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Volumn 93, Issue 7, 2011, Pages 1613-1620

Radial basis functions-finite differences collocation and a unified formulation for bending, vibration and buckling analysis of laminated plates, according to Murakami's zig-zag theory

Author keywords

Composites; Finite differences; Radial basis functions; Zig zag theory

Indexed keywords

BUCKLING; COMPOSITE MATERIALS; EQUATIONS OF MOTION; FINITE DIFFERENCE METHOD; FUNCTIONS; LAMINATED COMPOSITES; LAMINATING; RADIAL BASIS FUNCTION NETWORKS; VIBRATIONS (MECHANICAL);

EID: 79955485450     PISSN: 02638223     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.compstruct.2011.01.009     Document Type: Article
Times cited : (115)

References (44)
  • 2
    • 79955473344 scopus 로고
    • 2nd ed. New York: Gordon and Breach Science Publishers [translated from the 2nd Russian ed. by Tsai SW, Cheron, Bordon, Breach]
    • Lekhnitskii SG. Anisotropic plates. 2nd ed. New York: Gordon and Breach Science Publishers; 1968 [translated from the 2nd Russian ed. by Tsai SW, Cheron, Bordon, Breach].
    • (1968) Anisotropic plates
    • Lekhnitskii, S.G.1
  • 3
    • 0003800066 scopus 로고
    • Moskwa: Fizmatzig; 1961. NASA TTF-118 [translated from Russian]
    • Ambartsumian SA. Theory of anisotropic shells. Moskwa: Fizmatzig; 1961. NASA TTF-118; 1964 [translated from Russian].
    • (1964) Theory of anisotropic shells
    • Ambartsumian, S.A.1
  • 4
    • 0003800066 scopus 로고
    • Ashton JE, editor. Stamford: Technomic Publishing Company [translated from Russian by Cheron T]
    • Ambartsumian SA. In: Ashton JE, editor. Theory of anisotropic plates. Stamford: Technomic Publishing Company; 1969 [translated from Russian by Cheron T].
    • (1969) Theory of anisotropic plates
    • Ambartsumian, S.A.1
  • 6
    • 0036346225 scopus 로고    scopus 로고
    • Theories and finite elements for multilayered anisotropic, composite plates and shells
    • Carrera E. Theories and finite elements for multilayered anisotropic, composite plates and shells. Arch Comput Methods Eng State Art Rev 2002:87-140.
    • (2002) Arch Comput Methods Eng State Art Rev , pp. 87-140
    • Carrera, E.1
  • 7
    • 0742281181 scopus 로고    scopus 로고
    • Historical review of zig-zag theories for multilayered plates and shells
    • Carrera E. Historical review of zig-zag theories for multilayered plates and shells. Appl Mech Rev 2003(56):287-308.
    • (2003) Appl Mech Rev , vol.56 , pp. 287-308
    • Carrera, E.1
  • 8
    • 0022785323 scopus 로고
    • Laminated composite plate theory with improved in-plane response
    • Murakami H. Laminated composite plate theory with improved in-plane response. J Appl Mech 1986(53):661-6.
    • (1986) J Appl Mech , vol.53 , pp. 661-666
    • Murakami, H.1
  • 9
    • 13344279435 scopus 로고    scopus 로고
    • Developments, ideas and evaluations based upon the Reissner's mixed theorem in the modeling of multilayered plates and shells
    • Carrera E. Developments, ideas and evaluations based upon the Reissner's mixed theorem in the modeling of multilayered plates and shells. Appl Mech Rev 2001(54):301-29.
    • (2001) Appl Mech Rev , vol.54 , pp. 301-329
    • Carrera, E.1
  • 10
    • 0142179994 scopus 로고    scopus 로고
    • Theories and finite elements for multilayered plates and shells: a unified compact formulation with numerical assessment and benchmarking
    • Carrera E. Theories and finite elements for multilayered plates and shells: a unified compact formulation with numerical assessment and benchmarking. Arch Comput Methods 2003;10(3).
    • (2003) Arch Comput Methods , vol.10 , Issue.3
    • Carrera, E.1
  • 11
    • 0023164002 scopus 로고
    • A high-order laminated plate theory with improved in-plane responses
    • Toledano A, Murakami H. A high-order laminated plate theory with improved in-plane responses. Int J Solids Struct 1987(23):111-31.
    • (1987) Int J Solids Struct , vol.23 , pp. 111-131
    • Toledano, A.1    Murakami, H.2
  • 12
