Log in

The development of laminated composite plate theories: a review

  • Review Article
  • Published:
Journal of Materials Science Aims and scope Submit manuscript

Abstract

This study investigates and reviews approaches to modelling laminated composite plates. It explores theories that have been proposed and developed and assesses their suitability and functionality. The particular focus in this study has been on normal stresses and the through-thickness distributions of transverse shear. These are important for composite plates as stress-induced failures can occur in three different ways. Therefore, it is essential to understand and calculate transverse shear and normal stress through the thickness of the plate accurately. In this study, previous laminated composite plate theories are categorised and reviewed in a general sense, i.e. not problem specific, and the advantages and disadvantages of each model are discussed. This research mainly focuses on how accurate and efficient the models can predict the transverse shear. It starts with displacement-based theories from very basic models such as Classical laminate plate theory to more complicated and higher-order shear deformation theory. Models are furthermore categorised by how the models consider the overall laminate. In this article, the theories are divided into two parts: Single layer theory, where the whole plate is considered as one layer; and Layerwise theory, where each layer is treated separately. The models based on zig-zag and Discrete Theories are then reviewed, and finally the mixed (hybrid) plate theories are studied.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Subscribe and save

Springer+ Basic
EUR 32.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or Ebook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. Fu Y, Li S, Jiang Y (2008) Acta Mech Solida Sinica 21(2):127

    Google Scholar 

  2. Blanc M, Touratier M (2007) Compos Struct 77:193

    Article  Google Scholar 

  3. Onsy RL, Tran-Cong T (2002) Compos Struct 56:249

    Article  Google Scholar 

  4. Han SC, Tabiei A, Park WT (2008) Compos Struct 82:465

    Article  Google Scholar 

  5. Faimun1 F, Gosling PD, Polit O, Touratier M (2005) Analytical response sensitivity of laminated composite plate using trigonometric type element. 13th ACME Conference

  6. Khandan R, Noroozi S, Sewell P, Vinney J, Ramazani MR (2010) Optimum design of fibre orientation angles in composite laminate plates for minimum thickness. ASME 2010 International Mechanical Engineering Congress & Exposition, Canada

