Structural Engineering and Mechanics

  • 제6권6호
  • /
  • Pages.583-612
  • /
  • 1998
  • /
  • 1225-4568(pISSN)
  • /
  • 1598-6217(eISSN)
테크노프레스 (Techno-Press)
권호 표지
DOI QR코드

DOI QR Code

Analysis of composite plates using various plate theories -Part 1: Formulation and analytical solutions

  • Bose, P. (Department of Mechanical Engineering, Texas A&M University) ;
  • Reddy, J.N. (Department of Mechanical Engineering, Texas A&M University)
  • 발행 : 1998.09.25
⟨ 이전 논문 다음 논문 ⟩

초록

A unified third-order laminate plate theory that contains classical, first-order and third-order theories as special cases is presented. Analytical solutions using the Navier and L$\acute{e}$vy solution procedures are presented. The Navier solutions are limited to simply supported rectangular plates while the L$\acute{e}$vy solutions are restricted to rectangular plates with two parallel edges simply supported and other two edges having arbitrary combination of simply supported, clamped, and free boundary conditions. Numerical results of bending and vibration for a number of problems are discussed in the second part of the paper.

키워드

참고문헌

  1. Ambartsumyan, S.A. (1960), Theory fo Anisotropic Plates, Technomic.
  2. Averill, R.C. and Reddy, J.N. (1992), "An assessment of four-noded plate finite elements based on a generalized third-order theory", International Journal for Numerical Methods in Engineering, 33, 1553-1572. https://doi.org/10.1002/nme.1620330802
  3. Basset, A.B. (1890), "On the extension and flexure of cylindracal and spherical thin elastic shells", Phil. Trans. Royal Soc. Ser A, 181(6), 433-480. https://doi.org/10.1098/rsta.1890.0007
  4. Bert, C.W. and Mayberry, B.L. (1969), "Free vibration of unsymmetrically laminated anisotropic plats with clamped edges", Journal of Composite Materials, 3, 282-293. https://doi.org/10.1177/002199836900300207
  5. Bert, C.W. (1973), "Simplified analysis of static shear factors for beams of nonhomogeneous cross section", Journal of composite Materials, 7, 525-529. https://doi.org/10.1177/002199837300700410
  6. Bert, C.W. and Chen, T.L.C. (1978), "Effect of shear deformation of antisymmetric angle-ply laminated rectangular plates", International Journal of Solids and Structures, 14, 465-473. https://doi.org/10.1016/0020-7683(78)90011-2
  7. Bhimaraddi, A. and Stevens, L.K. (1984), A higher order theory for free vibration of orthotropic, homogeneous, and laminated rectangular plates", Journal of Applied Mechanics, Trans. ASME, 51, 195-198. https://doi.org/10.1115/1.3167569
  8. Bielski, W. and Telega, J.J. (1988), "On existence of solutions for geometrically nonlinear shells and plates", Zeitschrift fur Angewandte Mathematik and Mechanik, 68(4), 155-157. https://doi.org/10.1002/zamm.19880680312
  9. Bose, P. (1995), "An evaluation of classical and refined equivalent-single-layer laminate theories", M.S. Thesis, Virginia Polytechnic Institute and State University, Blackburg, VA.
  10. Brogan, W.L. (1985), Modern Control Theory, Pretice-Hall, Englewood Cliffs, New Jersey.
  11. Chatterjee, S.N. and Kulkarni, S.V. (1979), "Shear correction factors for laminated plates", AIAA Journal, 17(5), 498-499. https://doi.org/10.2514/3.61160
  12. Chaudhuri, R.A. (1989), "On boundary-discontinuous double fourier series solution to a system of coupled pdes", International Journal of Engineering Science, 27, 1005-1022. https://doi.org/10.1016/0020-7225(89)90080-3
  13. Chaudhuri, R.A. and Kabir, Humayun R.H. (1992), "Influence of lamination and boundary constraint on the deformation of moderately thick cross-ply rectangular plates", Journal of Composite Materials, 26(1), 51-77. https://doi.org/10.1177/002199839202600104
  14. Chen, C.T. (1984), Linear System Theory and Design, Holt, Rinehart and Winston.
  15. Cooke, D.W. and Levinson, M. (1983), "Thick rectangular plates-2: The generalized levy solution", Intl. J. Mech. Sci., 25(3), 207-215. https://doi.org/10.1016/0020-7403(83)90094-2
  16. Di Sciuva, M. (1986), "Bending, vibration and buckling of simply supported thick multi-layered orthotropic plate: An evaluation of a new displacement model", Journal of Sound and Vibration, 105(3), 425-442. https://doi.org/10.1016/0022-460X(86)90169-0
  17. Dong, S.B., Pister, K.S. and Taylor, R.L. (1962), "On the theory of laminated anisotropic shells and plates", Journal of Aerospace Sciences, 29, 969-975. https://doi.org/10.2514/8.9668
  18. Doong, J.L. (1987), "Vibration and stability of an initially stressed thick plate according to a high-order deformation theory", Journal of Sound and Vibration, 113(3), 425-440. https://doi.org/10.1016/S0022-460X(87)80131-1
  19. Durocher, L.L. and Soleck, R. (1975), "Steady-state vibrations and bending of transversely isotropic three-layer plates", In Developments in Mechanics, Vol. 8, Porc. 14th Midwestern Mech. Conf., 103-124.