    • 0027578686 scopus 로고
    • Refined shear deformation theory of laminated shells
    • Jing H, Tzeng KG. Refined shear deformation theory of laminated shells. Am Inst Aeronaut Astronaut J 1993(31):765-73.
    • (1993) Am Inst Aeronaut Astronaut J , vol.31 , pp. 765-773
    • Jing, H.1    Tzeng, K.G.2
  • 13
    • 0000089147 scopus 로고    scopus 로고
    • A study of transverse normal stress effects on vibration of multilayered plates and shells
    • Carrera E. A study of transverse normal stress effects on vibration of multilayered plates and shells. J Sound Vib 1999(225):803-29.
    • (1999) J Sound Vib , vol.225 , pp. 803-829
    • Carrera, E.1
  • 14
    • 0025139599 scopus 로고
    • Analysis of thick laminated anisotropic composites plates by the finite element method
    • Rao KM, Meyer-Piening HR. Analysis of thick laminated anisotropic composites plates by the finite element method. Compos Struct 1990:185-213.
    • (1990) Compos Struct , pp. 185-213
    • Rao, K.M.1    Meyer-Piening, H.R.2
  • 15
    • 0033723020 scopus 로고    scopus 로고
    • Multilayered shell finite element with interlaminar continuous shear stresses: a refinement of the Reissner-Mindlin formulation
    • Brank B, Carrera E. Multilayered shell finite element with interlaminar continuous shear stresses: a refinement of the Reissner-Mindlin formulation. Int J Numer Methods Eng 2000(48):843-74.
    • (2000) Int J Numer Methods Eng , vol.48 , pp. 843-874
    • Brank, B.1    Carrera, E.2
  • 16
    • 0031343046 scopus 로고    scopus 로고
    • Evaluation of geometrical nonlinear effects of thin and moderately thick multilayered composite shells
    • Carrera E, Parisch H. Evaluation of geometrical nonlinear effects of thin and moderately thick multilayered composite shells. Compos Struct 1998:11-24.
    • (1998) Compos Struct , pp. 11-24
    • Carrera, E.1    Parisch, H.2
  • 17
    • 0037704716 scopus 로고    scopus 로고
    • Refined first-order shear deformation theory models for composite laminates
    • Auricchio F, Sacco E. Refined first-order shear deformation theory models for composite laminates. J Appl Mech 2003(70):381-90.
    • (2003) J Appl Mech , vol.70 , pp. 381-390
    • Auricchio, F.1    Sacco, E.2
  • 18
    • 0037144335 scopus 로고    scopus 로고
    • Multilayered finite plate element based on Reissner mixed variational theorem, part I: theory and part II: numerical analysis
    • 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.
    • (2002) Int J Numer Methods Eng , vol.55 , pp. 191-231
    • Carrera, E.1    Demasi, L.2
  • 19
    • 0025798359 scopus 로고
    • A higher-order theory for bending analysis of laminated shells of revolution
    • Bhaskar K, Varadan TK. A higher-order theory for bending analysis of laminated shells of revolution. Comput Struct 1991(40):815-9.
    • (1991) Comput Struct , vol.40 , pp. 815-819
    • Bhaskar, K.1    Varadan, T.K.2
  • 20
    • 1842453722 scopus 로고    scopus 로고
    • On the use of Murakami's zig-zag function in the modeling of layered plates and shells
    • Carrera E. On the use of Murakami's zig-zag function in the modeling of layered plates and shells. Comput Struct 2004(82):541-54.
    • (2004) Comput Struct , vol.82 , pp. 541-554
    • Carrera, E.1
  • 21
    • 63449131763 scopus 로고    scopus 로고
    • Improved bending analysis of sandwich plate by using zig-zag function
    • Brischetto S, Carrera E, Demasi L. Improved bending analysis of sandwich plate by using zig-zag function. Compos Struct 2009;89:408-15.
    • (2009) Compos Struct , vol.89 , pp. 408-415
    • Brischetto, S.1    Carrera, E.2    Demasi, L.3
  • 22
    • 20944445651 scopus 로고    scopus 로고
    • Refined multilayered plate elements based on Murakami zig-zag functions
    • Demasi L. Refined multilayered plate elements based on Murakami zig-zag functions. Compos Struct 2005;70:308-16.
    • (2005) Compos Struct , vol.70 , pp. 308-316
    • Demasi, L.1
  • 23
    • 0025229330 scopus 로고
