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Volumn 79, Issue 1, 2009, Pages 25-44

Semi-analytical analysis for multi-directional functionally graded plates: 3-D elasticity solutions

Author keywords

3 D elasticity; Differential quadrature method; Multi directional functionally graded plates; Semi analytical analysis; State space method

Indexed keywords

DIFFERENTIATION (CALCULUS); ELASTICITY; ORTHOTROPIC PLATES; STATE SPACE METHODS;

EID: 68549130518     PISSN: 00295981     EISSN: 10970207     Source Type: Journal    
DOI: 10.1002/nme.2555     Document Type: Article
Times cited : (122)

References (52)
  • 4
    • 14844327509 scopus 로고    scopus 로고
    • Three-dimensional transient heat conduction in a functionally graded thick plate with a higher-order plate theory and a meshless local Petrov-Galerkin method
    • Qian LF, Batra RC. Three-dimensional transient heat conduction in a functionally graded thick plate with a higher-order plate theory and a meshless local Petrov-Galerkin method. Computational Mechanics 2005; 35(3):214-226.
    • (2005) Computational Mechanics , vol.35 , Issue.3 , pp. 214-226
    • Qian, L.F.1    Batra, R.C.2
  • 5
    • 1842685794 scopus 로고    scopus 로고
    • Non-linear analysis of the thermo-electro-mechanical behaviour of shear deformable FGM plates with piezoelectric actuators
    • Yang J, Kitipornchai S, Liew KM. Non-linear analysis of the thermo-electro-mechanical behaviour of shear deformable FGM plates with piezoelectric actuators. International Journal for Numerical Methods in Engineering 2004; 59(12):1605-1632.
    • (2004) International Journal for Numerical Methods in Engineering , vol.59 , Issue.12 , pp. 1605-1632
    • Yang, J.1    Kitipornchai, S.2    Liew, K.M.3
  • 6
    • 15544387659 scopus 로고    scopus 로고
    • A finite element formulation for analysis of functionally graded plates and shells
    • Naghdabadi R, Kordkheili SAH. A finite element formulation for analysis of functionally graded plates and shells. Archive of Applied Mechanics 2005; 74(5-6):375-386.
    • (2005) Archive of Applied Mechanics , vol.74 , Issue.5-6 , pp. 375-386
    • Naghdabadi, R.1    Kordkheili, S.A.H.2
  • 7
    • 35748932666 scopus 로고    scopus 로고
    • Geometrically non-linear thermoelastic analysis of functionally graded shells using finite element method
    • Kordkheili SAH, Naghdabadi R. Geometrically non-linear thermoelastic analysis of functionally graded shells using finite element method. International Journal for Numerical Methods in Engineering 2007; 72(8): 964-986.
    • (2007) International Journal for Numerical Methods in Engineering , vol.72 , Issue.8 , pp. 964-986
    • Kordkheili, S.A.H.1    Naghdabadi, R.2
  • 8
    • 0022794879 scopus 로고
    • Materials for aerospace
    • Steinberg MA. Materials for aerospace. Scientific American 1986; 255(4):59-64.
    • (1986) Scientific American , vol.255 , Issue.4 , pp. 59-64
    • Steinberg, M.A.1
  • 9
    • 0017960741 scopus 로고
    • On the theory of elasticity of a non-homogeneous medium
    • Dhaliwal RS, Singh BM. On the theory of elasticity of a non-homogeneous medium. Journal of Elasticity 1978; 8(2):211-219.
    • (1978) Journal of Elasticity , vol.8 , Issue.2 , pp. 211-219
    • Dhaliwal, R.S.1    Singh, B.M.2
  • 10
    • 0020816016 scopus 로고
    • The crack problem for nonhomogeneous plane
    • Delale F, Erdogan F. The crack problem for nonhomogeneous plane. Journal of Applied Mechanics 1983; 50(3):609-614.
    • (1983) Journal of Applied Mechanics , vol.50 , Issue.3 , pp. 609-614
    • Delale, F.1    Erdogan, F.2
  • 12
    • 0030415391 scopus 로고    scopus 로고
    • Study of an edge crack problem in a semi-infinite functionally graded medium with two dimensionally non-homogeneous coefficient of thermal expansion under thermal load
    • Nemat-Alla M, Noda N. Study of an edge crack problem in a semi-infinite functionally graded medium with two dimensionally non-homogeneous coefficient of thermal expansion under thermal load. Journal of Thermal Stresses 1996; 19(9):863-888.
