Advertisement

Theories and finite elements for multilayered, anisotropic, composite plates and shells

  • E. Carrera
Article

Summary

This work is an overview of available theories and finite elements that have been developed for multilayered, anisotropic, composite plate and shell structures. Although a comprehensive description of several techniques and approaches is given, most of this paper has been devoted to the so called axiomatic theories and related finite element implementations. Most of the theories and finite elements that have been proposed over the last thirty years are in fact based on these types of approaches. The paper has been divided into three parts.

Part I, has been devoted to the description of possible approaches to plate and shell structures: 3D approaches, continuum based methods, axiomatic and asymptotic two-dimensional theories, classical and mixed formulations, equivalent single layer and layer wise variable descriptions are considered (the number of the unknown variables is considered to be independent of the number of the constitutive layers in the equivalent single layer case). Complicating effects that have been introduced by anisotropic behavior and layered constructions, such as high transverse deformability, zig-zag effects and interlaminar continuity, have been discussed and summarized by the acronimC z 0 -Requirements.

Two-dimensional theories have been dealt with in Part II. Contributions based on axiomatic, asymtotic and continuum based approaches have been overviewed. Classical theories and their refinements are first considered. Both case of equivalent single-layer and layer-wise variables descriptions are discussed. The so-called zig-zag theories are then discussed. A complete and detailed overview has been conducted for this type of theory which relies on an approach that is entirely originated and devoted to layered constructions. Formulas and contributions related to the three possible zig-zag approaches, i.e. Lekhnitskii-Ren, Ambartsumian-Whitney-Rath-Das, Reissner-Murakami-Carrera ones have been presented and overviewed, taking into account the findings of a recent historical note provided by the author.

Finite Element FE implementations are examined in Part III. The possible developments of finite elements for layered plates and shells are first outlined. FEs based on the theories considered in Part II are discussed along with those approaches which consist of a specific application of finite element techniques, such as hybrid methods and so-called global/local techniques. The extension of finite elements that were originally developed for isotropic one layered structures to multilayerd plates and shells are first discussed. Works based on classical and refined theories as well as on equivalent single layer and layer-wise descriptions have been overviewed. Development of available zig-zag finite elements has been considered for the three cases of zig-zag theories. Finite elements based on other approches are also discussed. Among these, FEs based on asymtotic theories, degenerate continuum approaches, stress resultant methods, asymtotic methods, hierarchy-p,_-s global/local techniques as well as mixed and hybrid formulations have been overviewed.

Keywords

Composite Plate Transverse Shear Laminate Plate Sandwich Panel Shear Deformation Theory 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

List of symbols and acronims

a, b, h

plate/shell geometrical parameters (length, width and thickness)