  20. Engblom, J.J. and Ochao, O.O. (1986), "Finite element formulation including interlaminar stress calculations", Computers and Structures, 23(2), 241-249. https://doi.org/10.1016/0045-7949(86)90216-6
  21. Epstein, M. and Glockner, P.G. (1977), "Nonlinear analysis of multilayered shells", International Journal of Solids and Structures, 13, 1081-1089. https://doi.org/10.1016/0020-7683(77)90078-6
  22. Epstein, M. and Huttelmaier, H.P. (1983), "A finite element formulation for multilayered and thick plates", Computers and Structures, 16(5), 645-650. https://doi.org/10.1016/0045-7949(83)90113-X
  23. Franklin, J.N. (1968), Matrix Theory, Prentice-Hall, Englewood Cliffs, New Jersey.
  24. Gol'denveizer, A.L. (1958), "On reissner's theory of bending of plates", Izu. Akad Nauk SSSR, 5, 69-77.
  25. Gol'denveizer, A.L. (1962), "Derivation of an approximate theory of bending of a plate by the method of asymptotic integration of the equations of the theory of elasticity", Prikl. Math. Mech., 26(4), 668-686.
  26. Hencky, H. (1947), "Uber die berrucksichtigung der schubverzerrung in ebenen platten", Ing. Arch., 16, 72-76. https://doi.org/10.1007/BF00534518
  27. Hildebrand, F.B., Reissner, E. and Thomas, G.B. (1949), "Notes on the foundations of the theory of small displacements of orthotropic shells", Technical Report1833, NACA, March.
  28. Hinrichsen, R.L. and Palazotto, A.N. (1986), "Nonlinear finite element analysis of thick composite plates using cubic spline functions", AIAA Journal, 24(11), 1836-1842. https://doi.org/10.2514/3.9532
  29. Hinton, E. and Bicanic, N. (1979), "A comparison of lagrangian and serendipity mindlin plate elements for free vibration analysis", Computers and Structures, 10, 483-493. https://doi.org/10.1016/0045-7949(79)90023-3
  30. Huang, H.C. and Hinton, E. (1984), "A nine node lagranian mindlin plate element with enhanced shear interpolation", Engrg. Computers, 1, 369-379. https://doi.org/10.1108/eb023593
  31. Huffington, N.J. Jr. (1963), "Response of elastic columns of axial pulse loading", AIAA Journal, 1(9), 2099-2104. https://doi.org/10.2514/3.2000
  32. Hughes, T.J.R. and Cohen, M. (1978), "The 'heterosis' finite element for plate bending", Computers and Structures, 9, 445-450. https://doi.org/10.1016/0045-7949(78)90041-X
  33. Hughes, T.J.R., Taylor, R.L.and Kanoknukulchai, W. (1977), "A simple and efficient finite element for plate bending", International Journal for Numerical Methods in Engineering, 11, 1529-1543. https://doi.org/10.1002/nme.1620111005
  34. Jemeilita, G. (1975), "Techniczna teoria plyt sredniej grubosci (technical theory of plates with moderate thickness)", Rozprawy Inzynierskie (Engineering Transactions), Polska Akademia Nauk, 23(3), 483-499.
  35. Jones, A.T. (1970), "Exact frequencies for cross-ply laminates", Journal of Composite Materials, 4, 476-491. https://doi.org/10.1177/002199837000400404
  36. Kant, T. (1982), "Numerical analysis of thick plates", Comp. Methods Appl. Mech. Engrg., 31(1), 1-18. https://doi.org/10.1016/0045-7825(82)90043-3
  37. Kant, T. and Pandya, B.N. (1988), "A simple finite element formulation of a higher order theory for unsymmetrically laminated composite plates", Comp. Struc., 9(3), 215-246. https://doi.org/10.1016/0263-8223(88)90015-3
  38. Khdeir, A.A. (1988), "Free vibration and buckling of symmetric cross-ply laminated plates by an exact method", Journal of Sound and Vibration, 126(3), 447-461. https://doi.org/10.1016/0022-460X(88)90223-4
  39. Khdeir, A.A. and Librescu, L. (1988), "Analysis of symmetric cross-ply laminated elastic plates using a higher-order theory-part 2. bucking and free vibration", Comp. Struc., 9, 259-277. https://doi.org/10.1016/0263-8223(88)90048-7
  40. Khdeir, A.A. and Reddy, J.N. (1988), "Dynamic response of antisymmetric angle-ply laminated plates subjected to arbitrary loading", Journal of Sound and Vibration, 126(3), 437-445. https://doi.org/10.1016/0022-460X(88)90222-2
  41. Khdeir, A.A. and Reddy, J.N. (1989), "On theforced motions of the antisymmetric cross-ply laminated plates", Intl. J. Mech. Sci., 31(7), 499-510. https://doi.org/10.1016/0020-7403(89)90099-4
  42. Khdeir, A.A. and Reddy, J.N. (1989), "Exact solutions for the transient response of symmetric cross-ply laminates using a higher-order plate theory", Comp. Sci. Tech., 34, 205-224. https://doi.org/10.1016/0266-3538(89)90029-8
  43. Khdeir, A.A., Reddy, J.N. and Librescu, L. (1987), "Analytical solution of a refined shear deformation theory for rectangular composte plates", International Journal of Solids and Structures, 23(10), 1447-1463. https://doi.org/10.1016/0020-7683(87)90009-6
  44. Kromm, A. (1953), "Verallgeneinerte theorie der plattenstatik", Ing. Arch., 21, 266-286. https://doi.org/10.1007/BF00538133
  45. Kromm, A. (1955), "Uber die randquerkrafte bei gestutzten platten", Zeitschrift fur Angewandte Mathematik and Mechanik, 35, 231-242. https://doi.org/10.1002/zamm.19550350604
  46. Lee, C.W. (1967), "Three-dimensional solution for simply-supported thick rectangular plates", Nuclear Engineering and Design, 6, 155-162. https://doi.org/10.1016/0029-5493(67)90126-4
  47. Lee, Y.C. and Reismann, H. (1969), "Dynamics of rectangular plates", International Journal of Engineering Science, 7, 93-113. https://doi.org/10.1016/0020-7225(69)90025-1