  7. Fox DD (2000) Comput Struct 75:313

    Article  Google Scholar 

  8. Aydogdu M (2009) Compos Struct 89:94

    Article  Google Scholar 

  9. Wu Z, Chen R, Chen W (2005) Compos Struct 70:135

    Article  Google Scholar 

  10. Reissner E, Stavsky Y (1961) J Appl Mech 28:402

    Article  Google Scholar 

  11. Stavsky Y (1961) J Eng Mech ASCE 87(6):31

    Google Scholar 

  12. Dong SB, Pister KS, Taylor RL (1962) J Aeronaut Sci 29(8):969

    Google Scholar 

  13. Yang PC, Norris CH, Stavsky Y (1966) Int J Solids Struct 2:665

    Article  Google Scholar 

  14. Ambartsumyan SA (1969) Theory of anisotropic plates, translated from Russian by T Cheron. Technomic, Stamford

    Google Scholar 

  15. Whitney JM, Leissa AW (1969) J Appl Mech 36(2):261

    Article  Google Scholar 

  16. Reddy JN (2004) Mechanics of laminated composite plates and shells, 2nd edn. CRC Press, New York

    Google Scholar 

  17. Kirchhoff G (1850) J Reine Angew Math 40:51

    Article  Google Scholar 

  18. Love AEH (1934) The mathematical theory of elasticity. Cambridge University Press, Cambridge

    Google Scholar 

  19. Timoshenko S (1934) Theory of elasticity. McGraw-Hill, New York

    Google Scholar 

  20. Reissner E (1945) J Appl Mech 12:69

    Google Scholar 

  21. Reddy JN (1984) Energy and variational methods in applied mechanics. Wiley, London

    Google Scholar 

  22. Cosentino E, Weaver P (2010) Eur J Mech A 29(4):567

    Article  Google Scholar 

  23. Aydogdu M (2006) J Compos Mater 40:2143

    Article  Google Scholar 

  24. Pagano NJ, Hatfield SJ (1972) AIAA J 10(7):931

    Article  Google Scholar 

  25. Noor AK (1972) AIAA J 11(7):1038

    Article  Google Scholar 

  26. Noor AK (1975) Fibre Sci Technol 8(2):81

    Article  Google Scholar 

  27. Mindlin RD (1951) J Appl Mech ASME 18:31

    Google Scholar 

  28. Levinson M (1980) Mech Res Commun 7:343

    Article  Google Scholar 

  29. Murthy MVV (1981) An improved transverse shear deformation theory for laminated anisotropic plates. NASA Technical paper No 1903