k

sub/super-script used to denote parameters related to thek-layer

N

order of the expansions used for transverse stresses and displacements

Nl

Number of constituent layers of multilayered plate/shell

x,y,z

coordinates of Cartesian reference systems used for plates

α, β,z

curvilinear coordinates of reference systems used for shells

Acronyms

2D

two-Dimensional

3D

three-Dimensional

AWRD

Ambartsumian-Whitney-Rath-Das theory

CLT

Classical lamination Theory

ESLM

Equivalent Single Layer Models

FEs

Finite Elements

FEM

Finite Element Method

FSDT

First Shear Deformation Theory

HOT

Higher Order Theories

HTD

High Transverse Deformability

IC

Interlaminar Continuity

KR

Koiter's Recommendation

LR

Lekhnitskii-Ren theory

LFAT

Love First Approximation Theory

LSAT

Love Second Approximation Theory

LWM

Layer-Wise Models

RMC

Reissner-Murakami-Carrera theory

RMVT

Reissner's Mixed Variational Theorem

TA

Transverse Anisotropy

VRT

Vlasov-Reddy Theory

WFHL

Weak Form of Hooke's Law

ZZ

Zig-Zag.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Bogdonovic, A.E. and Sierakowsky, R. (1999), “Composite Materials and Structures: Science Technology and Application”,Applied Mechanics Review,52, 551–366.Google Scholar
  2. 2.
    Naghdi, P.M. (1956), “A survey of recent progress in the theory of elastic shells”,Applied Mechanics Review,9, 365–368.Google Scholar
  3. 3.
    Ambartusumyan, S.A. (1962), “Contributions to the theory of anisotropic layered shells”,Applied Mechanics Review,15, 345–249.Google Scholar
  4. 4.
    Bert, C.W.E. (1984), “A critical evaluations of new plate theories applied to laminated composites”,Composite Structures,38, 329–347.CrossRefGoogle Scholar
  5. 5.
    Reissner, E. (1985), “Reflections on the theory of elastic plates”,Applied Mechanics Review,38, 1453–1464.Google Scholar
  6. 6.
    Librescu, L. and Reddy, J.N. (1986), “A Critical Review and Generalization of Transverse Shear Deformable Anisotropic Plates”,Euromech Colloquium 219, Kassel, Sept 1986,Refined dynamical Theories of Beams, Plates and Shells and their Alications, Elishakoff and Irretier (Eds.), Springer Verlag, Berlin, 1987, 32–43.Google Scholar
  7. 7.
    Grigolyuk, E.I. and Kulikov, G.M. (1988), “General Direction of the Development of the Theory of Shells”,Mekhanica Kompozitnykh Materialov, No. 2, 287–298.Google Scholar
  8. 8.
    Kapania, R.K. and Raciti, S. (1989), “Recent advances in analysis of laminated beams and plates. Part I. Shear Effects and Buckling. Part II. Vibrations and wave propagations”,American Institute of Aeronautics and Astronautics Journal,27, 923–946.zbMATHMathSciNetGoogle Scholar
  9. 9.
    Kapania, R.K. (1989), “A Review on the Analysis of Laminated Shells”,Journal of Pressure Vessel Technology,111, 88–96.Google Scholar
  10. 10.
    Noor, A.K. and Burton, W.S. (1989), “Assessment of shear deformation theories for multilayered composite plates”,Applied Mechanics Review,41, 1–18.Google Scholar
  11. 11.
    Reddy, J.N. (1989), “On computational models for composite laminate”,International Journal for Numerical Methods in Engineering,27, 361–382.zbMATHMathSciNetCrossRefGoogle Scholar
  12. 12.
    Noor, A.K. and Burton, W.S. (1990), “Assessment of computational models for multilayered composite shells”,Applied Mechanics Review,43, 67–97.Google Scholar
  13. 13.
    Reddy, J.N. and Robbins, D.H. (1994), “Theories and computational models for composite laminates”,Applied Mechanics Review,47, 147–165.Google Scholar
  14. 14.
    Noor, A.K., Burton, S. and Bert, C.W. (1996), “Computational model for sandwich panels and shells”,Applied Mechanics Review,49, 155–199.Google Scholar
  15. 15.
    Varadan, T.K. and Bhaskar, K. (1997), “Review of different theories for the analysis of composites”,Journal of Aerospace Society of India,49, 202–208.Google Scholar
  16. 16.
    Carrera, E. (2000), “An assessment of mixed and classical theories for thermal stress analysis of orthotropic plates”,Journal of Thermal Stress,23, 797–831.CrossRefGoogle Scholar
  17. 17.
    Carrera, E. (2000), “An assessment of mixed and classical theories on global and local response of multilayered orthotropic plates”,Composite Structures,40, 183–198.CrossRefGoogle Scholar
  18. 18.
    Yang, H.T., Saigal, S., Masud, A. and Kapania, R.K. (2000), “A survey of recent shell finite elements”,International Journal for Numerical Methods in Engineering,47, 101–127.zbMATHMathSciNetCrossRefGoogle Scholar
  19. 19.
    Carrera, E. (2001), “Developments, ideas and evaluations based upon Reissner's Mixed Variational Theorem in the Modeling of Multilayered Plates and Shells”,Applied Mechanics Review,54, 301–329.CrossRefGoogle Scholar
  20. 20.
    Carrera, E., “A Historical Review of Zig-Zag Theories for Multilayered Plates and Shell”,Applied Mechanics Review, to be printed.Google Scholar
  21. 21.
    Goldenvaizer, A.L. (1961),Theory of thin elastic shells, International Series of Monograph in Aeronautics and Astronautics, Pergamon Press, New York.Google Scholar
  22. 22.
    Kraus, H. (1967),Thin elastic shells, John Wiley, N.Y.zbMATHGoogle Scholar
  23. 23.
    Lekhnitskii, S.G. (1968),Anisotropic Plates, 2nd Ed., Translated from the 2nd Russian Ed. by S.W. Tsai and Cheron, Bordon and Breach.Google Scholar
  24. 24.
    Ambartsumian, S.A. (1969),Theory of anisotropic plates, Translated from Russian by T. Cheron and Edited by J.E. Ashton Tech. Pub. Co.Google Scholar
  25. 25.
    Jones, R.M. (1975),Mechanics of Composite Materials, McGraw-Hill, New York.Google Scholar
  26. 26.
    Librescu, L. (1975),Elasto-statics and Kinetics of Anisotropic and Heterogeneous Shell-Type Structures, Noordhoff Int., Leyden, Netherland.Google Scholar
  27. 27.
    Palazotto, A.N. and Dennis, S.T. (1992),Nonlinear analysis of shell structures, AIAA Series.Google Scholar
  28. 28.
    Reddy, J.N. (1997),Mechanics of Laminated Composite Plates, Theory and Analysis, CRC Press.Google Scholar
  29. 29.
    Pagano, N.J. (1969), “Exact solutions for Composite Laminates in Cylindrical Bending”,Journal of Composite Materials,3, 398–411.CrossRefGoogle Scholar
  30. 30.
    Pagano, N.J. (1970), “Exact solutions for rectangular bi-direction composites and sandwich plates”,Journal of Composite Materials,4, 20–34.Google Scholar
  31. 31.
    Pagano, N.J. and Hatfield, S.J. (1972), “Elastic Behavior of Multilayered Bidirectional Composites”,American Institute of Aeronautics and Astronautics Journal,10, 931–933.Google Scholar
  32. 32.
    Noor, A.K. and Rarig, P.L. (1974), “Three-Dimensional Solutions of Laminated Cylinders”,Computer Methods in Applied Mechanics and Engineering,3, 319–334.CrossRefzbMATHGoogle Scholar
  33. 33.
    Noor, A.K. (1973), “Free vibrations of multilayerd composite plates”,American Institute of Aeronautics and Astronautics Journal,11, 1038–1039.Google Scholar
  34. 34.
    Pagano, N.J. (1978), “Stress fields in composite laminates”,International Journal of Solids and Structures,14, 385–400.zbMATHCrossRefGoogle Scholar
  35. 35.
    Ren, J.G. (1987), “Exact Solutions for Laminated Cylindrical Shells in Cylindrical Bending”,Composite Science and Technology,29, 169–187.CrossRefGoogle Scholar
  36. 36.
    Varadan, T.K. and Bhaskar, K. (1991), “Bending of Laminated Orthotropic Cylindrical Shells—An Elasticity Aroach”,Composite Structures,17, 141–156.CrossRefGoogle Scholar
  37. 37.
    Bhaskar, K. and Varadan, T.K. (1993), “Exact elasticity solution for Laminated Anisotropic Cylindrical Shells”, JAM,60, 41–47.zbMATHGoogle Scholar
  38. 38.
    Bhaskar, K. and Varadan, T.K. (1994), “Benchmark elasticity solutions for locally loaded laminated orthotropic Cylindrical Shells”,American Institute of Aeronautics and Astronautics Journal,32, 627–632.zbMATHGoogle Scholar
  39. 39.
    Ye, J.Q. and Soldatos, K.P. (1994), “Three-dimensional vibration of laminated cylinders and cylindrical panels with symmetric or antisymmetric cross-ply lay-up”,Composite Engineering,4, 429–444.Google Scholar
  40. 40.
    Teo, T.M. and Liew, K.M. (1999), “Three-dimensional elasticity solutions to some orthotropic plate problems”,International Journal of Solids and Structures,36, 5301–5326.zbMATHCrossRefGoogle Scholar
  41. 41.
    Meyer-Piening, H.R. and Stefanelli, R. (2000), “Stresses, deflections, buckling and frequencies of a cylindrical curved rectangular sandwich panel based on the elasticity solutions”, Proceedings of theFifth International Conference On Sandwich Constructions, Zurich, Switzerland, September 5–7,II, 705–716.Google Scholar
  42. 42.
    Meyer-Piening, H.R. (2000), “Experiences with ‘Exact’ linear sandwich beam and plate analyses regarding bending, instability and frequency investigations”, Proceedings of theFifth International Conference On Sandwich Constructions, Zurich, Switzerland, September 5–7,I, 37–48.Google Scholar
  43. 43.
    Anderson, T., Madenci, E., Burton, S.W. and Fish, J.C. (1998), “Analytical Solutions of Finite-Geometry Composite Panels under Transient Surface Loadings”,International Journal of Solids and Structures,35, 1219–1239.zbMATHCrossRefGoogle Scholar
  44. 44.
    Koiter, W.T. (Ed.) (1960), “Theory of thin elastic shells”, Proceedings ofFirst IUTAM Symposium, Delft 1959, North Holland.Google Scholar
  45. 45.
    Niordson, F.I. (Ed.) (1967), “Theory of thin shells”, Proceedings ofSecond IUTAM Symposium, Copenaghen 1967, Springer Verlag, Berlin.Google Scholar
  46. 46.