  48. Lekhnitskii, S.G. (1981), Anisotropic Plates, English Translation, Mir Publishers (First Edition in Russian, 1950).
  49. Levinson, M. (1980), "An accurate, simple theory of the statics and dynamics of elastic plates", Mech. Res. Comm., 7(6), 343-350. https://doi.org/10.1016/0093-6413(80)90049-X
  50. Levinson, M. and Cooke, D.W. (1983), "Thick rectangular plates-1: The generalized navier solution", Intl. J. Mech. Sci., 25(3), 199-205. https://doi.org/10.1016/0020-7403(83)90093-0
  51. Lewinski, T. (1986), "A note on recent developments in the theory of elastic plates with moderate thickness", Rozprawy Inz., 34(4), 531-542.
  52. Librescu, L. (1975), Electrostatics and Kinetics of Anisotropic and Heterogeneous Shell-Type Structures, Nordhoff, Leyden, Netherlands.
  53. Librescu, L. (1975), "Improved linear theory of elastic anisotropic multilayered shells, part 1", Mekhanika Polimerov, (6), 1038-1050.
  54. Librescu, L. (1976), "Improved linear theory of elastic anisotropic multilayered shells, part 2", Mekhanika Polimerov, (1), 100-109.
  55. Librescu, L. and Khdeir, A.A. (1988), "Analysis of symmetric cross-ply laminated elastic plates using a higher-order theory-part 1. stress and displacement", Comp. Struc., 9, 189-213. https://doi.org/10.1016/0263-8223(88)90014-1
  56. Liou, W.J. and Sun, C.T. (1987), "A three-dimensional hybrid stress isoparametric element for the analysis of laminated composite plates", Computers and Structures, 25(2), 241-249. https://doi.org/10.1016/0045-7949(87)90147-7
  57. Lo, K.H.,Christensen, R.M. and Wu, E.M. (1977), "A high-order theory of plate deformation, part 1: Homogeneous plates", Journal of Applied Mechnics, 44(4), 663-668. https://doi.org/10.1115/1.3424154
  58. Lo, K.H.;Christensen, R.M.;Wu, E.M. (1977), "A high-order of plate deformation, part 2: Laminated plates", Journal OF Applied Mechnics, 44(4), 669-676. https://doi.org/10.1115/1.3424155
  59. Lo, K.H., Christensen, R.M. and Wu, E.M. (1978), "Stress solution determination for high order plate theory", Interntional Journal of Solids and Structures, 14, 655-662. https://doi.org/10.1016/0020-7683(78)90004-5
  60. Mau, S.T. (1973), "A refined laminated plate theory", Jouranl of Applied Mechanics, Trans. ASME, 40(2), 606-607. https://doi.org/10.1115/1.3423032
  61. Mindlin, R.D. (1951), "Influence of rotary inertia and shear on flexural motions of isotropic, elastic plates", Journal of Applied Mechanics, 18, 31-38.
  62. Murakami, H. (1986), "Laminated composite plate theory with imporve in-plane responses", Journal of Applied Mechanics, Trans. ASME, 35(3), 661-666.
  63. Murty, A.V.Krishna (1977), "Higher order theory for vibration of thick plates", AIAA Journal, 15(12), 1823-1824. https://doi.org/10.2514/3.7490
  64. Murty, A.V. Krishna (1977), "Flexure of composite plates", Composite Structures, 7(3), 161-177. https://doi.org/10.1016/0045-7949(77)90033-5
  65. Murty, A.V. Krishna (1986), "Toward a consistent plate theory", AIAA Journal, 24(6), 1047-1048. https://doi.org/10.2514/3.9388
  66. Murty, M.V.V. (1981), "An improved transverse shear deformation theory for laminated anisotropic plates", Technical Report 1903, NASA, Nov.
  67. Nelson, R.B. and Lorch, D.R. (1974), "A refined theory of laminated orthotropic plates", Journal of Applied Mechanics, 41, 171-183.
  68. Noor, A.K. and Scott, W. (1989), "Assessment of shear deformation theories for multilayered composite plates", Applied Mechanics Reviews, 42(1), 1-12. https://doi.org/10.1115/1.3152418
  69. Noor, A.K. and Scott Burton, W. (1989), "Three-dimensional solutions for anti symmetrically laminated anisotropic plates", Journal of Applied Mechanics, Trans. ASME, pages 1-7.