    • (1996) Journal of Thermal Stresses , vol.19 , Issue.9 , pp. 863-888
    • Nemat-Alla, M.1    Noda, N.2
  • 13
    • 0034481310 scopus 로고    scopus 로고
    • Edge crack problem in a semi-infinite FGM plate with a bi-directional coefficient of thermal expansion under two-dimensional thermal loading
    • Nemat-Alla M, Noda N. Edge crack problem in a semi-infinite FGM plate with a bi-directional coefficient of thermal expansion under two-dimensional thermal loading. Acta Mechanica 2000; 144(3-4):211-229.
    • (2000) Acta Mechanica , vol.144 , Issue.3-4 , pp. 211-229
    • Nemat-Alla, M.1    Noda, N.2
  • 14
    • 28244485498 scopus 로고    scopus 로고
    • Crack analysis in unidirectionally and bidirectionally functionally graded materials
    • Zhang C, Sladek J, Sladek V. Crack analysis in unidirectionally and bidirectionally functionally graded materials. International Journal of Fracture 2004; 129(4):385-406.
    • (2004) International Journal of Fracture , vol.129 , Issue.4 , pp. 385-406
    • Zhang, C.1    Sladek, J.2    Sladek, V.3
  • 15
    • 0030104033 scopus 로고    scopus 로고
    • Thermoelastic theory for the response of materials functionally graded in two directions
    • Aboudi J, Pindera MJ, Arnold SM. Thermoelastic theory for the response of materials functionally graded in two directions. International Journal of Solids and Structures 1996; 33(7):931-966.
    • (1996) International Journal of Solids and Structures , vol.33 , Issue.7 , pp. 931-966
    • Aboudi, J.1    Pindera, M.J.2    Arnold, S.M.3
  • 16
    • 0030414190 scopus 로고    scopus 로고
    • Thermoplasticity theory for bi-directionally functionally graded materials
    • Aboudi J, Pindera MJ, Arnold SM. Thermoplasticity theory for bi-directionally functionally graded materials. Journal of Thermal Stresses 1996; 19(9):809-861.
    • (1996) Journal of Thermal Stresses , vol.19 , Issue.9 , pp. 809-861
    • Aboudi, J.1    Pindera, M.J.2    Arnold, S.M.3
  • 18
    • 0242490336 scopus 로고    scopus 로고
    • Reduction of thermal stresses by developing two-dimensional functionally graded materials
    • Nemat-Alla M. Reduction of thermal stresses by developing two-dimensional functionally graded materials. International Journal of Solids and Structures 2003; 40(26):7339-7356.
    • (2003) International Journal of Solids and Structures , vol.40 , Issue.26 , pp. 7339-7356
    • Nemat-Alla, M.1
  • 19
    • 23144465498 scopus 로고    scopus 로고
    • Comparison of one-dimensional and two-dimensional functionally graded materials for the backing shell of the cemented acetabular cup
    • Hedia HS. Comparison of one-dimensional and two-dimensional functionally graded materials for the backing shell of the cemented acetabular cup. Journal of Biomedical Materials Research Part B-Applied Biomaterials 2005; 74B(2):732-739.
    • (2005) Journal of Biomedical Materials Research Part B-Applied Biomaterials , vol.74 B , Issue.2 , pp. 732-739
    • Hedia, H.S.1
  • 21
    • 10044250030 scopus 로고    scopus 로고
    • The simple boundary element method for transient heat conduction in functionally graded materials
    • Sutradhar A, Paulino GH. The simple boundary element method for transient heat conduction in functionally graded materials. Computer Methods in Applied Mechanics and Engineering 2004; 193(42-44):4511-4539.
    • (2004) Computer Methods in Applied Mechanics and Engineering , vol.193 , Issue.42-44 , pp. 4511-4539
    • Sutradhar, A.1    Paulino, G.H.2
  • 22
    • 2542573897 scopus 로고    scopus 로고
    • Green's function for a two-dimensional exponentially graded elastic medium
    • Chan YS, Gray LJ, Kaplan T et al. Green's function for a two-dimensional exponentially graded elastic medium. Proceedings of Royal Society of London-Series A 2004; 460(2046):1689-1706.