  30. Bhaskar K, Varadan TK (1993) J Sound Vib 168(3):469

    Article  Google Scholar 

  31. Kant T, Swaminathan K (2000) Compos Struct 49:65

    Article  Google Scholar 

  32. Karama M, Abou Harb B, Mistou S, Caperaa S (1998) Compos Part B 29B:223

    Article  Google Scholar 

  33. Whitney JM, Sun CT (1973) J Sound Vib 30(1):85

    Article  Google Scholar 

  34. Pagano NJ (1974) J Comput Mater 8:65

    Article  Google Scholar 

  35. Tang S (1975) J Comp Mater 9:33

    Article  Google Scholar 

  36. Tang S, Levy A (1975) J Comp Mater 9:42

    Article  Google Scholar 

  37. Hsu PW, Herakovich CT (1977) J Comp Mater 11:422

    Article  CAS  Google Scholar 

  38. Pipes RB, Pagano NJ (1974) ASME J Appl Mech 41:668

    Article  Google Scholar 

  39. Pagano NJ (1978) Int J Solids Struct 14(4):385

    Article  Google Scholar 

  40. Pagano NJ (1978) Int J Solids Struct 14:401

    Article  Google Scholar 

  41. Wang SS, Choi I (1982) ASME J Appl Mech 49:541550

    Google Scholar 

  42. Wang SS, Choi I (1982) ASME J Appl Mech 49:549

    Article  Google Scholar 

  43. Wang SS, Choi I (1983) ASME J Appl Mech 50:169

    Article  Google Scholar 

  44. Wang SS, Choi I (1983) ASME J Appl Mech 50:179

    Article  Google Scholar 

  45. Lehknitskii SG (1963) Theory of elasticity of an anisotropic elastic body. Holden Day, San Francisco

    Google Scholar 

  46. Ambartsumian SA (1958) Izv Otd Tech Nauk AN SSSR 5:69

    Google Scholar 

  47. Soldatos KP, Timarci T (1993) Compos Struct 25:165

    Article  Google Scholar 

  48. Touratier M (1991) Int J Eng Sci 29(8):901

    Article  Google Scholar 

  49. Karama M, Afaq KS, Mistou S (2003) Int J Solids Struct 40:1525

    Article  Google Scholar 

  50. Soldatos KP (1992) Acta Mech 94:195

    Article  Google Scholar 

  51. Swaminathan K, Patil SS (2008) Compos Struct 82:209

    Article  Google Scholar 

  52. Matsunaga H (1994) Int J Solids Struct 31(22):3113

    Article  Google Scholar 

  53. Matsunaga H (1997) Comput Struct 62(1):205

    Article  Google Scholar 

  54. Matsunaga H (2000) Compos Struct 48(4):231

    Article  Google Scholar 

  55. Matsunaga H (2001) Int J Mech Sci 43:1925

    Article  Google Scholar 

  56. Matsunaga H (2006) Compos Struct 72:177

    Article  Google Scholar 

  57. Matsunaga H (2007) Compos Struct 77:249

    Article  Google Scholar 

  58. Fiedler L, Lacarbonara W, Vestroni F (2010) Compos Struct 92:3011

    Article  Google Scholar 

  59. Schmidt R (1977) Ind. Math. 27(1):23

    Google Scholar 

  60. Jemielita G (1975) Eng Trans 23:483

    Google Scholar 

  61. Reissner E (1985) Appl Mech Rev 38:1453

    Article  Google Scholar 

  62. Phan ND, Reddy JN (1985) Int J Numer Methods Eng 21(12):2201

    Article  Google Scholar 

  63. Vuksanovic DJ (2000) Compos Struct 48:205

    Article  Google Scholar 

  64. Pandya BN, Kant T (1988) Comput Methods Appl Mech Eng 66:173

    Article  Google Scholar 

  65. Vlasov BF (1957) Dokla Ak Nauk Azerbeijanskoi SSR 3:955 (in Russian)

    Google Scholar 

  66. Reddy JN (1990) Int J Nonlinear Mech 25:677

    Article  Google Scholar 

  67. Carrera E (2007) Compos Struct 77:341

    Article  Google Scholar 

  68. IdIbi A, Karama M, Touratier M (1997) Compos Struct 37(2):173

    Article  Google Scholar 

  69. Stein M (1986) AIAA J 24(9):1537

    Article  Google Scholar 

  70. Stein M, Jogley DC (1987) AIAA J 25(1):123

    Article  CAS  Google Scholar 

  71. Kassapoglou C, Lagace PA (1986) ASME J Appl Mech 53:744

    Article  Google Scholar 

  72. Kassapoglou C, Lagace PA (1987) J Comp Mater 21(4):292

    Article  CAS  Google Scholar 

  73. Kassapoglou C (1990) J Reinf Plast Comp 9(1):33

    Article  Google Scholar 

  74. Becker W (1993) Comp Struct 26(2):39

    Article  Google Scholar 

  75. Mortan SK, Webber JPH (1993) Comp Sci Technol 46:175

    Article  Google Scholar 

  76. Lu X, Liu D (1990) In: Proceedings of the fifth technical conference of the American society for composites. Technomic, Lancaster, pp 479–561