  70. Nosier, A. and Reddy, J.N. (1992), "Vibration and stability analyses of cross-ply laminated circular cylindrical shells", Journal of Sound and Vibration, 157(1), 139-159. https://doi.org/10.1016/0022-460X(92)90571-E
  71. Owen, D.R.J. and Li, Z.H. (1987), "A refined analysis of laminated plates by finite element displacement methods-1. fundamentals of static analysis", Computers and Structures, 26(6), 907-914. https://doi.org/10.1016/0045-7949(87)90107-6
  72. Owen, D.R.J. and Li, Z.H. (1987), "A refined analysis of laminated plates by finite element displacement methods-2. vibration and stability", Computers and Structures, 26(6), 915-923. https://doi.org/10.1016/0045-7949(87)90108-8
  73. Pagano, N.J. (1970), "Exact solutions for rectangular bidirectional composites and sandwich plates", Journal of Composite Materials, 4, 20-34. https://doi.org/10.1177/002199837000400102
  74. Pagano, N.J. (1969), "Exact solutions for composite laminates in cylindrical bending", Journal of Composite Materials, 3, 398-411. https://doi.org/10.1177/002199836900300304
  75. Pagano, N.J. (1978), "Stress fields in composite laminates", International Journal of Solids and Structures, 14(4), 385-400. https://doi.org/10.1016/0020-7683(78)90020-3
  76. Pagano, N.J. and Hatfield, S.J. (1972), "Elastic behavior of multilayered bidirectional composites", AIAA Journal, 10, 931-933. https://doi.org/10.2514/3.50249
  77. Panc, V. (1964), "Verscharfte theorie der elastichen platte", Ing. Arch., 33, 351-371. https://doi.org/10.1007/BF00531894
  78. Panc, V. (1975), Theories of Elastic Plates, Nordhoff, Leyden, Netherlands.
  79. Phan, N.D. and Reddy, J.N. (1985), "Analysis of laminated composite mplates using a higher-order shear deformation theory", International Journal for Numerical Methods in Engineering, 12, 2201-2219.
  80. Pryor, C.W. and Barker, R.M. (1971), "A finite element analysis including transverse shear effects for applications to laminated plates", AIAA Journal, 9, 912-917. https://doi.org/10.2514/3.6295
  81. Pryor, C.W., Barker, R.M. and Frederick, D. (1970), "Finite element bending analysis of reissner plates", ASCE J. Engrg. Mech., 96(EM6), 967-981.
  82. Putcha, N.S. and Reddy, J.N. (1982), "Three dimensional finite element analysis of layered composite plates", In Laurensom, R. M. and Yuceoglu, U. editors, 1982 Advances in Aerospace Structures and Materials, pages 29-35. ASME, AD-03, Nov.
  83. Putcha, N.S. and Reddy, J.N. (1986), "A refined mixed shear flexible finite element for the nonlinear analysis of laminated plates", Computers and Structures, 22(2), 529-538. https://doi.org/10.1016/0045-7949(86)90002-7
  84. Putcha, N.S. and Reddy, J.N. (1986), "Stability and natural vibration analysis of laminated plates by using a mixed element based on a refined plate theory", Journal of Sound and Vibration, 104(2), 285-300. https://doi.org/10.1016/0022-460X(86)90269-5
  85. Reddy, J.N. (1979), "Simple finite elements with relaxed continuity for nonlinear analysis of plates, In Proc. 3rd International Conference on Finite Element Methods, Australia, pages 265-281, July.
  86. Reddy, J.N. (1980), "A penalty plate-bending element for the analysis of laminated anisotropic composite plates", International Journal for Numerical Methods in Engineering, 15, 1187-1206. https://doi.org/10.1002/nme.1620150807
  87. Reddy, J.N. (1983), "An accurate prediction of natural frequencies of laminated plates by a higher-order theory", In Advances in Aerospace Structures, Materials and Dynamics-A Symposium on Composites, Boston, AD-06, 157-162. ASME.
  88. Reddy, J.N. (1983), "Geometrically nonlinear transient analysis of laminated composite plates", AIAA Journal, 21(4), 621-629. https://doi.org/10.2514/3.8122
  89. Reddy, J.N. (1984), "A simple higher-order theory for laminated composite plates", Journal of Applied Mechanics, Trans. ASME, 51, 745-752. https://doi.org/10.1115/1.3167719
  90. Reddy, J.N. (1984), "A refined nonliner theory of plates with transverse shear deformation", International Journal of Solids and Structures, 20(9/10), 881-896. https://doi.org/10.1016/0020-7683(84)90056-8
  91. Reddy, J.N. (1984), Energy and Variational Methods in Applied Mechanics, John Wiley and Sons.
  92. Reddy, J.N. (1985), "A review of the literature on finite element modeling of laminated composite plates", Shock and Vibration Digest, 17(4), 3-8.