    • (2004) Proceedings of Royal Society of London-Series A , vol.460 , Issue.2046 , pp. 1689-1706
    • Chan, Y.S.1    Gray, L.J.2    Kaplan, T.3
  • 23
    • 9644260451 scopus 로고    scopus 로고
    • Design of bidirectional functionally graded plate for optimal natural frequencies
    • Qian LF, Batra RC. Design of bidirectional functionally graded plate for optimal natural frequencies. Journal of Sound and Vibration 2005; 280(1-2):415-424.
    • (2005) Journal of Sound and Vibration , vol.280 , Issue.1-2 , pp. 415-424
    • Qian, L.F.1    Batra, R.C.2
  • 24
    • 3142730561 scopus 로고    scopus 로고
    • Static and dynamic analysis of 2-D functionally graded elasticity by using meshless local Petrov-Galerkin method
    • Qian LF, Ching HK. Static and dynamic analysis of 2-D functionally graded elasticity by using meshless local Petrov-Galerkin method. Journal of the Chinese Institute of Engineers 2004; 27(4):491-503.
    • (2004) Journal of the Chinese Institute of Engineers , vol.27 , Issue.4 , pp. 491-503
    • Qian, L.F.1    Ching, H.K.2
  • 25
    • 33751547491 scopus 로고    scopus 로고
    • Optimization of natural frequencies of bidirectional functionally graded beams
    • Goupee AJ, Vel SS. Optimization of natural frequencies of bidirectional functionally graded beams. Structural and Multidisciplinary Optimization 2006; 32(6):473-484.
    • (2006) Structural and Multidisciplinary Optimization , vol.32 , Issue.6 , pp. 473-484
    • Goupee, A.J.1    Vel, S.S.2
  • 27
    • 0029724421 scopus 로고    scopus 로고
    • Differential quadrature method in computational mechanics: A review
    • Bert CW, Malik M. Differential quadrature method in computational mechanics: a review. Applied Mechanics Reviews 1996; 49(1):1-28.
    • (1996) Applied Mechanics Reviews , vol.49 , Issue.1 , pp. 1-28
    • Bert, C.W.1    Malik, M.2
  • 29
    • 0032496861 scopus 로고    scopus 로고
    • Modeling via differential quadrature method: Three-dimensional solutions for rectangular plates
    • Liew KM, Teo TM. Modeling via differential quadrature method: three-dimensional solutions for rectangular plates. Computer Methods in Applied Mechanics and Engineering 1998; 159(3-4):369-381.
    • (1998) Computer Methods in Applied Mechanics and Engineering , vol.159 , Issue.3-4 , pp. 369-381
    • Liew, K.M.1    Teo, T.M.2
  • 30
    • 0032665076 scopus 로고    scopus 로고
    • Three-dimensional elasticity solutions to some orthotropic plate problems
    • Teo TM, Liew KM. Three-dimensional elasticity solutions to some orthotropic plate problems. International Journal of Solids and Structures 1999; 36(34):5301-5326.
    • (1999) International Journal of Solids and Structures , vol.36 , Issue.34 , pp. 5301-5326
    • Teo, T.M.1    Liew, K.M.2
  • 31
    • 0034557414 scopus 로고    scopus 로고
    • Static analysis of thick rectangular laminated plates: Three-dimensional elasticity solutions via differential quadrature element method
    • Liu FL. Static analysis of thick rectangular laminated plates: three-dimensional elasticity solutions via differential quadrature element method. International Journal of Solids and Structures 2000; 37(51):7671-7688.
    • (2000) International Journal of Solids and Structures , vol.37 , Issue.51 , pp. 7671-7688
    • Liu, F.L.1
  • 32
    • 0037135315 scopus 로고    scopus 로고
    • Differential quadrature-layerwise modeling technique for three-dimensional analysis of cross-ply laminated plates of various edge-supports
    • Liew KM, Ng TY, Zhang JZ. Differential quadrature-layerwise modeling technique for three-dimensional analysis of cross-ply laminated plates of various edge-supports. Computer Methods in Applied Mechanics and Engineering 2002; 191(35):3811-3832.
    • (2002) Computer Methods in Applied Mechanics and Engineering , vol.191 , Issue.35 , pp. 3811-3832
    • Liew, K.M.1    Ng, T.Y.2    Zhang, J.Z.3
  • 33
    • 0037378266 scopus 로고    scopus 로고
    • Three-dimensional modelling of elastic bonding in composite laminates using layerwise differential quadrature
    • Liew KM, Zhang JZ, Ng TY et al. Three-dimensional modelling of elastic bonding in composite laminates using layerwise differential quadrature. International Journal of Solids and Structures 2003; 40(7):1745-1764.