    Koiter, W.T. (1960), “A Consistent First Approximations in the General Theory of Thin Elastic Shells”, Proceedings ofFirst Symposium on the Theory of Thin Elastic Shells, Aug. 1959, North-Holland, Amsterdam, 12–23.Google Scholar
  47. 47.
    Goldenvaizer, A.L. (1967), “Problem in the rigorous deduction of theory of thin elastic shells”, Proceedings ofSecond Symposium on the Theory of Thin Elastic Shells, Cophenagen, Springer Verlag, 31–38.Google Scholar
  48. 48.
    John, F. (1967), “Refined interior shell equations”, Proceedings ofSecond Symposium on the Theory of Thin Elastic Shells, Cophenagen, Springer Verlag, 1–14.Google Scholar
  49. 49.
    Green, A.E. and Naghdi, P.M. (1967), “Shells in the light of generalized continua”, Proceedings ofSecond Symposium on the Theory of Thin Elastic Shells, Cophenagen, Springer Verlag, 39–58.Google Scholar
  50. 50.
    Reissner, E. (1967), “On the foundation of generalized linear shell theory”, Proceedings ofSecond Symposium on the Theory of Thin Elastic Shells, Cophenagen, Springer Verlag, 15–30.Google Scholar
  51. 51.
    Cosserat, E. and Cosserat, F. (1999), “Theories des corps deformable”,In Traite de Physique, 2nd Ed., Chwolson, Paris.Google Scholar
  52. 52.
    Cicala, P. (1959), “Sulla teoria elastica della parete sottile”,Giornale del Genio Civile, fascicoli 4, 6 e 9.Google Scholar
  53. 53.
    Cicala, P. (1965),Systematic approach to linear shell theory, Levrotto & Bella, Torino.Google Scholar
  54. 54.
    Antona, E. (1991), “Mathematical model and their use in Engineering”, Published inApplied Mathematics in the Aerospace Science/Engineering, Edited by Miele, A. and Salvetti, A.,44, 395–433.Google Scholar
  55. 55.
    Reissner, E. (1984), “On a certain mixed variational theory and a proposed application”,International Journal for Numerical Methods in Engineering,20, 1366–1368.zbMATHCrossRefGoogle Scholar
  56. 56.
    Reissner, E. (1986), “On a mixed variational theorem and on a shear deformable plate theory”,International Journal for Numerical Methods in Engineering 23, 193–198.zbMATHCrossRefGoogle Scholar
  57. 57.
    Reissner, E. (1986), “On a certain mixed variational theorem and on laminated elastic shell theory”, Proceedings of theEuromech-Colloquium,219, 17–27.Google Scholar
  58. 58.
    Washizu, K. (1968),Variational Methods in Elasticity and Plasticity, Pergamon Press, N.Y.zbMATHGoogle Scholar
  59. 59.
    Atluri, S.N., Tong, P. and Murakawa, H. (1983), “Recent studies in Hybrid and Mixed Finite element Methods in Mechanics”, inHybrid and Mixed Finite Element Methods, Edited by Atluri, S.N., Callagher, R.H. and Zienkiewicz, O.C., John Wiley and Sons, Ltd, 51–71.Google Scholar
  60. 60.
    Barbero, E.J., Reddy, J.N. and Teply, J.L. (1990), “General Two-Dimensional Theory of laminated Cylindrical Shells”,American Institute of Aeronautics and Astronautics Journal,28, 544–553.zbMATHGoogle Scholar
  61. 61.
    Nosier, A., Kapania, R.K. and Reddy, J.N. (1993), “Free Vibration Analysis of Laminated Plates Using a Layer-Wise Theory”,American Institute of Aeronautics and Astronautics Journal,31, 2335–2346.zbMATHGoogle Scholar
  62. 62.
    Carrera, E. (1995), “A class of two-dimensional theories for anisotropic multilayered plates analysis”,Accademia delle Scienze di Torino, Memorie Scienze Fisiche,19–20, (1995–1996), 1–39.Google Scholar
  63. 63.
    Carrera, E. (1997), “C z0 Requirements—Models for the two dimensional analysis of multilayered structures”,Composite Structures,37, 373–384.CrossRefGoogle Scholar
  64. 64.
    Librescu, L. (1987), “Refined geometrically non-linear theories of anisotropic laminated shells”,Quarterly of Applied Mathematics,55, 1–22.MathSciNetGoogle Scholar
  65. 65.
    Sun, C.T. and Chin, H. (1987), “Analysis of asymmetric composite laminates”,American Institute of Aeronautics and Astronautics Journal,26, 714–718.Google Scholar
  66. 66.
    Carrera, E. (1991), “Postbuckling behaviors of multilayered shells”,Ph. Dissertation, DIASP, Politecnico di Torino.Google Scholar
  67. 67.
    Chen, H.P. and Shu, J.C. (1992), “Cylindrical bending of unsymmetric composite laminates”,American Institute of Aeronautics and Astronautics Journal,30, 1438–1440.Google Scholar
  68. 68.
    Carrera, E. (1993), “Nonlinear Response of asymmetrically laminated plates in cylindrical bending”,American Institute of Aeronautics and Astronautics Journal,31, 1353–1357.Google Scholar
  69. 69.
    Carrera, E. (1994), “Reply by the author to C.T. Sun”,American Journal of Aeronautics and Astronautics,32, 2135–2136.Google Scholar
  70. 70.
    Cauchy, A.L. (1828), “Sur l'equilibre et le mouvement d'une plaque solide”,Execrises de Matematique,3, 328–355.Google Scholar
  71. 71.
    Poisson, S.D. (1829), “Memoire sur l'equilibre et le mouvement des corps elastique”,Mem. Acad. Sci.,8, 357.Google Scholar
  72. 72.
    Kirchhoff, G. (1850), “Über das Gleichgewicht und die Bewegung einer elastischen Scheibe”,J. Angew. Math.,40, 51–88.zbMATHGoogle Scholar
  73. 73.
    Love, A.E.H. (1927),The mathematical theory of elasticity, 4th edition, Cambridge University Press, Cambridge.zbMATHGoogle Scholar
  74. 74.
    Reissner, E. and Stavsky, Y. (1961), “Bending and stretching of certain type of heterogeneous elastic plates”,Journal of Applied Mechanics,9, 402–408.MathSciNetGoogle Scholar
  75. 75.
    Carrera, E. (1991), “The effects of shear deformation and curvature on buckling and vibrations of cross-ply laminated composites shells”,Journal of Sound and Vibration,150, 405–433.CrossRefGoogle Scholar
  76. 76.
    Reissner, E. (1945), “The effect of transverse shear deformation on the bending of elastic plates”,Journal of Applied Mechanics,12, 69–76.MathSciNetGoogle Scholar
  77. 77.
    Mindlin (1951), “Influence of rotatory inertia and shear in flexural motions of isotropic elastic plates”,Journal of Applied Mechanics,18, 1031–1036.Google Scholar
  78. 78.
    Yang, P.C., Norris, C.H. and Stavsky, Y. (1966), “Elastic Wave propagation in hetereogenous plates”,International Journal of Solids and Structures,2, 665–684.CrossRefGoogle Scholar
  79. 79.
    Vlasov, B.F. (1957), “On the equations of Bending of plates”,Dokla Ak. Nauk. Azerbeijanskoi-SSR,3, 955–979.Google Scholar
  80. 80.
    Reddy, J.N. (1984b), “A simple higher order theories for laminated composites plates”,Journal of Applied Mechanics,52, 745–742.Google Scholar
  81. 81.
    Reddy, J.N. and Phan, N.D. (1985), “Stability and Vibration of Isotropic, Orthotropic and Laminated Plates”, According to a Higher order Shear Deformation Theory,Journal of Sound and Vibration,98, 157–170.zbMATHCrossRefGoogle Scholar
  82. 82.
    Hildebrand, F.B., Reissner, E. and Thomas, G.B. (1938), “Notes on the foundations of the theory of small displacements of orthotropic shells”, NACA TN-1833, Washington, D.C.Google Scholar
  83. 83.
    Sun, C.T. and Whitney, J.M. (1973), “On the theories for the dynamic response of laminated plates”,American Institute of Aeronautics and Astronautics Journal,11, 372–398.Google Scholar
  84. 84.
    Lo, K.H., Christensen, R.M. and Wu, E.M. (1977), “A Higher-Order Theory of Plate Deformation. Part 2: Laminated Plates”,Journal of Applied Mechanics,44, 669–676.zbMATHGoogle Scholar
  85. 85.
    Soldatos, K.P. (1987), “Cylindrical bending of Cross-ply Laminated Plates: Refined 2D Plate theories in comparison with the Exact 3D elasticity solution”,Tech Report No. 140, Dept. of Math., University of Ioannina, Greece.Google Scholar
  86. 86.
    Librescu, L. and Schmidt, R. (1988), “Refined theories of elastic anisotropic shells accounting for small strains and moderate rotations”,International Journal of Non-linear Mechanics,23, 217–229.zbMATHCrossRefGoogle Scholar
  87. 87.
    Touratier, M. (1988), “A refined theory for thick composites plates”,Mechanics Research Communications,15, 229–236.zbMATHCrossRefGoogle Scholar
  88. 88.
    Touratier, M. (1989), “Un modele simple et efficace em mechanique dees structures composites”,C.R. Adad. Sci. Paris,309, 933–938.zbMATHGoogle Scholar
  89. 89.
    Librescu, L., Khdeir, A.A. and Frederick, D. (1989), “A Shear Deformable Theory of Laminated Composite Shallow Shell-Type Panels and Their Response Analysis. Part I: Vibration and Buckling”,Acta Mechanica,77, 1–12.MathSciNetCrossRefzbMATHGoogle Scholar
  90. 90.
    Dennis, S.T. and Palazotto, A.N. (1991), “Laminated Shell in Cylindrical Bending, Two-Dimensional Approach vs Exact”,American Institute of Aeronautics and Astronautics Journal,29, 647–650.Google Scholar
  91. 91.
    Touratier, M. (1991), “An efficient standard plate theory”, IJES,29, 901–916.zbMATHCrossRefGoogle Scholar
  92. 92.
    Gaudenzi, P. (1992), “A general formulation of higher order theories for the analysis of laminated plates”,Composite Structures,20, 103–112.CrossRefGoogle Scholar
  93. 93.
    Touratier, M. (1992), “A refined theory of laminated shallow shells”,International Journal of Solids and Structures,29, 1401–1415.zbMATHCrossRefGoogle Scholar
  94. 94.
    Touratier, M. (1992), “A generalization of shear deformation theories for axisymmetric multilayered shells”,International Journal of Solids and Structures,29, 1379–1399.zbMATHCrossRefGoogle Scholar
  95. 95.
    Savoia, M., Laudero, F. and Tralli, A. (1993), “A refined theory for laminated beams. Part I—A new higher order approach”,Meccanica,28, 39–51.zbMATHCrossRefGoogle Scholar
  96. 96.
    Librescu, L. and Lin, W. (1996), “Two models of shear deformable laminated plates and shells and their use in prediction of global response behavior”,European Journal of Mechanics, Part A: Solids,15, 1095–1120.zbMATHGoogle Scholar