  93. Reddy, J.N. (1987), "A small strain and moderate rotation theory of laminated anisotropic plates, Journal of Applied Mechanics, Trans. ASME, 54, 623-626. https://doi.org/10.1115/1.3173079
  94. Reddy, J.N. (1989), "On refined computational models of composite laminates", International Journal for Numerical Methods in Engineering, 27, 361-382. https://doi.org/10.1002/nme.1620270210
  95. Reddy, J.N. (1990), "A review of refined theories of laminated composite plates", The Shock and Vibration Digest, 22(7), 3-17.
  96. Reddy, J.N. (1990), "A general nonlinear third-order theory of plates with moderate thickness", International Journal of Non-linear Mechanics, 25(6), 677-686. https://doi.org/10.1016/0020-7462(90)90006-U
  97. Reddy, J.N. (1997), Mechanics of Laminated Plates: Theory and Analysis, CRC Press, Boca Raton, FL.
  98. Reddy, J.N. (1998), Thery and Analysis of Elastic Plates, Taylor & Francis.
  99. Reddy, J.N. and Chao, C.W. (1981), "A comparison of closed form and finite element solutions of thick laminated anisotropic rectangular plates", Nuclear Engineering Design, 64, 153-167. https://doi.org/10.1016/0029-5493(81)90001-7
  100. Reddy, J.N. and Khdeir, A.A. (1989), "Buckling and vibration of laminated composte plates using various plate theories", AIAA Journal, 27(12)1, 1808-1817. https://doi.org/10.2514/3.10338
  101. Reddy, J.N., Khdeir, A.A. and Librescu, L. (1987), "Levy type solutions for symmetrically laminated rectangular plates using a first-order shear deformation theory", Journal of Applied Mechanics, Trans. ASME, 54(3), 740-742. https://doi.org/10.1115/1.3173104
  102. Reddy, J.N. and Phan, N.D. (1985), "Stability and vibration of isotropic, orthotropic, and laminated plates according to a higher-order shear deformationtheory", Journal of Sound and Vibration, 98, 157-170. https://doi.org/10.1016/0022-460X(85)90383-9
  103. Rehfield, L.W. and Murthy, P.L.N. (1982), "Toward a new engineering theory of bending: Fundamentals", AIAA Journal, 20(5), 693-699. https://doi.org/10.2514/3.7938
  104. Rehfield, L.W. and Valisetty, R.R. (1983), "A comprehensive theory for planar bending of composite laminates", Computers and Structures, 15, 441-447.
  105. Reissner, E. (1944), "On the theory of bending of elastic plates", J. Math. Physics, 23(4), 184-191. https://doi.org/10.1002/sapm1944231184
  106. Reissner, E. (1945), "The effect of transverse shear deformation on the bending of elastic plates", Journal of Applied Mechanics, Trans. ASME, 12, 69-77.
  107. Reissner, E. (1947), "On bending of elastic plates", Quart. Appl. Math., 5(1), 55-68.
  108. Reissner, E. (1961), "A consistent treatment of transverse shear deformations in laminated anisotropic plates", AIAA Journal, 10(5), 716-718.
  109. Reissner, E. (1984), "On a certain mixed variational theorem and a porposed application", International Journal for Numerical Methods in Engineering, 20, 1366-1368. https://doi.org/10.1002/nme.1620200714
  110. Reissner, E. (1986), "On a mixed variational theorem and on shear deformable plate theory", International Journal for Numerical Methods in Engineering, 23, 193-198. https://doi.org/10.1002/nme.1620230203
  111. Reissner, E. and Stavsky, Y. (1961), "Bending and stretching of certain types of heterogeneous aelotropic elastic plates", Journal of Applied Mechanics, 28, 402-408. https://doi.org/10.1115/1.3641719
  112. Ren, J.G. (1987), "Bending of simply-supported antisymmetrically laminated rectangular plate under transverse loading", Com. Sci. Tech., 28(3), 231-243. https://doi.org/10.1016/0266-3538(87)90004-2
  113. Ren, J.G. and Hinton, E. (1986), "The finite element analysis of homogeneous and laminated composite plates using a simple higher order theory", Comm. Appl. Numer. Methods, 2(2), 217-228. https://doi.org/10.1002/cnm.1630020214
  114. Salerno, V.L. and Goldberg, M.A. (1960), "Effect of shear deformation on the bending of rectangular plates", Journal of Applied Mechanics, Trans ASME, 27(1), 54-58. https://doi.org/10.1115/1.3643934
  115. Savoia, M. and Reddy, J.N. (1992), "A variational approach to three-dimensional elasticity solutions of laminated composite plates", J. Appl. Mech., 59(2), S166-S175. https://doi.org/10.1115/1.2899483
  116. Schmidt, R. (1977), "A refined nonlinear theory of plates with transverse shear deformation", Jnl. Indus. Math. Soc., 27(1), 23-38.
  117. Sciuva, M.Di (1984), "An improved shear-deformation theory for moderately thick multilayered anisotropic plates and shells", Journal of Applied Mechanics, Trans. ASME, 54, 589-596.
  118. Seide, P. (1975), Small Elastic Deformations of Thin Shells, Nordhoff, Leyden, Netherlands.
  119. Seide, P. (1980), "An improved approximate theory for the bending of laminated plates", Mechanics Today, 5, 451-466.