    • (2003) International Journal of Solids and Structures , vol.40 , Issue.7 , pp. 1745-1764
    • Liew, K.M.1    Zhang, J.Z.2    Ng, T.Y.3
  • 34
    • 0043021903 scopus 로고    scopus 로고
    • Three-dimensional theory of elasticity for free vibration analysis of composite laminates via layerwise differential quadrature modelling
    • Zhang JZ, Ng TY, Liew KM. Three-dimensional theory of elasticity for free vibration analysis of composite laminates via layerwise differential quadrature modelling. International Journal for Numerical Methods in Engineering 2003; 57(13):1819-1844.
    • (2003) International Journal for Numerical Methods in Engineering , vol.57 , Issue.13 , pp. 1819-1844
    • Zhang, J.Z.1    Ng, T.Y.2    Liew, K.M.3
  • 35
    • 1542539007 scopus 로고    scopus 로고
    • Three-dimensional vibration analysis of rectangular thick plates on Pasternak foundation
    • Zhou D, Cheung YK, Lo SH et al. Three-dimensional vibration analysis of rectangular thick plates on Pasternak foundation. International Journal for Numerical Methods in Engineering 2004; 59(10):1313-1334.
    • (2004) International Journal for Numerical Methods in Engineering , vol.59 , Issue.10 , pp. 1313-1334
    • Zhou, D.1    Cheung, Y.K.2    Lo, S.H.3
  • 36
  • 37
    • 27144494274 scopus 로고    scopus 로고
    • Free vibration of orthotropic functionally graded beams with various end conditions
    • Lü CF, Chen WQ. Free vibration of orthotropic functionally graded beams with various end conditions. Structural Engineering and Mechanics 2005; 20(4):465-476.
    • (2005) Structural Engineering and Mechanics , vol.20 , Issue.4 , pp. 465-476
    • Lü, C.F.1    Chen, W.Q.2
  • 39
    • 28444444911 scopus 로고    scopus 로고
    • Nonlinear vibration of a coating-FGM-substrate cylindrical panel subjected to a temperature gradient
    • Liew KM, Yang J, Wu YF. Nonlinear vibration of a coating-FGM-substrate cylindrical panel subjected to a temperature gradient. Computer Methods in Applied Mechanics and Engineering 2006; 195(9-12):1007-1026.
    • (2006) Computer Methods in Applied Mechanics and Engineering , vol.195 , Issue.9-12 , pp. 1007-1026
    • Liew, K.M.1    Yang, J.2    Wu, Y.F.3
  • 40
    • 0041517714 scopus 로고    scopus 로고
    • Elasticity solution for free vibration of laminated beams
    • Chen WQ, Lü CF, Bian ZG. Elasticity solution for free vibration of laminated beams. Composite Structures 2003; 62(1):75-82.
    • (2003) Composite Structures , vol.62 , Issue.1 , pp. 75-82
    • Chen, W.Q.1    Lü, C.F.2    Bian, Z.G.3
  • 41
    • 0347317892 scopus 로고    scopus 로고
    • Free vibration of generally laminated beams via state-space-based differential quadrature
    • Chen WQ, Lü CF, Bian ZG. Free vibration of generally laminated beams via state-space-based differential quadrature. Composite Structures 2004; 63(3-4):417-425.
    • (2004) Composite Structures , vol.63 , Issue.3-4 , pp. 417-425
    • Chen, W.Q.1    Lü, C.F.2    Bian, Z.G.3
  • 42
    • 11244327837 scopus 로고    scopus 로고
    • 3D free vibration analysis of cross-ply laminated plates with one pair of opposite edges simply supported
    • Chen WQ, Lü CF. 3D free vibration analysis of cross-ply laminated plates with one pair of opposite edges simply supported. Composite Structures 2005; 69(1):77-87.
    • (2005) Composite Structures , vol.69 , Issue.1 , pp. 77-87
    • Chen, W.Q.1    Lü, C.F.2
  • 43
    • 43049105453 scopus 로고    scopus 로고
    • Semi-analytical elasticity solutions for bi-directional functionally graded beams
    • Lü CF, Chen WQ, Xu RQ et al. Semi-analytical elasticity solutions for bi-directional functionally graded beams. International Journal of Solids and Structures 2008; 45(1):258-275.