    • Multiquadrics - a scattered data approximation scheme with applications to computational fluid dynamics. I: surface approximations and partial derivative estimates
    • 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):127-45.
    • (1990) Comput Math Appl , vol.19 , Issue.8-9 , pp. 127-145
    • Kansa, E.J.1
  • 24
    • 29144506799 scopus 로고    scopus 로고
    • High-accuracy discretization methods for solid mechanics
    • Tolstykh AI, Lipavskii MV, Shirobokov DA. High-accuracy discretization methods for solid mechanics. Arch Mech 2003;55(5-6):531-53.
    • (2003) Arch Mech , vol.55 , Issue.5-6 , pp. 531-553
    • Tolstykh, A.I.1    Lipavskii, M.V.2    Shirobokov, D.A.3
  • 25
    • 1942539307 scopus 로고    scopus 로고
    • Numerical methods for high dimensional Hamilton-Jacobi equations using radial basis functions
    • Cecil T, Qian J, Osher S. Numerical methods for high dimensional Hamilton-Jacobi equations using radial basis functions. J Comput Phys 2004;196(1):327-47.
    • (2004) J Comput Phys , vol.196 , Issue.1 , pp. 327-347
    • Cecil, T.1    Qian, J.2    Osher, S.3
  • 26
    • 29144437684 scopus 로고    scopus 로고
    • Scattered node compact finite difference-type formulas generated from radial basis functions
    • Wright GB, Fornberg B. Scattered node compact finite difference-type formulas generated from radial basis functions. J Comput Phys 2006;212(1):99-123.
    • (2006) J Comput Phys , vol.212 , Issue.1 , pp. 99-123
    • Wright, G.B.1    Fornberg, B.2
  • 27
    • 0036488118 scopus 로고    scopus 로고
    • A formulation of the multiquadric radial basis function method for the analysis of laminated composite plates
    • Ferreira AJM. A formulation of the multiquadric radial basis function method for the analysis of laminated composite plates. Compos Struct 2003;59:385-92.
    • (2003) Compos Struct , vol.59 , pp. 385-392
    • Ferreira, A.J.M.1
  • 28
    • 0043029995 scopus 로고    scopus 로고
    • Thick composite beam analysis using a global meshless approximation based on radial basis functions
    • Ferreira AJM. Thick composite beam analysis using a global meshless approximation based on radial basis functions. Mech Adv Mater Struct 2003;10:271-84.
    • (2003) Mech Adv Mater Struct , vol.10 , pp. 271-284
    • Ferreira, A.J.M.1
  • 29
    • 0042229158 scopus 로고    scopus 로고
    • Analysis of composite plates using higher-order shear deformation theory and a finite point formulation based on the multiquadric radial basis function method
    • 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;34:627-36.
    • (2003) Composites: Part B , vol.34 , pp. 627-636
    • Ferreira, A.J.M.1    Roque, C.M.C.2    Martins, P.A.L.S.3
  • 30
    • 0942300715 scopus 로고    scopus 로고
    • Some observations regarding interpolants in the limit of flat radial basis functions
    • Fornberg B, Wright G, Larsson E. Some observations regarding interpolants in the limit of flat radial basis functions. Comput Math Appl 2004;47:37-55.
    • (2004) Comput Math Appl , vol.47 , pp. 37-55
    • Fornberg, B.1    Wright, G.2    Larsson, E.3
  • 31
    • 1842453722 scopus 로고    scopus 로고
    • The use of Murakami's zig-zag function in the modeling of layered plates and shells
    • Carrera E. The use of Murakami's zig-zag function in the modeling of layered plates and shells. Compos Struct 2004;82:541-54.
    • (2004) Compos Struct , vol.82 , pp. 541-554
    • Carrera, E.1
  • 32
    • 40849140904 scopus 로고    scopus 로고
    • 3 hierarchy plate theories for thick and thin composite plates: the generalized unified formulation
    • 3 hierarchy plate theories for thick and thin composite plates: the generalized unified formulation. Compos Struct 2008;84:256-70.
    • (2008) Compos Struct , vol.84 , pp. 256-270
    • Demasi, L.1
  • 33
    • 0030168293 scopus 로고    scopus 로고
    • 0 Reissner-Mindlin multilayered plate elements including zig-zag and interlaminar stress continuity
    • 0 Reissner-Mindlin multilayered plate elements including zig-zag and interlaminar stress continuity. Int J Numer Methods Eng 1996;39:1797-820.