  120. Srinivas, S. (1973), "A refined analysis of composite laminates", Journal of Sound and Vibration, 30, 495-507. https://doi.org/10.1016/S0022-460X(73)80170-1
  121. Srinivas, S., Joga Rao, C.V. and Rao, A.K. (1970), "An exact analysis for vibration of simply-supported homogeneous and laminated thick rectangular plates", Journal of Sound and Vibration, 12, 187-199. https://doi.org/10.1016/0022-460X(70)90089-1
  122. Srinivas, S. and Rao, A.K. (1970), "Bending, vibrations and buckling of simply supported thick orthotropic rectangular plates and laminates", International Journal of Solids and Structures, 6, 1464-1481.
  123. Srinivas, S.. Rao, A.K. and Joga Rao, C.V. (1966), "Flexure of simply supported thick homogeneous and laminated rectangular plates", Zeitschrift fut Angewandte Mathematik and Mechanik, 49, 449-458.
  124. Stavsky, Y. (1960), On the Theory of Hetergeneous Anisotropic Plates, PhD thesis, MIT.
  125. Stavsky, Y. (1961), "Bending and stretching of laminated aelotropic plates", Proc. ASCE, Jnl. Engg. Mech. Div., EM6, 87.
  126. Sun, C.T. (1971), "Theory of laminated plates", Journal of Applied Mechanics, Trans. ASME, 38, 231-238. https://doi.org/10.1115/1.3408748
  127. Sun, C.T. and Cheng, N.C. (1972), "On the governing equations for a laminated plate", Journal of Sound and Vibration, 21(3), 307-316. https://doi.org/10.1016/0022-460X(72)90815-2
  128. Sun, C.T. and Whitney, J.M. (1973), "On theories for the dynamic response of laminated plates", AIAA Journal, 11(2), 178-183. https://doi.org/10.2514/3.50448
  129. Stein, M. (1986), "Nonlinear theory for plates and shells including the effects of transverse shearing", AIAA Journal, 24(9), 1537-1544. https://doi.org/10.2514/3.9477
  130. Tessler, A. (1991), "A higher-order plate theory with ideal finite element suitability", Comp. Methods Appl. Mech. Eng., 85.
  131. Tessler, A. and Saether, E. (1991), "A computationally viable higher-order plate theory for laminated composite plates", International Journal for Numerical Methods in Engineering, 31, 1069-1086. https://doi.org/10.1002/nme.1620310604
  132. Timoshenko, S.P. and Woinowsky-Kreiger, S. (1961), Theory of Plates and Shells, McGraw-Hill, New York, 1961.
  133. Toledano, A. and Murakami, H. (1987), "A composite plate theory for arbitrary laminate configurations", Journal of Applied Mechanics, 54, 181-189. https://doi.org/10.1115/1.3172955
  134. Uflyand, Y.S. (1948), "The propagation of waves in the transverse vibrations of bars and plates", Izv. Akad. Nauk SSSR, Prikladnaya Matematika i Mekhanika, 12, 287-300.
  135. Vlasov, B.F. (1957), "On one case of bending of rectangular thick plates", Vestnik Moskovskogo Universitieta, 2, 25-34.
  136. Vlasov, B.F. (1958), "Ob uravneniyakh teovii isgiba plastinok on the equations of the theory of bending of plates", Izv. Akd. Nauk SSR, OTN, 4, 102-109.
  137. Voyiadjis, G.Z. and Baluch, M.H. (1981), "Refined theory for flexural motions of isotropic elastic plates", Journal of Sound and Vibration, 76(1), 57-64. https://doi.org/10.1016/0022-460X(81)90290-X
  138. Voyiadjis, G.Z. and Baluch, M.H. (1988), "Refined theory for thick composite plates", ASCE J. Engrg. Mech., 114(4), 671-687. https://doi.org/10.1061/(ASCE)0733-9399(1988)114:4(671)
  139. Whitney, J.M. (1969), "The effect of transverse shear deformation on the bending of laminated plates", Journal of Composite Materials, 3, 534-547. https://doi.org/10.1177/002199836900300316
  140. Whitney, J.M. (1973), "Shear correction factors for orthotropic laminates under static load", Journal of Applied Mechanics, Trans. ASME, 40(1), 302-304. https://doi.org/10.1115/1.3422950
  141. Whitney, J.M. (1987), Structural Analysis of Laminated Anisotropic Plates, Technomic.
  142. Whitney, J.M. and Leissa, A.W. (1969), "Analysis of heterogeneousanisotropic plates", Journal of Applied Mechanics, 36(2), 261-266. https://doi.org/10.1115/1.3564618
  143. Whitney, J.M. and Pagano, N.J. (1970), "Shear deformation in heterogeneous anisotropic plates", Journal of Applied Mechanics, Trans. ASME, 37(4), 1031-1036. https://doi.org/10.1115/1.3408654
  144. Yang, P.C., Norris, C.H. and Stavsky, Y. (1966), "Elastic wave propagation in heterogeneous plates", International Journal of Solids and Structures, 2, 665-684. https://doi.org/10.1016/0020-7683(66)90045-X
  145. Yu, Y.Y. (1959), "A new theory of elastic sandwich plates-one dimensional case", Journal of Applied Mechanics, 26, 415-421.