    • (2008) International Journal of Solids and Structures , vol.45 , Issue.1 , pp. 258-275
    • Lü, C.F.1    Chen, W.Q.2    Xu, R.Q.3
  • 44
    • 34250341228 scopus 로고    scopus 로고
    • Free vibration of generally supported rectangular Kirchhoff plates: State-space-based differential quadrature method
    • Lü CF, Zhang ZC, Chen WQ. Free vibration of generally supported rectangular Kirchhoff plates: state-space-based differential quadrature method. International Journal for Numerical Methods in Engineering 2007; 70(12):1430-1450.
    • (2007) International Journal for Numerical Methods in Engineering , vol.70 , Issue.12 , pp. 1430-1450
    • Lü, C.F.1    Zhang, Z.C.2    Chen, W.Q.3
  • 45
    • 0343660288 scopus 로고
    • Dynamic analysis of large space structures using transfer matrices and joint coupling matrices
    • Nagem RJ, Williams JH. Dynamic analysis of large space structures using transfer matrices and joint coupling matrices. Mechanics of Structures and Machines 1989; 17(3):349-371.
    • (1989) Mechanics of Structures and Machines , vol.17 , Issue.3 , pp. 349-371
    • Nagem, R.J.1    Williams, J.H.2
  • 46
    • 0025749119 scopus 로고
    • Differential quadrature method in the buckling analysis of beams and composite plates
    • Sherbourne AN, Pandey MD. Differential quadrature method in the buckling analysis of beams and composite plates. Computers and Structures 1991; 40(4):903-913.
    • (1991) Computers and Structures , vol.40 , Issue.4 , pp. 903-913
    • Sherbourne, A.N.1    Pandey, M.D.2
  • 47
    • 12344328662 scopus 로고    scopus 로고
    • Three-dimensional elasticity solution for bending of functionally graded rectangular plates
    • Kashtalyan M. Three-dimensional elasticity solution for bending of functionally graded rectangular plates. European Journal of Mechanics-A/Solids 2004; 23(5):853-864.
    • (2004) European Journal of Mechanics-A/Solids , vol.23 , Issue.5 , pp. 853-864
    • Kashtalyan, M.1
  • 49
    • 34247581039 scopus 로고
    • Bending, vibration and buckling of simply supported thick orthotropic rectangular plates and laminates
    • Srinvas S, Rao AK. Bending, vibration and buckling of simply supported thick orthotropic rectangular plates and laminates. International Journal of Solids and Structures 1970; 6(11):1463-1481.
    • (1970) International Journal of Solids and Structures , vol.6 , Issue.11 , pp. 1463-1481
    • Srinvas, S.1    Rao, A.K.2
  • 50
    • 0036758292 scopus 로고    scopus 로고
    • A state of stress and displacement of elastic plates using simple and mixed shear deformation theories
    • Zenkour AM. A state of stress and displacement of elastic plates using simple and mixed shear deformation theories. Journal of Engineering Mathematics 2002; 44(1):1-20.
    • (2002) Journal of Engineering Mathematics , vol.44 , Issue.1 , pp. 1-20
    • Zenkour, A.M.1
  • 51
    • 46749157005 scopus 로고    scopus 로고
    • Semi-analytical three-dimensional elasticity solutions for generally laminated composite plates
    • Lü CF, Chen WQ, Shao JW. Semi-analytical three-dimensional elasticity solutions for generally laminated composite plates. European Journal of Mechanics A-Solids 2008; 27(5):899-917.
    • (2008) European Journal of Mechanics A-Solids , vol.27 , Issue.5 , pp. 899-917
    • Lü, C.F.1    Chen, W.Q.2    Shao, J.W.3
  • 52
    • 34548716366 scopus 로고    scopus 로고
    • Semi-analytical solution for three-dimensional vibration of functionally graded circular plates
    • Nie GJ, Zhong Z. Semi-analytical solution for three-dimensional vibration of functionally graded circular plates. Computer Methods in Applied Mechanics and Engineering 2007; 196(49-52):4901-4910.
    • (2007) Computer Methods in Applied Mechanics and Engineering , vol.196 , Issue.49-52 , pp. 4901-4910
    • Nie, G.J.1    Zhong, Z.2


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