  97. 97.
    Zenkour, A.M. (1999), “Transverse shear and normal deformation theory for bending analysis of laminated and sandwich elastic beams”,Mechanics of Composite Materials and Structures, 267–283.Google Scholar
  98. 98.
    Zenkour, A.M. and Fares, M.E. (1999), “Non-homogeneous response of cross-ply laminated elastic plates using high-order theory”,Composite Structures, 297–305.Google Scholar
  99. 99.
    Sokolinsky, V. and Frosting, Y. (1999), “Nonlinear behavior of Sandwich panels with transversely Flexible core”,American Institute of Aeronautics and Astronautics Journal,37, 1474–1482.Google Scholar
  100. 100.
    Rabinovitch, O. and Frosting, Y. (2001), “Higher-Order Analysis of Unidirectional Sandwich panels with Flat and generally curved faces and a ‘soft’ core”,Sandwich Structures and Materials,3, 89–116.CrossRefGoogle Scholar
  101. 101.
    Hsu, T. and Wang, J.T. (1970), “A theory of laminated cylindrical shells consisting of layers of orthotropic laminae,”American Institute of Aeronautics and Astronautics Journal,8, 2141–2146.zbMATHGoogle Scholar
  102. 102.
    Hsu, T. and Wang, J.T. (1971), “Rotationally Symmetric Vibrations of Orthotropic Layered Cylindrical Shells,”Journal of Sound and Vibration,16, 473–487.CrossRefzbMATHGoogle Scholar
  103. 103.
    Cheung, Y.K. and Wu, C.I. (1972), “Free Vibrations of Thick, Layered Cylinders Having Finite Longth with Various Boundary Conditions,”Journal of Sound and Vibration,24, 189–200.zbMATHCrossRefGoogle Scholar
  104. 104.
    Srinivas, S. (1973), “A refined analysis of composite laminates,”Journal of Sound and Vibration,30, 495–507.CrossRefzbMATHGoogle Scholar
  105. 105.
    Cho, K.N., Bert, C.W. and Striz, A.G. (1991), “Free Vibrations of Laminated Rectangular Plates Analyzed by Higher order Individual-Layer Theory,”Journal of Sound and Vibration,145, 429–442.CrossRefGoogle Scholar
  106. 106.
    Robbins, D.H. Jr. and Reddy, J.N. (1993), “Modeling of thick composites using a layer-wise theory,”International Journal for Numerical Methods in Engineering,36, 655–677.zbMATHCrossRefGoogle Scholar
  107. 107.
    Carrera, E. (2000), “A Priori vs a Posteriori Evaluation of Transverse Stresses in Multilayered Orthotropic Plates,”Composite Structures 48, 245–260.CrossRefGoogle Scholar
  108. 108.
    Lekhnitskii, S.G. (1935), “Strength Calculation of Composite Beams”,Vestnik Inzhen. i Tekhnikov, No.9.Google Scholar
  109. 109.
    Ambartsumian, S.A. (1958), “On a theory of bending of anisotropic plates”,Investiia Akad. Nauk SSSR, Ot. Tekh. Nauk., No 4.Google Scholar
  110. 110.
    Ambartsumian, S.A. (1958), “On a general theory of anisotropic shells,”PMM,22, No. 2, 226–237.Google Scholar
  111. 111.
    Ambartsumian, S.A. (1961),Theory of anisotropic shells, Fizmatzig, Moskwa; Translated from Russian, NASA TTF-118, 1964.Google Scholar
  112. 112.
    Ambartsumian, S.A. (1962), “Contributions to the theory of anisotropic layered shells,”Applied Mechanics Review,15, 245–249.Google Scholar
  113. 113.
    Ambartsumian, S.A. (1969),Theory of anisotropic plates, Translated from Russian by T. Cheron and Edited by J.E. Ashton Tech. Pub. Co.Google Scholar
  114. 114.
    Ren, J.G. (1986), “A new theory of laminated plates,”Composite Science and Technology,26, 225–239.CrossRefGoogle Scholar
  115. 115.
    Ren, J.G. (1986), “Bending theory of laminated plates,”Composite Science and Technology,27, 225–248.CrossRefGoogle Scholar
  116. 116.
    Whitney, J.M. (1969), “The effects of transverse shear deformation on the bending of laminated plates,”Journal of Composite Materials,3, 534–547.CrossRefGoogle Scholar
  117. 117.
    Rath, B.K. and Das, Y.C. (1973), “Vibration of Layered Shells,”Journal of Sound and Vibration,28, 737–757.CrossRefzbMATHGoogle Scholar
  118. 118.
    Sun, C.T. and Whitney, J.M. (1973), “On the theories for the dynamic response of laminated plates,”American Institute of Aeronautics and Astronautics Journal,11, 372–398.Google Scholar
  119. 119.
    Yu, Y.Y. (1959), “A new theory of elastic sandwich plates. One dimensional case,”Journal of Applied Mechanics,37, 1031–1036.Google Scholar
  120. 120.
    Chou and Carleone (1973), “Transverse Shear in Laminated Plates Theories,”American Institute of Aeronautics and Astronautics Journal,11, 1333–1336.Google Scholar
  121. 121.
    Dischiuva, M. (1984), “A refinement of the transverse shear deformation theory for multilayered plates,”Aerotecnica Missili e Spazio,63, 84–92.Google Scholar
  122. 122.
    Dischiuva, M., Cicorello, A. and Dalle Mura, E. (1985), “A class of multilayered anisotropic plate elements including the effects of transverse shear deformabilty”,AIDAA Conference, Torino, 877–892.Google Scholar
  123. 123.
    Dischiuva, M. (1987), “An improved shear deformation theory for moderately thick multilayered anisotropic shells and plates,”Journal of Applied Mechanics,54, 589–596.CrossRefGoogle Scholar
  124. 124.
    Dischiuva, M. and Carrera, E. (1992), “Elasto-dynamic Behavior of relatively thick, symmetrically laminated, anisotropic circular cylindrical shells,”Journal of Applied Mechanics,59, 222–223.Google Scholar
  125. 125.
    Cho, M. and Parmerter, R.R. (1993), “Efficient higher order composite plate theory for general lamination configurations,”American Institute of Aeronautics and Astronautics Journal,31, 1299–1305.zbMATHGoogle Scholar
  126. 126.
    Bhashar, B. and Varadan, T.K. (1989), “Refinement of Higher-Order laminated plate theories”,American Institute of Aeronautics and Astronautics Journal,27, 1830–1831.Google Scholar
  127. 127.
    Savithri, S. and Varadan, T.K. (1990), “Refinement of Higher-Order laminated plate theories,”American Institute of Aeronautics and Astronautics Journal,28, 1842–1843.Google Scholar
  128. 128.
    Lee, K.H., Senthilnathan, N.R., Lim, S.P. and Chow, S.T. (1990), “An improved zig-zag model for the bending analysis of laminated composite plates,”Composite Structures,15, 137–148.CrossRefGoogle Scholar
  129. 129.
    Li, X. and Liu, D. (1994), “Zig-zag theories for composites laminates,”American Institute of Aeronautics and Astronautics Journal,33, 1163–1165.Google Scholar
  130. 130.
    Bekou, A. and Touratier, M. (1993), “A Rectangular Finite Element for analysis composite multilayered shallow shells in static, vibration and buckling,”International Journal for Numerical Methods in Engineering,36, 627–653.CrossRefGoogle Scholar
  131. 131.
    Touratier, M. (1992), “A generalization of shear deformation theories for axisymmetric multilayered shells,”International Journal of Solids and Structures,29, 1379–1399.zbMATHCrossRefGoogle Scholar
  132. 132.
    Touratier, M. (1992), “A refined theories for laminated shallow shells,”International Journal of Solids and Structures,29, 1401–1415.zbMATHCrossRefGoogle Scholar
  133. 133.
    Soldatos, K.P. and Timarci, T. (1993), “A unified formulation of laminated composites, shear deformable, five-degrees-of-freedom cylindrical shell theories,”Composite Structures,25, 165–171.CrossRefGoogle Scholar
  134. 134.
    Timarci, T. and Soldatos, K.P. (1995), “Comparative dynamic studies for symmetric cross-ply circular cylindrical shells on the basis a unified shear deformable shell theories,”Journal of Sound and Vibration,187, 609–624.CrossRefGoogle Scholar
  135. 135.
    Idlbi, A., Karama, M. and Touratier, M. (1997), “Comparison of various laminated plate theories,”Composite Structures,37, 173–184.CrossRefGoogle Scholar
  136. 136.
    Ossodzow, C., Muller, P. and Touratier, M. (1998), “Wave dispersion in deep multilayered doubly curved viscoelastic shells,”Journal of Sound and Vibration,214, 531–552.CrossRefGoogle Scholar
  137. 137.
    Ossodzow, C., Touratier, M. and Muller, P. (1999), “Deep doubly curved multilayered shell theory,”American Institute of Aeronautics and Astronautics Journal,37, 100–109.Google Scholar
  138. 138.
    Murakami, H. (1984), “A laminated beam theory with interlayer slip,”Journal of Applied Mechanics,51, 551–559.zbMATHGoogle Scholar
  139. 139.
    Murakami, H. (1985), “Laminated composite plate theory with improved in-plane responses”,ASME Proceedings of PVP Conference, New Orleans, June 24–26, PVP-98-2, 257–263.Google Scholar
  140. 140.
    Murakami, H. (1986), “Laminated composite plate theory with improved in-plane responses,”Journal of Applied Mechanics,53, 661–666.zbMATHGoogle Scholar
  141. 141.
    Toledano, A. and Murakami, H. (1987), “A composite plate theory for arbitrary laminate configurations,”Journal of Applied Mechanics,54, 181–189.zbMATHGoogle Scholar
  142. 142.
    Toledano, A. and Murakami, H. (1987), “A high-order laminated plate theory with improved in-plane responses,”International Journal of Solids and Structures,23, 111–131.zbMATHCrossRefGoogle Scholar
  143. 143.
    Murakami, H. and Yamakawa, J. (1996), “Dynamic response of plane anisotropic beams with shear deformation,”ASCE Journal of Engineering Mechanics,123, 1268–1275.CrossRefGoogle Scholar
  144. 144.
    Murakami, H., Reissner, E. and Yamakawa, J. (1996), “Anisotropic beam theories with shear deformation,”Journal of Applied Mechanics,63, 660–668.zbMATHGoogle Scholar
  145. 145.
    Carrera, E. (1998), “Mixed Layer-Wise Models for Multilayered Plates Analysis,”Composite Structures,43, 57–70.CrossRefGoogle Scholar
  146. 146.
    Carrera, E. (1998), “Evaluation of Layer-Wise Mixed Theories for Laminated Plates Analysis,”American Institute of Aeronautics and Astronautics Journal,26, 830–839.Google Scholar
  147. 147.