피인용 문헌

  1. Analysis of damped composite sandwich plates using plate bending elements with substitute shear strain fields based on Reddy's higher-order theory vol.216, pp.5, 2002, https://doi.org/10.1243/0954406021525377
  2. Axisymmetric vibrations of composite annular sandwich plates of quadratically varying thickness by harmonic differential quadrature method vol.226, pp.6, 2015, https://doi.org/10.1007/s00707-014-1284-0
  3. Linear static analysis and finite element modeling for laminated composite plates using third order shear deformation theory vol.62, pp.1, 2003, https://doi.org/10.1016/S0263-8223(03)00081-3
  4. Accurate determination of coupling effects on free edge interlaminar stresses in piezoelectric laminated plates vol.30, pp.8, 2009, https://doi.org/10.1016/j.matdes.2009.01.005
  5. Analytical solutions for bending, vibration, and buckling of FGM plates using a couple stress-based third-order theory vol.103, 2013, https://doi.org/10.1016/j.compstruct.2013.03.007
  6. On the free vibration analysis of laminated composite and sandwich plates: A review of recent literature with some numerical results vol.129, 2015, https://doi.org/10.1016/j.compstruct.2015.04.007
  7. Natural frequencies of laminated composite plates using third order shear deformation theory vol.72, pp.3, 2006, https://doi.org/10.1016/j.compstruct.2004.11.012
  8. Finite element linear and nonlinear, static and dynamic analysis of structural elements – an addendum – A bibliography (1996‐1999) vol.17, pp.3, 2000, https://doi.org/10.1108/02644400010324893
  9. Buckling analysis of composite laminates under end shortening by higher-order shear deformable finite strips vol.55, pp.10, 2002, https://doi.org/10.1002/nme.547
  10. Macro and micro deformations in a sandwich foam core vol.35, pp.6-8, 2004, https://doi.org/10.1016/j.compositesb.2003.11.011
  11. A laminated composite plate finite element a-priori corrected for locking vol.28, pp.5, 2008, https://doi.org/10.12989/sem.2008.28.5.603
  12. Wave propagation in a sandwich plate with a periodic composite core vol.16, pp.3, 2014, https://doi.org/10.1177/1099636214528652
  13. A literature review on computational models for laminated composite and sandwich panels vol.1, pp.1, 2011, https://doi.org/10.2478/s13531-011-0005-x
  14. Large deformation dynamic finite element analysis of delaminated composite plates using contact–impact conditions vol.144, 2014, https://doi.org/10.1016/j.compstruc.2014.07.025
  15. Transient response of composite sandwich plates vol.64, pp.3-4, 2004, https://doi.org/10.1016/S0263-8223(03)00135-1
  16. Analysis of composite plates using various plate theories -Part 2: Finite element model and numerical results vol.6, pp.7, 1998, https://doi.org/10.12989/sem.1998.6.7.727
  17. Prediction of delamination onset and growth for AP-PLY composite laminates using the finite element method vol.101, 2017, https://doi.org/10.1016/j.compositesa.2017.06.032
  18. Investigation on the Vibration and Stability of Hybrid Composite Plates vol.24, pp.16, 2005, https://doi.org/10.1177/0731684405052186
  19. The nonlinear vibration of an initially stressed laminated plate vol.38, pp.4, 2007, https://doi.org/10.1016/j.compositesb.2006.09.002
  20. Isogeometric analysis of laminated composite and sandwich plates using a layerwise deformation theory vol.104, 2013, https://doi.org/10.1016/j.compstruct.2013.04.002
  21. Stochastic buckling behaviour of laminated composite structures with uncertain material properties vol.66, 2017, https://doi.org/10.1016/j.ast.2017.01.028
  22. Finite element modeling for bending and vibration analysis of laminated and sandwich composite plates based on higher-order theory vol.49, pp.4, 2010, https://doi.org/10.1016/j.commatsci.2010.03.045
  23. FE analysis of laminated composite plates using a higher order shear deformation theory with assumed strains vol.10, pp.3, 2013, https://doi.org/10.1590/S1679-78252013000300005
  24. A Review of Refined Shear Deformation Theories of Isotropic and Anisotropic Laminated Plates vol.21, pp.9, 2002, https://doi.org/10.1177/073168402128988481
  25. Isogeometric finite element analysis of composite sandwich plates using a higher order shear deformation theory vol.55, 2013, https://doi.org/10.1016/j.compositesb.2013.06.044
  26. Analysis of laminated composite and sandwich plates based on the scaled boundary finite element method vol.187, 2018, https://doi.org/10.1016/j.compstruct.2017.11.001
  27. A Postprocessing Approach to Determine Transverse Stresses in Geometrically Nonlinear Composite and Sandwich Structures vol.37, pp.24, 2003, https://doi.org/10.1177/002199803038111
  28. Isogeometric analysis of laminated composite and sandwich plates using a new inverse trigonometric shear deformation theory vol.43, 2014, https://doi.org/10.1016/j.euromechsol.2013.09.001
  29. Higher-order shear deformable finite strip for the flexure analysis of composite laminates vol.23, pp.2, 2001, https://doi.org/10.1016/S0141-0296(00)00010-9
