzinger KU, Bazilevs Y, Rabczuk T.Rotation free isogeometric thin shell analysis using PHT-splines. Computer Methods in Applied Mechanics and Engineering 2011; 200(47-48):3410-3424.