    Carrera, E. (1998), “Layer-Wise Mixed Models for Accurate Vibration Analysis of Multilayered Plates,”Journal of Applied Mechanics,65, 820–828.Google Scholar
  148. 148.
    Carrera, E. (1990), “Multilayered Shell Theories that Account for a Layer-Wise Mixed Description. Part I. Governing Equations,”American Institute of Aeronautics and Astronautics Journal,37, No. 9, 1107–1116.Google Scholar
  149. 149.
    Carrera, E. (1999), “Multilayered Shell Theories that Account for a Layer-Wise Mixed Description. Part II. Numerical Evaluations,”American Institute of Aeronautics and Astronautics Journal,37, No. 9, 1117–1124.Google Scholar
  150. 150.
    Carrera, E. (1999), “A Reissner's Mixed Variational Theorem Applied to Vibration Analysis of Multilayered Shells,”Journal of Applied Mechanics,66, No. 1, 69–78.Google Scholar
  151. 151.
    Carrera, E. (1999), “A Study of Transverse Normal Stress Effects on Vibration of Multilayered Plates and Shells,”Journal of Sound and Vibration,225, 803–829.CrossRefGoogle Scholar
  152. 152.
    Carrera, E. (1999), “Transverse Normal Stress Effects in Multilayered Plates,”Journal of Applied Mechanics,66, 1004–1012.Google Scholar
  153. 153.
    Carrera, E. (2000), “Single-Layer vs Multi-Layers Plate Modelings on the Basis of Reissner's Mixed Theorem,”American Institute of Aeronautics and Astronautics Journal,38, 342–343.Google Scholar
  154. 154.
    Messina, A. (2000), “Two generalized higher order theories in free vibration studies of multilayered plates,”Journal of Sound and Vibration,242, 125–150.CrossRefGoogle Scholar
  155. 155.
    Bhaskar, K. and Varadan, T.K. (1992), “Reissner's New Mixed Variational Principle Applied to Laminated Cylindrical Shells,”Journal of Pressure Vessel Technology,114, 115–119.CrossRefGoogle Scholar
  156. 156.
    Jing, H. and Tzeng, K.G. (1993b), “Refined Shear Deformation Theory of Laminated Shells,”American Institute of Aeronautics and Astronautics Journal,31, 765–773.zbMATHGoogle Scholar
  157. 157.
    Ali, J.S.M., Bhaskar, K. and Varadan, T.K. (1999), “A new theory for accurate thermal/mechanical flexural analysis of symmetric laminated plates,”Composite Structures,45, 227–232.CrossRefGoogle Scholar
  158. 158.
    Reissner, E. (1950), “On variational theorem in elasticity,”Journal of Mathematics & Physics,20, 90.Google Scholar
  159. 159.
    Zenkour, A.M. (1998), “Vibration of axisymmetric shear deformable cross-ply laminated cylindrical shells-a variational approach,”Composite Structures,36, 219–231.Google Scholar
  160. 160.
    Fares, M.E. and Zenkour, A.M. (1998), “Mixed variational formula for the thermal bending of laminated plates,”Journal of Thermal Stress,22, 347–365.CrossRefGoogle Scholar
  161. 161.
    Zenkour, A.M. and Fares, M.E. (2001), “Bending, buckling and free vibration of nonhomogeneous composite laminated cylindrical shell using a refined first order theory,”Composites Part B,32, 237–247.CrossRefGoogle Scholar
  162. 162.
    Auricchio, F. and Sacco, E. (2001), “Partial-mixed formulation and refined models for the analysis of composites laminated within FSDT”,Composite Structures,46, 103–113.CrossRefGoogle Scholar
  163. 163.
    Fettahlioglu, O.A. and Steele, C.R. (1974), “Asymptotic Solutions for Orthotropic Non-homogeneous Shells of Reution”,Journal of Applied Mechanics,41, 753–758.zbMATHGoogle Scholar
  164. 164.
    Berdichevsky, V.L. (1979), “Variational-Asymptotic Method of Shell Theory Construction”,PMM,43, 664–667.Google Scholar
  165. 165.
    Widera, G.E.O. and Logan, D.L. (1980), “A Refined Theories for Non-homogeneous Anisotropic, Cylindrical Shells: Part I-Derivation”,Journal of Engineering Mechanics Division, ASCE,106, 1053–1073.Google Scholar
  166. 166.
    Widera, G.E.O. and Fan, H. (1988), “On the derivation of a Refined Theory for Non-homogeneous Anisotropic Shells of Reution”,Journal of Applied Mechanics,110, 102–105.Google Scholar
  167. 167.
    Berdichevsky, V.L. and Misyura, V. (1992), “Effect of Accuracy Loss in Classical Shell Theory”,Journal of Applied Mechanics,59, S217-S223.Google Scholar
  168. 168.
    Hodges, D.H., Lee, B.W. and Atilgan, A.R. (1993), “Application of the variational-asymptotic method to laminated composite plates”,American Institute of Aeronautics and Astronautics Journal,31, 1674–1983.zbMATHGoogle Scholar
  169. 169.
    Tarn, J. and Wang, S. (1994), “An asymptotic theory for dynamic response of inhomogeneous laminated plates”,International Journal of Solids and Structures,31, 231–246.zbMATHMathSciNetCrossRefGoogle Scholar
  170. 170.
    Wang, S. and Tarn, J. (1994), “A three-dimensional analysis of anisotropic inhomogeneous laminated plates”,International Journal of Solids and Structures,31, 497–415.zbMATHMathSciNetCrossRefGoogle Scholar
  171. 171.
    Satyrin, V.G. and Hodges, D.H. (1996), “On asymptotically correct linear laminated plate theory”,International Journal of Solids and Structures,33, 3649–3671.CrossRefGoogle Scholar
  172. 172.
    Satyrin, V.G. (1997), “Derivation of Plate Theory Accounting Asymptotically Correct Shear Deformation”,Journal of Applied Mechanics,64, 905–915.Google Scholar
  173. 173.
    Wu, W., Tarn, J. and Tang, S. (1997), “A refined asymptotic theory for dynamic analysis of doubly curved laminated shells”,Journal of Sound and Vibration,35, 1953–79.Google Scholar
  174. 174.
    Antona, E. and Frulla, G. (2001), “Cicala's asymptotic approach to the linear shell theory”,Composite Structures,52, 13–26.CrossRefGoogle Scholar
  175. 175.
    Erikssen, J.L. and Truesdell, C. (1958), “Exact theory for stress and strain in rods and shells”,Archive of Rational Mechanics and Analysis,1, 295–323.CrossRefGoogle Scholar
  176. 176.
    Green, A.E. and Naghdi, P.M. (1982), “A theory of laminated composite plates”,Journal of Applied Mathematics,29, 1–23.zbMATHGoogle Scholar
  177. 177.
    Sun, C.T., Achenbach, J.D. and Herrmann (1968), “Continuum theory for a laminated medium”,Journal of Applied Mechanics, 467–475.Google Scholar
  178. 178.
    Grot, R.A. (1972), “A Continuum model for curvilinear laminated composites”,International Journal of Solids and Structures,8, 439–462.CrossRefzbMATHGoogle Scholar
  179. 179.
    Epstein, M. and Glockner, P.G. (1977), “Nonlinear analysis of multilayred shells”,International Journal of Solids and Structures,13, 1081–1089.zbMATHCrossRefGoogle Scholar
  180. 180.
    Esptein, M. and Glockner, P.G. (1979), “Multilayerd shells and directed surfaces”,International Journal of Engineering Sciences,17, 553–562.CrossRefGoogle Scholar
  181. 181.
    Noor, A.K. and Rarig, P.L. (1974), “Three-Dimensional solutions of laminated cylinders”,Computer Methods in Applied Mechanics and Engineering,3, 319–334.CrossRefzbMATHGoogle Scholar
  182. 182.
    Malik, M. (1994), “Differential quadrature method in computational mechanics: new development and applications”,Ph.D. dissertation, University of Oklahoma, Oklahoma.Google Scholar
  183. 183.
    Malik, M. and Bert, C.W. (1995), “Differential quadrature analysis of free vibration of symmetric cross-ply laminates with shear deformation and rotatory inertia”,Shock Vibr., 2, 321–338.Google Scholar
  184. 184.
    Liew, K.M., Han, B. and Xiao, M. (1996), “Differential quadrature method for thick symmetric cross-ply laminates with first-order shear flexibility”,International Journal of Solids and Structures,33, 2647–2658.zbMATHCrossRefGoogle Scholar
  185. 185.
    Davi, G. (1996), “Stress field in general composite laminates”,American Institute of Aeronautics and Astronautics Journal,34, 2604–2608.zbMATHGoogle Scholar
  186. 186.
    Davi, G. and Milazzo, A. (1999), “Bending Stress fields in composite laminate beams by a boundary integral formulation”,Composite Structures,71, 267–276.CrossRefGoogle Scholar
  187. 187.
    Milazzo, A. (2000), “Interlaminar Stress in Laminated Composite Beam-Type Structures Under Shear/Bending”,American Institute of Aeronautics and Astronautics Journal,38, 687–694.Google Scholar
  188. 188.
    Noor, A.K. and Burton, W.S. (1989a), “Stress and Free Vibration Analyses of Multilayered Composite Plates”,Composite Structures,11, 183–204.CrossRefGoogle Scholar
  189. 189.
    Noor, A.K. and Peters, J.M. (1989), “A posteriori estimates of shear correction factors in multilayered composite cylinders”,Journal of Engineering Mechanics, ASCE,115, 1225–1244.Google Scholar
  190. 190.
    Noor, A.K., Burton, W.S. and Peters, J.M. (1990), “Predictor corrector procedures for stress and free vibration analysis of multilayered composite plates and shells”,Computer Methods in Applied Mechanics and Engineering,82, 341–363.zbMATHCrossRefGoogle Scholar
  191. 191.
    Vel, S.S. and Batra, R.C. (1999), “Analysis solution for rectangular thick plates subjected to arbitrary boundary conditions”,American Institute of Aeronautics and Astronautics Journal,37, 1464–1473.Google Scholar
  192. 192.
    Vel, S.S. and Batra, R.C. (2000), “A generalized plane strain deformation of thick anisotropic composite laminates plates”,International Journal of Solids and Structures,37, 715–733.zbMATHCrossRefGoogle Scholar
  193. 193.
    Zienkiwicz, O.C. (1986),The finite element method, Mc Graw-Hill, London.Google Scholar
  194. 194.
    Abel, J.F. and Popov, E.P. (1968), “Static and dynamic finite element analysis of sandwich structures”, Proceedings of theSecond Conference of Matrix Methods in Structural Mechanics, AFFSL-TR-68-150, 213–245.Google Scholar
  195. 195.