  30. On the radially symmetric vibrations of circular sandwich plates with polar orthotropic facings and isotropic core of quadratically varying thickness by harmonic differential quadrature method vol.51, pp.3, 2016, https://doi.org/10.1007/s11012-015-0226-9
  31. Free vibration analysis of composite sandwich plates based on Reddy's higher-order theory vol.33, pp.7, 2002, https://doi.org/10.1016/S1359-8368(02)00035-5
  32. On radially symmetric vibrations of circular sandwich plates of non-uniform thickness vol.99, 2015, https://doi.org/10.1016/j.ijmecsci.2015.04.016
  33. Free Vibration of Two-layered Cross-Ply Laminated Plates Using Layer-wise Trigonometric Shear Deformation Theory vol.23, pp.4, 2004, https://doi.org/10.1177/0731684404031893
  34. Accurate Determination of Interlaminar Stresses in General Cross-Ply Laminates vol.11, pp.1, 2004, https://doi.org/10.1080/15376490490257657
  35. Dynamic simulation of crack initiation and propagation in cross-ply laminates by DEM vol.71, pp.11, 2011, https://doi.org/10.1016/j.compscitech.2011.05.014
  36. A further study on nonlinear vibration of initially stressed plates vol.172, pp.1, 2006, https://doi.org/10.1016/j.amc.2005.02.007
  37. Vibration and Stability of Functionally Graded Plates Based on a Higher-order Deformation Theory vol.28, pp.10, 2009, https://doi.org/10.1177/0731684408088884
  38. A generalized unconstrained theory and isogeometric finite element analysis based on Bézier extraction for laminated composite plates vol.32, pp.3, 2016, https://doi.org/10.1007/s00366-015-0426-x
  39. Assessment of plate theories for initially stressed hybrid laminated plates vol.88, pp.2, 2009, https://doi.org/10.1016/j.compstruct.2008.03.034
  40. A modified Fourier–Ritz solution for vibration and damping analysis of sandwich plates with viscoelastic and functionally graded materials vol.106, 2016, https://doi.org/10.1016/j.ijmecsci.2015.11.031
  41. Free vibration and transverse stresses of viscoelastic laminated plates vol.30, pp.1, 2009, https://doi.org/10.1007/s10483-009-0111-y
  42. Deformation characteristics of composite laminates—part II: an experimental/numerical study on equivalent single-layer theories vol.62, pp.1, 2002, https://doi.org/10.1016/S0266-3538(01)00184-1
  43. Free edge stress analysis of general cross-ply composite laminates under extension and thermal loading vol.60, pp.1, 2003, https://doi.org/10.1016/S0263-8223(02)00290-8
  44. Quadrilateral finite elements for multilayer sandwich plates vol.38, pp.5, 2003, https://doi.org/10.1243/03093240360713441
  45. A serendipity plate element free of modeling deficiencies for the analysis of laminated composites vol.154, 2016, https://doi.org/10.1016/j.compstruct.2016.07.042
  46. Free vibration and stability analysis of piezolaminated plates using the finite element method vol.22, pp.12, 2013, https://doi.org/10.1088/0964-1726/22/12/125040
  47. Analysis of laminated composite and sandwich plate structures using generalized layerwise HSDT and improved meshfree radial point interpolation method vol.58, 2016, https://doi.org/10.1016/j.ast.2016.09.017
  48. Analytical solutions for bending analysis of rectangular laminated plates with arbitrary lamination and boundary conditions vol.23, pp.8, 2009, https://doi.org/10.1007/s12206-009-0511-4
  49. A nonlinear modified couple stress-based third-order theory of functionally graded plates vol.94, pp.3, 2012, https://doi.org/10.1016/j.compstruct.2011.10.006
  50. Estimation of transverse/interlaminar stresses in laminated composites – a selective review and survey of current developments vol.49, pp.1, 2000, https://doi.org/10.1016/S0263-8223(99)00126-9
  51. Identification and elimination of parasitic shear in a laminated composite beam finite element vol.37, pp.8, 2006, https://doi.org/10.1016/j.advengsoft.2005.11.001
  52. Transient response analysis of cross-ply composite laminated rectangular plates with general boundary restraints by the method of reverberation ray matrix vol.152, 2016, https://doi.org/10.1016/j.compstruct.2016.05.035
  53. Through-the-thickness distribution of strains in laminated composite plates subjected to bending vol.64, pp.1, 2004, https://doi.org/10.1016/S0266-3538(03)00201-X
  54. Nonlinear vibration analysis of composite laminated and sandwich plates with random material properties vol.52, pp.7, 2010, https://doi.org/10.1016/j.ijmecsci.2010.03.002
  55. Free vibration analysis of moderately thick rectangular laminated composite plates with arbitrary boundary conditions vol.35, pp.2, 1998, https://doi.org/10.12989/sem.2010.35.2.217
  56. NURBS-based thermo-elastic analyses of laminated and sandwich composite plates vol.44, pp.4, 1998, https://doi.org/10.1007/s12046-019-1063-7
  57. Development of a 2D Isoparametric Finite-Element Model Based on Reddy’s Third-Order Theory for the Bending Behavior Analysis of Composite Laminated Plates vol.55, pp.2, 1998, https://doi.org/10.1007/s11029-019-09807-y
  58. Evaluation of bending and post-buckling behavior of thin-walled FG beams in geometrical nonlinear regime with CUF vol.275, pp.None, 1998, https://doi.org/10.1016/j.compstruct.2021.114408