  77. Lu X, Liu D (1992) AIAA J 30(4):1063

    Article  Google Scholar 

  78. Lee CY, Liu D (1992) Comput Struct 42(1):69

    Article  Google Scholar 

  79. Ramalingeswara R, Ganesan N (1996) Mech Comp Mater Struct 3:321

    Article  Google Scholar 

  80. Rohwer K (1992) Int J Solids Struct 29(1):105

    Article  Google Scholar 

  81. Kabir HRH (1992) Comput Struct 43(4):769

    Article  Google Scholar 

  82. Kabir HRH (1994) Comput Struct 51(3):299

    Article  Google Scholar 

  83. Kabir HRH (1996) Mech Comp Mater Struct 3:341

    Article  CAS  Google Scholar 

  84. Ko CC, Lin CC (1992) AIAA J 30(1):197

    Article  Google Scholar 

  85. Ko CC, Lin CC (1993) AIAA J 31(6):1118

    Article  Google Scholar 

  86. Wang X, Li SJ (1992) Int J Solids Struct 29(10):1293

    Article  Google Scholar 

  87. Matsunaga H (2002) Compos Struct 56:279

    Article  Google Scholar 

  88. Soldatos KP (2004) J Mech Phys Solids 52:341

    Article  Google Scholar 

  89. Soldatos KP, Watson P (1997) Acta Mech 123:163

    Article  Google Scholar 

  90. Soldatos KP, Watson P (1997) Math Mech Solids 2:459

    Article  Google Scholar 

  91. Soldatos KP (2006) Math Mech Solids 11:596

    Article  Google Scholar 

  92. Wu CP, Chen WY (1994) J Sound Vib 177(4):503

    Article  Google Scholar 

  93. Cho KN, Bert CW, Striz AG (1991) J Sound Vib 145(3):429

    Article  Google Scholar 

  94. Plagianakos TS, Saravanos DA (2009) Compos Struct 87(1):23

    Article  Google Scholar 

  95. Fares ME, Elmarghany MK (2008) Compos Struct 82:71

    Article  Google Scholar 

  96. Nosier A, Kapania RK, Reddy JN (1993) AIAA J 31(12):2335

    Article  Google Scholar 

  97. Di Sciuva M, Icardi U (1995) AIAA J 33(12):2435

    Article  Google Scholar 

  98. Cho MH, Parmerter RR (1993) AIAA J 31(7):1299

    Article  Google Scholar 

  99. Lekhnitskii SG (1968) Anisotropic plates. Gordon and Breach Science Publishers, New York

    Google Scholar 

  100. Ren JG (1986) Compos Sci Technol 27:225

    Article  Google Scholar 

  101. Reissner E (1944) J Math Phys 23:184

    Google Scholar 

  102. Noor AK, Burton WS (1989) ASME Appl Mech Rev 42(1):1

    Article  Google Scholar 

  103. Carrera E (1998) ASME J Appl Mech 65(12):820

    Article  Google Scholar 

  104. Di Sciuva M (1987) ASME J Appl Mech 54:589

    Article  Google Scholar 

  105. Di Sciuva M (1993) Comput Struct 47(1):91

    Article  Google Scholar 

  106. Touratier M (1992) Int J Solids Struct 29(11):1379

    Article  Google Scholar 

  107. Beakou A (1991) Homogtntisation et modtlisation des coques composites multicouches. Thesis ENSAM, Paris (in French)

  108. Idlbi A (1995) Comparaison de thtories de plaque et estimation de la qualite des solutions dans la zone bord. Thesis, ENSAM, Paris (in French)

  109. He LH (1994) Int J Solids Struct 31(5):613

    Article  Google Scholar 

  110. Ossadzow C, Muller P, Touratier M (1995) Une thtorie gtnerale des coques composites multicouches. Deuxibme colloque national en calcul des structures. Tome 1. Hermes

  111. Lee KH, Senthilnathan NR, Lim SP, Chow ST (1990) Compos Struct 15:137

    Article  Google Scholar 

  112. Di Sciuva M (1992) Compos Struct 22:149

    Article  Google Scholar 

  113. Cho M, Parmerter R (1992) Compos Struct 20:113

    Article  Google Scholar 

  114. Sun CT, Whitney JM (1973) AIAA J 11:178261

    Article  Google Scholar 

  115. Srinivas S (1973) J Sound Vib 30:495

    Article  Google Scholar 

  116. Seide P (1980) In: Nemat-Nasser S (ed), Mechanics Today, vol 5. Pergamon Press, Oxford, pp 451–517

  117. He JF (1989) In: Proceedings of the seventh international conference on the composite materials, vol 4, pp 180–183

  118. He JF (1992) J Compos Struct 21:67

    Article  Google Scholar 

  119. He JF, Chou M, Zhang X (1993) J Compos Struct 24:125

    Article  Google Scholar 

  120. He JF, Zhang ZZ (1996) Compos Struct 34:437

    Article  Google Scholar 

  121. Savoia M, Reddy JN (1992) J Appl Mech 59:166

    Article  Google Scholar 

  122. Robbins DH, Reddy JN (1993) Int J Numer Methods Eng 36:655

    Article  Google Scholar 

  123. Chaudhri RA (1986) Comput Struct 23:139

    Article  Google Scholar 

  124. Barbero EJ, Reddy JN, Teply JL (1989) Int J Numer Methods Eng 28:2275

    Article  Google Scholar 

  125. Han J, Hao SV (1993) Int J Numer Methods Eng 36:3903

    Article  Google Scholar 

  126. Wu CP, Kuo HC (1992) Comp Struct 20(4):237

    Article  Google Scholar 

  127. Carrera E, Ciuffreda A (2005) Compos Struct 69:271

    Article  Google Scholar 

  128. Hellinger E (1914) Encykl Math Wiss 4(4):654

    Google Scholar 

  129. Carrera E (1995) Atti Accad Sci Torino, Mem Sci Fis 19:49

    Google Scholar 

  130. Shimpi RP, Patel HG, Arya H (2007) J Appl Mech 4:523

    Article  Google Scholar 

  131. Tessler A, Di Sciuva M, Gherone M (2009) Refined zigzag theory for laminated composite and sandwich plates. NASA Report, NASA/TP-2009–215561