    Monforton, G.R. and Schmidt, L.A. (1968), “Finite element analyses of sandwich plates and cylindrical shells with laminated faces”, Proceedings of theSecond Conference of Matrix Methods in Structural Mechanics, AFFSL-TR-68-150, 573–308.Google Scholar
  196. 196.
    Sharif, P. and Popov, E.P. (1973), “Nonlinear finite element analysis of sandwich shells of reutions”,American Institute of Aeronautics and Astronautics Journal, 715–722.Google Scholar
  197. 197.
    Pryor, C.W. and Barker, R.M. (1971), “A finite element analysis including transverse shear effect for applications to laminated plates”,American Institute of Aeronautics and Astronautics Journal,9, 912–917.Google Scholar
  198. 198.
    Noor, A.K. (1972), “Finite Element Analysis of Anisotropic Plates”,American Institute of Aeronautics and Astronautics Journal,11, 289–307.Google Scholar
  199. 199.
    Mantegazza, P. and Borri, M. (1974), “Elementi finiti per l'analisi di di pannelli anisotropi”,Aerotecnica Missili e Spazio,53, 181–191.Google Scholar
  200. 200.
    Noor, A.K. and Mathers, M.D. (1977), “Finite Element Analysis of Anisotropic Plates”,International Journal for Numerical Methods in Engineering,11, 289–370.zbMATHCrossRefGoogle Scholar
  201. 201.
    Panda, S.C. and Natarayan, (1979), “Finite Element Analysis of Laminated Composites Plates”,International Journal for Numerical Methods in Engineering,14, 69–79.zbMATHCrossRefGoogle Scholar
  202. 202.
    Reddy, J.N. (1979), “Free vibration of antisymmetric angle ply laminated plates including transverse shear deformation by finite element methods”,Journal of Sound and Vibration,66, 565–576.zbMATHCrossRefGoogle Scholar
  203. 203.
    Reddy, J.N. (1980), “A penalty plate-bending element for the analysis of laminated anisotropic composites plates”,International Journal for Numerical Methods in Engineering,12, 1187–1206.CrossRefGoogle Scholar
  204. 204.
    Reddy, J.N. and Chao, W.C. (1981), “A comparison of closed-form and finite-element solutions of thick laminated anisotropic rectangular plates”,Nuclear Engrg. Design, 153–167.Google Scholar
  205. 205.
    Ganapathy, M. and Touratier, M. (1997), “A study on thermal postbuckling behaviors if laminated composite plates using a shear flexible finite element”,Finite Element Analysis and Design,28, 115–135.CrossRefGoogle Scholar
  206. 206.
    Pugh, E.D.L., Hinton, E. and Zienkiewicz, O.C. (1978), “A study of quadrilater plate bending elements with reduced integration”,International Journal for Numerical Methods in Engineering,12, 1059–1079.zbMATHCrossRefGoogle Scholar
  207. 207.
    Hughes, T.J.R., Cohen, M. and Horaun, M. (1978), “Reduced and selective integration techniques in the finite element methods”,Nuclear Engineering and Design,46, 203–222.CrossRefGoogle Scholar
  208. 208.
    Malkus, D.S. and Hughes, T.J.R. (1978), “Mixed finite element methods—reduced and selective integration techniques: a unified concepts”,Computer Methods in Applied Mechanics and Engineering,15, 63–81.CrossRefzbMATHGoogle Scholar
  209. 209.
    Bathe, K.J. and Dvorkin, E.N. (1985), “A four node plate bending element based on Mindlin/Reissner plate theory and mixed interpolation”,International Journal for Numerical Methods in Engineering,21, 367–383.zbMATHCrossRefGoogle Scholar
  210. 210.
    Briossilis, D. (1992), “TheC 0 structural finite elements reformulated”,International Journal for Numerical Methods in Engineering,35, 541–561.CrossRefGoogle Scholar
  211. 211.
    Briossilis, D. (1993), “The four nodeC 0 Mindlin plate bending elements reformulated. Part I: formulation”,Computer Methods in Applied Mechanics and Engineering,107, 23–43.CrossRefGoogle Scholar
  212. 212.
    Briossilis, D. (1993), “The four nodeC 0 Mindlin plate bending elements reformulated. Part II: verification”,Computer Methods in Applied Mechanics and Engineering,107, 45–100.CrossRefGoogle Scholar
  213. 213.
    Brank, B., Perić, D. and Damjanić, F.B. (1995), “On the implementation of a nonlinear four node shell element for thin multilayered elastic shells”,Computational Mechanics,16, 341–359.zbMATHCrossRefGoogle Scholar
  214. 214.
    Auricchio, F. and Taylor, R.L. (1994), “A shear deformable plate elements with an exact thin limits”,Computer Methods in Applied Mechanics and Engineering,118, 493–415.MathSciNetCrossRefGoogle Scholar
  215. 215.
    Auricchio, F. and Sacco, L. (1999), “A mixed-enhanced finite elements for the analysis of laminated composites”,International Journal for Numerical Methods in Engineering,44, 1481–1504.zbMATHCrossRefGoogle Scholar
  216. 216.
    Brank, B. and Carrera, E. (2000), “A Family of Shear-Deformable Shell Finite Elements for Composite Structures”,Computer & Structures,76, 297–297.CrossRefGoogle Scholar
  217. 217.
    Auricchio, F., Lovadina and Sacco, E. (2000), “Finite element for laminated plates”,AIMETA GIMC Conference 195–209, Brescia, Nov. 13–15.Google Scholar
  218. 218.
    Seide, P. and Chaudhury, R.A. (1987), “Triangular finite elements for thick laminated shells”,International Journal for Numerical Methods in Engineering,27, 1747–1755.Google Scholar
  219. 219.
    Kant, T., Owen, D.R.J. and Zienkiewicz O.C. (1982), “Refined higher orderC 0 plate bending element”,Computer & Structures,15, 177–183.zbMATHMathSciNetCrossRefGoogle Scholar
  220. 220.
    Pandya, B.N. and Kant, T. (1988), “Higher-order shear deformable for flexural of sandwich plates. Finite element evaluations”,International Journal of Solids and Structures,24, 1267–1286.zbMATHCrossRefGoogle Scholar
  221. 221.
    Kant T. and Kommineni, J.R. (1989), “Large Amplitude Free Vibration Analysis of Cross-Ply Composite and Sandwich Laminates with a Refined Theory andC 0 Finite Elements”,Computer & Structures,50, 123–134.CrossRefGoogle Scholar
  222. 222.
    Babu, C.S. and Kant, T. (1999), “Two shear deformable finite element models for buckling analysis of skew fiber-reinforced composites and sandwich panels”,Composite Structures,46, 115–124.CrossRefGoogle Scholar
  223. 223.
    Phan, N.D. and Reddy, J.N. (1985), “Analysis Analysis of laminated composites plates using a higher order shear deformation theory”,International Journal for Numerical Methods in Engineering,12, 2201–2219.CrossRefGoogle Scholar
  224. 224.
    Tessler, A. (1991), “A Higher-order plate theory with ideal finite element suitability”,Computer Methods in Applied Mechanics and Engineering,85, 183–205.zbMATHCrossRefGoogle Scholar
  225. 225.
    Tessler, A. and Hughes, T.J.R. (1985), “A three-node Mindlin plate elements with improved transverse shear”,Computer Methods in Applied Mechanics and Engineering,50, 71–101.zbMATHCrossRefGoogle Scholar
  226. 226.
    Tessler, A. (1985), “A priori identification of shear locking and stiffening in in triangular Mindlin element”,Computer Methods in Applied Mechanics and Engineering,53, 183–200.zbMATHCrossRefGoogle Scholar
  227. 227.
    Barboni, R. and Gaudenzi, P. (1992), “A class ofC 0 finite elements for the static and dynamic analysis of laminated plates”,Computer & Structures,44, 1169–1178.CrossRefGoogle Scholar
  228. 228.
    Singh, G., Venkateswara, R. and Ivengar, N.G.R. (1992), “Nonlinear bending of their and thick plates unsymmetrically laminated composite beams using refined finite element models”,Computer & Structures,42, 471–479.CrossRefGoogle Scholar
  229. 229.
    Bhaskar, K. and Varadan, T.K. (1991), “A Higher-order Theory for bending analysis of laminated shells of reution”,Computer & Structures,40, 815–819.zbMATHCrossRefGoogle Scholar
  230. 230.
    Ganapathy, M. and Makhecha, D.P. (2001), “Free vibration analysis of multi-layered composite laminates based on an accurate higher order theory”,Composites Part B,32, 535–543.CrossRefGoogle Scholar
  231. 231.
    Reddy, J.N., Barbero, E.J., and Teply, J.L. (1989), “A plate bending element based on a generalized laminate theory”,International Journal for Numerical Methods in Engineering,28, 2275–2292.zbMATHCrossRefGoogle Scholar
  232. 232.
    Reddy, J.N. (1993), “An evaluation of equivalent single layer and layer-wise theories of composite laminates”,Composite Structures,25, 21–35.CrossRefGoogle Scholar
  233. 233.
    Gaudenzi, P., Barboni, R. and Mannini, A. (1995), “A finite element evaluation of single-layer and multi-layer theories for the analysis of laminated plates”,Computer & Structures 30, 427–440.CrossRefGoogle Scholar
  234. 234.
    Botello, S., Oñate, E., and Miquel, J. (1999), “A layer-wise triangle for analysis of laminated composite plates and shells”,Computer & Structures,70, 635–646.zbMATHCrossRefGoogle Scholar
  235. 235.
    Sacco, E. and Reddy, J.N. (1992), “On the first- and second-order moderate rotation theory of laminated plates”,International Journal for Numerical Methods in Engineering,33, 1–17.zbMATHCrossRefGoogle Scholar
  236. 236.
    Sacco, E. (1992), “A consistent model for first-order moderate rotation plate-theory”,International Journal for Numerical Methods in Engineering,35, 2049–2066.zbMATHCrossRefGoogle Scholar
  237. 237.
    Bruno, D., Lato, S. and Sacco, L. (1992), “Nonlinear behavior od sandwich plates”, Proceedings ofEngineering System Design and Analysis Conference, Istanbul, Turkey,47/6, 115–120.Google Scholar
  238. 238.
    Schmidt, R. and Reddy, J.N. (1988), “A Refined small strain and moderate rotation theory of elastic anisotropic shells”,Journal of Applied Mechanics,55, 611–617.zbMATHGoogle Scholar
  239. 239.
    Palmiero, A.F., Reddy, J.N. and Schmidt, R. (1990), “On a moderate rotation theory of laminated anisotropic shells-Part 1. Theory. And Part-2”,International Journal for Non-linear Mechanics,25, 687–700.CrossRefGoogle Scholar