    • (1996) Int J Numer Methods Eng , vol.39 , pp. 1797-1820
    • Carrera, E.1
  • 34
    • 0040657378 scopus 로고    scopus 로고
    • Zig-zag and interlaminar equilibria effects in large deflection and post-buckling analysis of multilayered plates
    • 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.
    • (1997) Mech Compos Mater Struct , vol.4 , pp. 69-94
    • Carrera, E.1    Kroplin, B.2
  • 35
    • 0000483402 scopus 로고    scopus 로고
    • Evaluation of layer-wise mixed theories for laminated plate analysis
    • Carrera E. Evaluation of layer-wise mixed theories for laminated plate analysis. AIAA J 1998(36):830-9.
    • (1998) AIAA J , vol.36 , pp. 830-839
    • Carrera, E.1
  • 36
    • 78349312305 scopus 로고    scopus 로고
    • Analysis of thick isotropic and cross-ply laminated plates by radial basis functions and unified formulation
    • Ferreira AJM, Roque CC, 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):771-87.
    • (2011) J Sound Vib , vol.330 , pp. 771-787
    • Ferreira, A.J.M.1    Roque, C.C.2    Carrera, E.3    Cinefra, M.4
  • 37
    • 33846557376 scopus 로고    scopus 로고
    • Computation of natural frequencies of shear deformable beams and plates by a RBF-pseudospectral method
    • 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;196:134-46.
    • (2006) Comput Methods Appl Mech Eng , vol.196 , pp. 134-146
    • Ferreira, A.J.M.1    Fasshauer, G.E.2
  • 38
    • 0021621010 scopus 로고
    • A simple higher-order theory for laminated composite plates
    • Reddy JN. A simple higher-order theory for laminated composite plates. J Appl Mech 1984;51:745-52.
    • (1984) J Appl Mech , vol.51 , pp. 745-752
    • Reddy, J.N.1
  • 39
    • 0019549085 scopus 로고
    • A comparison of closed-form and finite-element solutions of thick laminated anisotropic rectangular plates
    • Reddy JN, Chao WC. A comparison of closed-form and finite-element solutions of thick laminated anisotropic rectangular plates. Nuclear Eng Des 1981;64:153-67.
    • (1981) Nuclear Eng Des , vol.64 , pp. 153-167
    • Reddy, J.N.1    Chao, W.C.2
  • 40
    • 0014728757 scopus 로고
    • Exact solutions for rectangular bidirectional composites and sandwich plates
    • Pagano NJ. Exact solutions for rectangular bidirectional composites and sandwich plates. J Compos Mater 1970;4:20-34.
    • (1970) J Compos Mater , vol.4 , pp. 20-34
    • Pagano, N.J.1
  • 41
    • 0023834793 scopus 로고
    • Analysis of symmetric cross-ply elastic plates using a higher-order theory, part II: buckling and free vibration
    • 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;9:259-77.
    • (1988) Compos Struct , vol.9 , pp. 259-277
    • Khdeir, A.A.1    Librescu, L.2
  • 42
    • 0037981478 scopus 로고    scopus 로고
    • Vibration analysis of symmetrically laminated plates based on FSDT using the moving least squares differential quadrature method
    • Liew KM, Huang YQ, Reddy JN. Vibration analysis of symmetrically laminated plates based on FSDT using the moving least squares differential quadrature method. Comput Methods Appl Mech Eng 2003;192:2203-22.
    • (2003) Comput Methods Appl Mech Eng , vol.192 , pp. 2203-2222
    • Liew, K.M.1    Huang, Y.Q.2    Reddy, J.N.3
  • 43
    • 0023834793 scopus 로고
    • Analysis of symmetric cross-ply elastic plates using a higher-order theory. Part II: buckling and free vibration
    • 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;9:259-77.
    • (1988) Compos Struct , vol.9 , pp. 259-277
    • Khdeir, A.A.1    Librescu, L.2
  • 44
    • 0037262952 scopus 로고    scopus 로고
    • Bending and buckling of thick symmetric rectangular laminates using the moving least-squares differential quadrature method
    • Liew KM, Huang YQ. Bending and buckling of thick symmetric rectangular laminates using the moving least-squares differential quadrature method. Int J Mech Sci 2003;45:95-114.
    • (2003) Int J Mech Sci , vol.45 , pp. 95-114
    • Liew, K.M.1    Huang, Y.Q.2


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