  132. Cen S, Long Y, Yao Z (2002) Comput Struct 80:819

    Article  Google Scholar 

  133. Wu CP, Li HY (2010) Compos Struct 92:2591

    Article  Google Scholar 

  134. Daghia F, de Miranda S, Ubertini F, Viola E (2008) Int J Solids Struct 45:1766

    Article  Google Scholar 

  135. Demasi L (2009) Compos Struct 87:1

    Article  Google Scholar 

  136. Demasi L (2009) Compos Struct 87:12

    Article  Google Scholar 

  137. Demasi L (2009) Compos Struct 87:183

    Article  Google Scholar 

  138. Demasi L (2009) Compos Struct 87:195

    Article  Google Scholar 

  139. Demasi L (2009) Compos Struct 88:1

    Article  Google Scholar 

  140. Bhar A, Satsangi SK (2011) Eur J Mech A 30:46

    Article  Google Scholar 

  141. Moleiro F (2008) Comput Struct 86:826

    Article  Google Scholar 

  142. Chou TW, Kelly A (1980) J Mater Sci 15:327. doi:10.1007/BF02396779

    Article  CAS  Google Scholar 

  143. Moleiro F, Mota Soares CM, Mota Soares CA, Reddy JN (2009) Comput Methods Appl Mech Eng 198:1848

    Article  Google Scholar 

  144. Moleiro F (2010) Compos Struct 92:2328

    Article  Google Scholar 

  145. Moleiro F (2011) Compos Struct 92:2328

    Article  Google Scholar 

  146. Ramesh SS, Wang CM, Reddy JN, Ang KK (2008) Eng Struct 30:2687

    Article  Google Scholar 

  147. Carrera E, Demasi L (2002) Int J Numer Methods Eng 55:191

    Article  Google Scholar 

  148. Carrera E, Demasi L (2002) Int J Numer Methods Eng 55:253

    Article  Google Scholar 

  149. Ramesh SS, Wang CM, Reddy JN, Ang KK (2009) Compos Struct 91:337

    Article  Google Scholar 

  150. Sheikh AH, Chakrabarti A (2003) Finite Elem Anal Des 39:883

    Article  Google Scholar 

  151. Cho M, Parmerter R (1994) AIAA J 32:2241

    Article  Google Scholar 

  152. Oh J, Cho M (2004) Int J Solids Struct 41:1357

    Article  Google Scholar 

  153. Ugo I (1998) Compos Part B 29B:425

    Google Scholar 

  154. Han SC, Kim KD, Kanok-Nukulchai W (2004) Struct Eng Mech Int J 18(6):807

    Google Scholar 

  155. Zhang YX, Kim KS (2005) Comput Mech 36:331

    Article  Google Scholar 

  156. Kim KD, Liu GZ, Han SC (2005) Comput Mech 35(5):315

    Article  CAS  Google Scholar 

  157. Kreja I, Schmidt R (2006) Int J Non-linear Mech 41(1):101

    Article  Google Scholar 

  158. **ang S, Jiang SX, Bi ZY, ** YX, Yang MS (2011) Compos Struct 93:299

    Article  Google Scholar 

  159. Liew KM, Zhao X, Ferreira AJM (2011) Compos Struct 93:2031

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Rasoul Khandan.

Electronic supplementary material

Below is the link to the electronic supplementary material.

Supplementary material 1 (DOCX 13 kb)

Rights and permissions

Reprints and permissions

About this article

Cite this article

Khandan, R., Noroozi, S., Sewell, P. et al. The development of laminated composite plate theories: a review. J Mater Sci 47, 5901–5910 (2012). https://doi.org/10.1007/s10853-012-6329-y

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10853-012-6329-y

Keywords

Navigation