  240. 240.
    Palmiero, A.F., Reddy, J.N. and Schmidt, R. (1990), “On a moderate rotation theory of laminated anisotropic shells. Part-2. Finite element analysis”,International Journal for Non-linear Mechanics,25, 701–714.CrossRefGoogle Scholar
  241. 241.
    Kapania, R.K. and Mohan, P. (1996), “Static, free vibration and thermal analysis of composite plates and shells using a flat triangular shell element”,Computational Mechanics,17, 343–357.zbMATHCrossRefGoogle Scholar
  242. 242.
    Hammerand, D.C. and Kapania, R.K. (1999), “Thermo-viscoelastic analysis of composite structures using a triangular flat shell element”,American Institute of Aeronautics and Astronautics Journal,37, 238–247.Google Scholar
  243. 243.
    Hammerand, D.C. and Kapania, R.K. (2000), “Geometrically nonlinear shell element for hydro thermo rheologically simple linear visco-elastic materials”,American Institute of Aeronautics and Astronautics Journal,38, 2305–2319.Google Scholar
  244. 244.
    Krätzig, W.B. (1971), “Allgemeine Schalentheorie beliebiger Werkstoffe und Verformungen”,Ingeniere Archieve,40, 311–326.zbMATHCrossRefGoogle Scholar
  245. 245.
    Pietraszkiewicz (1983), “Lagrangian description and incremental formulation in the non-linear theory of thin shells”,International Journal of Non-linear Mechanics,19, 115–140.CrossRefGoogle Scholar
  246. 246.
    Rothert, H. and Dehemel, W. (1987), “Nonlinear analysis of isotropic, orthotropic and laminated plates and shells,”Computer Methods in Applied Mechanics and Engineering,64, 429–446.zbMATHCrossRefGoogle Scholar
  247. 247.
    Gruttman, F., Wagner, W., Meyer, L. and Wriggers, P. (1993), “A nonlinear composite shell element with continuous interlaminar shear stresses”,Computational Mechanics,13, 175–188.CrossRefGoogle Scholar
  248. 248.
    Basar, Y., Ding, Y. and Shultz, R. (1993), “Refined shear deformation models for composite laminates with finite rotation”,International Journal of Solids and Structures,30, 2611–2638.zbMATHCrossRefGoogle Scholar
  249. 249.
    Basar, Y. (1993), “Finite-rotation theories for composite laminates”,Acta Mechanica,98, 159–176.zbMATHMathSciNetCrossRefGoogle Scholar
  250. 250.
    Braun, M., Bischoff, M. and Ramm, E. (1994), “Nonlinear shell formulation for complete three-dimensional constitutive laws including composites and laminates”,Computational Mechanics,15, 1–18.zbMATHCrossRefGoogle Scholar
  251. 251.
    Putcha, N.S. and Reddy, J.N. (1986), “A refined mixed shear flexible finite element for the nonlinear analysis of laminated plates”,Computer & Structures,22, 529–538.zbMATHCrossRefGoogle Scholar
  252. 252.
    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 theory”,International Journal for Numerical Methods in Engineering,12, 2201–2219.Google Scholar
  253. 253.
    Auricchio, F. and Sacco, E. (1999), “Partial Mixed formulation and refined models for the analysis of composite laminates within and FSDT”,Composite Structures,46, 103–113.CrossRefGoogle Scholar
  254. 254.
    Auricchio, F. and Sacco, E. (1999), “MITC finite elements for laminated composites plates”,International Journal for Numerical Methods in Engineering,50, 707–738.Google Scholar
  255. 255.
    Ren, J.G. and Owen, D.R.J. (1989), “Vibration and buckling of laminated plates”,International Journal of Solids and Structures,25, 95–106.zbMATHCrossRefGoogle Scholar
  256. 256.
    Dischiuva, M., Cicorello, A. and Dalle Mura, E. (1985), “A class of multilayered anisotropic plate elements including the effects of transverse shear deformabily”, Proceedings ofAIDAA Conference, Torino, 877–892.Google Scholar
  257. 257.
    Dischiuva, M. (1993), “A general quadrilater, multilayered plate element with continuous interlaminar stresses”,Composite Structures,47, 91–105.CrossRefGoogle Scholar
  258. 258.
    Dischiuva, M. (1995), “A third order triangular multilayered plate elements with continuous interlaminar stresses”,International Journal for Numerical Methods in Engineering,38, 1–26.CrossRefGoogle Scholar
  259. 259.
    Ganapathy, M., Polit, O. and Touratier, M. (1996), “AC 0 eight-node membrane-shear-bending element for geometrically non linear (static and dynamics) analysis of laminated”,International Journal for Numerical Methods in Engineering,39, 3453–3474.CrossRefGoogle Scholar
  260. 260.
    Ganapathy, M., Polit, O. and Touratier, M. (1997), “A study on thermal postbuckling behavior of laminated composite plates using a shear flexible finite element”,Computer Methods in Applied Mechanics and Engineering,28, 115–135.Google Scholar
  261. 261.
    Ganapathy, M., Patel, B.P., Saravan, J. and Touratier, M. (1998), “Application of spline element for large amplitude free vibrations of laminated orthotropic straight/curved beams”,Composites Part B,29, 1–8.CrossRefGoogle Scholar
  262. 262.
    Ganapathy, M. and Patel, B.P. (1999), “Influence of amplitude of vibrations on loss factors of laminated composite beams and plates”,Journal of Sound and Vibration,219, 730–738.CrossRefGoogle Scholar
  263. 263.
    Ganapathy, M., Patel, B.P., Sambandan and Touratier, M. (1999), “Dynamic instability analysis of circular conical shells”,Composite Structures,46, 59–64.CrossRefGoogle Scholar
  264. 264.
    Patel, B.P., Ganapathy, M. and Touratier, M. (1999), “Nonlinear free flexural vibration/postbuckling analysis of laminated orthotropic beams/columns on a two parameter elastic foundation”,Composite Structures,49, 186–196.Google Scholar
  265. 265.
    Ganapathy, M., Patel, B.P., Saravan, J. and Touratier, M. (1999), “Shear Flexible curved spline beam element for static analysis”,Finite Element Analysis and Design, 181–202.Google Scholar
  266. 266.
    Ganapathy, M., Patel, B.P., Polit, O. and Touratier, M. (1999), “AC 1 finite element including transverse shear and torsion warping for rectangular sandwich beams”,International Journal for Numerical Methods in Engineering,45, 47–75.CrossRefGoogle Scholar
  267. 267.
    Polit, O. and Touratier, M. (2000), “Higher order triangular sandwich plate finite elements for linear and nonlinear analyses”,Computer Methods in Applied Mechanics and Engineering,185, 305–324.zbMATHMathSciNetCrossRefGoogle Scholar
  268. 268.
    Cho, M. and Parmerter, R. (1994), “Finite element for composite plate bending based on efficient higher order theories”,American Institute of Aeronautics and Astronautics Journal,32, 2241–2248.zbMATHGoogle Scholar
  269. 269.
    Lee, D. and Waas, A.M. (1996), “Stability analysis of rotating multilayer annular plate with a stationary frictional follower load”,International Journal of Mechanical Sciences,39, 1117–38.CrossRefGoogle Scholar
  270. 270.
    Lee, D., Waas, A.M. and Karnopp, B.H. (1997), “Analysis of rotating multilayer annular plate modeled via a layer-wise zig-zag theory: free vibration and transient analysis”,Composite Structures,66, 313–335.Google Scholar
  271. 271.
    Iscsro, U. (1998), “Eight node zig-zag element for deflection and analysis of plate with general lay up”,Composites Part B, 425–441.Google Scholar
  272. 272.
    Averill, R.C. (1994), “Static and dynamic response of moderately thick laminated beams with damage”,Composite Engineering,4, 381–395.Google Scholar
  273. 273.
    Averill, R.C. (1996), “Thick beam theory and finite element model with zig-zag sublaminate approximations”,American Institute of Aeronautics and Astronautics Journal,34, 1627–1632.zbMATHGoogle Scholar
  274. 274.
    Aitharaju, V.R. and Averill R.C. (1999), “C 0 zig-zag kinematic displacement models for the analysis of laminated composites”,Mechanics of Composite Materials and Structures,6, 31–56.CrossRefGoogle Scholar
  275. 275.
    Cho, Y.B. and Averill, R.C. (2000), “First order zig-zag sublaminate plate theory and finite element model for laminated composite and sandwich panels”,Computer & Structures,50, 1–15.CrossRefGoogle Scholar
  276. 276.
    Jing, H. and Liao, M.L. (1989), “Partial hybrid stress element for the analysis of thick laminate composite plates”,International Journal for Numerical Methods in Engineering,28, 2813–2827.zbMATHCrossRefGoogle Scholar
  277. 277.
    Rao, K.M. and Meyer-Piening, H.R. (1990), “Analysis of thick laminated anisotropic composites plates by the finite element method,”Composite Structures,15, 185–213.CrossRefGoogle Scholar
  278. 278.
    Carrera, E. (1996), “C o Reissner-Mindlin multilayered plate elements including zig-zag and interlaminar stresses continuity,”International Journal for Numerical Methods in Engineering,39, 1797–1820.zbMATHCrossRefGoogle Scholar
  279. 279.
    Carrera, E. and Kröplin, B. (1997), “Zig-Zag and interlaminar equilibria effects in large deflection and postbuckling analysis of multilayered plates,”Mechanics of Composite Materials and Structures,4, 69–94.Google Scholar
  280. 280.
    Carrera, E. (1997), “An improved Reissner-Mindlin-Type model for the electromechanical analysis of multilayered plates including piezo-layers”,Journal of Intelligent Materials System and Structures,8, 232–248.Google Scholar
  281. 281.
    Carrera, E. and Krause, H. (1998), “An investigation on nonlinear dynamics of multilayered plates accounting forC z/0 requirements”,Computer & Structures,69, 463–486.CrossRefGoogle Scholar
  282. 282.
    Carrera, E. (1998), “A refined Multilayered Finite Element Model Applied to Linear and Nonlinear Analysis of Sandwich Structures”Composite Science and Technology,58, 1553–1569.CrossRefGoogle Scholar
  283. 283.
    Carrera, E. and Parisch, H. (1998), “Evaluation of geometrical nonlinear effects of thin and moderately thick multilayered composite shells”,Composite Structures,40, 11–24.CrossRefGoogle Scholar
  284. 284.
    Brank, B. and Carrera, E. (2000), “Multilayered Shell Finite Element with Interlaminar Continuous Shear Stresses: A Refinement of the Reissner-Mindlin Formulation”,International Journal for Numerical Methods in Engineering,48, 843–874.zbMATHCrossRefGoogle Scholar
  285. 285.
    Carrera, E. and Demasi, L. (2000), “An assessment of Multilayered Finite Plate Element in view of the fulfillment of theC z0-Requirements”,AIMETA GIMC Conference, 340–348, Brescia, Nov. 13–15.Google Scholar
  286. 286.
    Carrera, E. and Demasi, L. (2000), “Sandwich Plate Analysis by Finite Plate Element and Reissner Mixed Theorem”,V Int. Conf. on Sandwich Construction,I, 301–312, Zurich, Sept. 5–7. IGoogle Scholar
  287. 287.
    Carrera, E. and Demasi, L., “Multilayered Finite Plate Element based on Reissner Mixed Variational Theorem. Part I: Theory”,International Journal for Numerical Methods in Engineering, to appear.Google Scholar
  288. 288.
    Carrera, E. and Demasi, L., “Multilayered Finite Plate Element based on Reissner Mixed Variational Theorem. Part II: Numerical Analysis”,International Journal for Numerical Methods in Engineering, to appear.Google Scholar
  289. 289.
    Ahamad, S., Iron, B.M. and Zienkiewicz, O.C. (1970), “Analysis of thick and thin shell structures by curved finite elements”,International Journal for Numerical Methods in Engineering,2, 419–471.CrossRefGoogle Scholar
  290. 290.
    Ramm, H. (1977), “A Plate/shell element for large deflection and rotations”, in K.J. Bathe (Eds.),Formulation and Computational Alghorthim in Finite Element Analysis, MIT Press.Google Scholar
  291. 291.
    Kräkeland, B. (1977),Large displacement analysis and shell considering elastic-plastic and elasto-visco-plastic materials, Report No. 776, The Norwegian Institute of Technology, Norway.Google Scholar
  292. 292.
    Bathe, K.J. and Bolourichi, S. (1980), “A geometric and material nonlinear plate and shell elements”,Composite Structures,11, 23–48.zbMATHCrossRefGoogle Scholar
  293. 293.
    Chang, T.Y. and Sawimiphakdi, K. (1981), “Large deformation analysis of laminated shells by finite element method”,Composite Structures,13, 331–340.zbMATHCrossRefGoogle Scholar
  294. 294.
    Chao, W.C. and Reddy, J.N. (1984), “Analysis of laminated composite shells using a degenerated 3D elements”,International Journal for Numerical Methods in Engineering,20, 1991–2007.zbMATHCrossRefGoogle Scholar
  295. 295.
    Liao, C.L. and Reddy, J.N. (1988), “A solid shell transient element for geometrically nonlinear analysis of laminated composite structures,”International Journal for Numerical Methods in Engineering,26, 1843–1854.zbMATHCrossRefGoogle Scholar
  296. 296.
    Liao, C.L. and Reddy, J.N. (1989), “A continuum-based stiffened shell element for geometrically nonlinear analysis of laminated composite structures”,American Institute of Aeronautics and Astronautics Journal,27, 95–101.zbMATHGoogle Scholar
  297. 297.
    Pinsky, P.M. and Kim, K.K. (1986), “A multi-director formulation for elastic-viscoelastic layered shells”,International Journal for Numerical Methods in Engineering,23, 2213–2224.zbMATHCrossRefGoogle Scholar
  298. 298.
    Epstein, M. and Huttelmeier, H.P. (1983), “A finite element formulation for multilayered and thick plates”,Computer & Structures,16, 645–650.CrossRefGoogle Scholar
  299. 299.
    Simo, J.C. and Fox, D.D. (1989), “On a stress resultant geometrically exact shell model. Part I: Formulation and optimal parameterization”,Computer Methods in Applied Mechanics and Engineering,72, 276–304.MathSciNetCrossRefGoogle Scholar
  300. 300.
    Simo, J.C., Fox, D.D. and Rifai, M.S. (1989), “On a stress resultant geometrically exact shell model. Part II: The linear theory, computational aspects”,Computer Methods in Applied Mechanics and Engineering,73, 53–93.zbMATHMathSciNetCrossRefGoogle Scholar
  301. 301.
    Simo, J.C., Fox, D.D. and Rifai, M.S. (1990), “On a stress resultant geometrically exact shell model. Part III: Computational aspects of the nonlinear theory”,Computer Methods in Applied Mechanics and Engineering,79, 21–70.zbMATHMathSciNetCrossRefGoogle Scholar
  302. 302.
    Argyris, J. and Tenek, L. (1994), “Linear and geometrically nonlinear bending of isotropic and multilayered composite plates by the natural mode method”,Computer Methods in Applied Mechanics and Engineering,113, 207–251.zbMATHMathSciNetCrossRefGoogle Scholar
  303. 303.
    Argyris, J. and Tenek, L. (1994), “An efficient and locking free flat anisotropic plate and shell triangular element”,Computer Methods in Applied Mechanics and Engineering,118, 63–119.zbMATHMathSciNetCrossRefGoogle Scholar
  304. 304.
    Argyris, J. and Tenek, L. (1994), “A practicable and locking-free laminated shallow shell triangular element of varying and adaptable curvature”,Computer Methods in Applied Mechanics and Engineering,119, 215–282.zbMATHMathSciNetCrossRefGoogle Scholar
  305. 305.
    Turn, J.Q., Wang, Y.B. and Wang, Y.M. (1996), “Three-dimensional asymptotic finite element method for anisotropic inhomogeneous and laminated plates”,International Journal of Solids and Structures,33, 1939–1960.MathSciNetCrossRefGoogle Scholar
  306. 306.
    Babuska, I., Szabo, B.A. and Actis, R.L. (1992), “Hierarchy models for laminated composites”,International Journal for Numerical Methods in Engineering,33, 503–535.zbMATHMathSciNetCrossRefGoogle Scholar
  307. 307.
    Szabo, B.A. (1986), “Estimation and control of error based onp convergence”,International Journal for Numerical Methods in Engineering,33, 503–535.Google Scholar
  308. 308.
    Szabo, B.A. and Sharman, G.J. (1988), “Hierarchy plate and shell model based onp- extension”,International Journal for Numerical Methods in Engineering,26, 1855–1881.zbMATHCrossRefGoogle Scholar
  309. 309.
    Merk, K.J. (1988), “Hierarchische, kontinuumbasiert Shalenelemente höhere Ordnung”, PhD, Institute für Statik und Dynamik, University of Stuttgart.Google Scholar
  310. 310.
    Liu, J.H. and Surana, K.S. (1994), “Piecewise hierarchical p-version axisymmetric shell element for laminated composites”,Computer & Structures,50, 367–381.zbMATHCrossRefGoogle Scholar
  311. 311.
    Fish, J. and Markolefas, S. (1992), “Thes-version of the finite element method for multilayer laminates”,International Journal for Numerical Methods in Engineering,33, 1081–1105.CrossRefGoogle Scholar
  312. 312.
    Mote, C.D. (1971), “Global-Local finite element”,International Journal for Numerical Methods in Engineering,3, 565–574.zbMATHMathSciNetCrossRefGoogle Scholar
  313. 313.
    Pagano, N.J. and Soni, R.S. (1983), “Global-Local laminate variational model”,International Journal of Solids and Structures,19, 207–228.zbMATHCrossRefGoogle Scholar
  314. 314.
    Noor, A.K. (1986), “Global-Local methodologies and their application to non-linear analysis”,Finite Element Analysis and Design,2, 333–346.CrossRefGoogle Scholar
  315. 315.
    Pian, T.H.H. (1964), “Derivation of element stiffness matrices by assumed stress distributions”,American Institute of Aeronautics and Astronautics Journal, 1333–1336.Google Scholar
  316. 316.
    Pian, T.H.H. and Mau, S.T. (1972), “Some recent studies in assumed-stress hybrid models”, inAdvances in Computational Methods in Structural Mechanics and Design (Eds. Oden, Clought, Yamamoto).Google Scholar
  317. 317.
    Mau, S.T., Tong, P. and Pian, T.H.H. (1972), “Finite element solutions for laminated thick plates”,Journal of Composite Materials,6, 304–311.CrossRefGoogle Scholar
  318. 318.
    Spilker, R.L., Orringer, O. and Witmer, O. (1976), “Use of hybrid/stress finite element model for the static and dynamic analysis of multilayer composite plates and shells”, MIT ASRL TR 181–2.Google Scholar
  319. 319.
    Spilker, R.L., Chou, S.C. and Orringer, O. (1977), “Alternate hybrid-stress elements for analysis of multilayer composite plates”,Journal of Composite Materials,11, 51–70.CrossRefGoogle Scholar
  320. 320.
    Spilker, R.L. (1980), “A hybrid/stress formulation for thick multilayer laminates”, MIT ASRL TR 181-2.Google Scholar
  321. 321.
    Spilker, R.L. (1980), “A hybrid/stress eight-node elements for thin and thick multilayer laminated plates”,International Journal for Numerical Methods in Engineering,18, 801–828.MathSciNetCrossRefGoogle Scholar
  322. 322.
    Moriya, K. (1986), “Laminated plate and shell elements for finite element analysis of advanced fiber reinforced composite structure”,Laminated Composite Plates, in Japanese, Trans. Soc. Mech.,52, 1600–1607.Google Scholar
  323. 323.
    Liou, W.J. and Sun, C.T. (1987), “A three-dimensional hybrid stress isoparametric element for the analysis of laminated composite plates”,Computer & Structures,25, 241–249.zbMATHCrossRefGoogle Scholar
  324. 324.
    Di, S. and Ramm, E. (1993), “Hybrid stress formulation for higher-order theory of laminated shell analysis”,Computer Methods in Applied Mechanics and Engineering,109, 359–376.zbMATHCrossRefGoogle Scholar
  325. 325.
    Rothert, H. and Di, S. (1994), “Geometrically non-linear analysis of laminated shells by hybrid formulation and higher order theory”,Bulletin of the International Journal for Shell and Spatial Structures, IASS,35, 15–32.Google Scholar

Copyright information

© CIMNE,Barcelona(Spain) 2002

Authors and Affiliations

  1. 1.Aerospace DepartmentPolitecnico di TorinoTorinoItaly

Personalised recommendations