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 0 z -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.
Similar content being viewed by others
Abbreviations
- 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
- N l :
-
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
- 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.
References
Bogdonovic, A.E. and Sierakowsky, R. (1999), “Composite Materials and Structures: Science Technology and Application”,Applied Mechanics Review,52, 551–366.
Naghdi, P.M. (1956), “A survey of recent progress in the theory of elastic shells”,Applied Mechanics Review,9, 365–368.
Ambartusumyan, S.A. (1962), “Contributions to the theory of anisotropic layered shells”,Applied Mechanics Review,15, 345–249.
Bert, C.W.E. (1984), “A critical evaluations of new plate theories applied to laminated composites”,Composite Structures,38, 329–347.
Reissner, E. (1985), “Reflections on the theory of elastic plates”,Applied Mechanics Review,38, 1453–1464.
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.
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.
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.
Kapania, R.K. (1989), “A Review on the Analysis of Laminated Shells”,Journal of Pressure Vessel Technology,111, 88–96.
Noor, A.K. and Burton, W.S. (1989), “Assessment of shear deformation theories for multilayered composite plates”,Applied Mechanics Review,41, 1–18.
Reddy, J.N. (1989), “On computational models for composite laminate”,International Journal for Numerical Methods in Engineering,27, 361–382.
Noor, A.K. and Burton, W.S. (1990), “Assessment of computational models for multilayered composite shells”,Applied Mechanics Review,43, 67–97.
Reddy, J.N. and Robbins, D.H. (1994), “Theories and computational models for composite laminates”,Applied Mechanics Review,47, 147–165.
Noor, A.K., Burton, S. and Bert, C.W. (1996), “Computational model for sandwich panels and shells”,Applied Mechanics Review,49, 155–199.
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.
Carrera, E. (2000), “An assessment of mixed and classical theories for thermal stress analysis of orthotropic plates”,Journal of Thermal Stress,23, 797–831.
Carrera, E. (2000), “An assessment of mixed and classical theories on global and local response of multilayered orthotropic plates”,Composite Structures,40, 183–198.
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.
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.
Carrera, E., “A Historical Review of Zig-Zag Theories for Multilayered Plates and Shell”,Applied Mechanics Review, to be printed.
Goldenvaizer, A.L. (1961),Theory of thin elastic shells, International Series of Monograph in Aeronautics and Astronautics, Pergamon Press, New York.
Kraus, H. (1967),Thin elastic shells, John Wiley, N.Y.
Lekhnitskii, S.G. (1968),Anisotropic Plates, 2nd Ed., Translated from the 2nd Russian Ed. by S.W. Tsai and Cheron, Bordon and Breach.
Ambartsumian, S.A. (1969),Theory of anisotropic plates, Translated from Russian by T. Cheron and Edited by J.E. Ashton Tech. Pub. Co.
Jones, R.M. (1975),Mechanics of Composite Materials, McGraw-Hill, New York.
Librescu, L. (1975),Elasto-statics and Kinetics of Anisotropic and Heterogeneous Shell-Type Structures, Noordhoff Int., Leyden, Netherland.
Palazotto, A.N. and Dennis, S.T. (1992),Nonlinear analysis of shell structures, AIAA Series.
Reddy, J.N. (1997),Mechanics of Laminated Composite Plates, Theory and Analysis, CRC Press.
Pagano, N.J. (1969), “Exact solutions for Composite Laminates in Cylindrical Bending”,Journal of Composite Materials,3, 398–411.
Pagano, N.J. (1970), “Exact solutions for rectangular bi-direction composites and sandwich plates”,Journal of Composite Materials,4, 20–34.
Pagano, N.J. and Hatfield, S.J. (1972), “Elastic Behavior of Multilayered Bidirectional Composites”,American Institute of Aeronautics and Astronautics Journal,10, 931–933.
Noor, A.K. and Rarig, P.L. (1974), “Three-Dimensional Solutions of Laminated Cylinders”,Computer Methods in Applied Mechanics and Engineering,3, 319–334.
Noor, A.K. (1973), “Free vibrations of multilayerd composite plates”,American Institute of Aeronautics and Astronautics Journal,11, 1038–1039.
Pagano, N.J. (1978), “Stress fields in composite laminates”,International Journal of Solids and Structures,14, 385–400.
Ren, J.G. (1987), “Exact Solutions for Laminated Cylindrical Shells in Cylindrical Bending”,Composite Science and Technology,29, 169–187.
Varadan, T.K. and Bhaskar, K. (1991), “Bending of Laminated Orthotropic Cylindrical Shells—An Elasticity Aroach”,Composite Structures,17, 141–156.
Bhaskar, K. and Varadan, T.K. (1993), “Exact elasticity solution for Laminated Anisotropic Cylindrical Shells”, JAM,60, 41–47.
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.
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.
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.
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.
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.
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.
Koiter, W.T. (Ed.) (1960), “Theory of thin elastic shells”, Proceedings ofFirst IUTAM Symposium, Delft 1959, North Holland.
Niordson, F.I. (Ed.) (1967), “Theory of thin shells”, Proceedings ofSecond IUTAM Symposium, Copenaghen 1967, Springer Verlag, Berlin.
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.
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.
John, F. (1967), “Refined interior shell equations”, Proceedings ofSecond Symposium on the Theory of Thin Elastic Shells, Cophenagen, Springer Verlag, 1–14.
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.
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.
Cosserat, E. and Cosserat, F. (1999), “Theories des corps deformable”,In Traite de Physique, 2nd Ed., Chwolson, Paris.
Cicala, P. (1959), “Sulla teoria elastica della parete sottile”,Giornale del Genio Civile, fascicoli 4, 6 e 9.
Cicala, P. (1965),Systematic approach to linear shell theory, Levrotto & Bella, Torino.
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.
Reissner, E. (1984), “On a certain mixed variational theory and a proposed application”,International Journal for Numerical Methods in Engineering,20, 1366–1368.
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.
Reissner, E. (1986), “On a certain mixed variational theorem and on laminated elastic shell theory”, Proceedings of theEuromech-Colloquium,219, 17–27.
Washizu, K. (1968),Variational Methods in Elasticity and Plasticity, Pergamon Press, N.Y.
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.
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.
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.
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.
Carrera, E. (1997), “C 0 z Requirements—Models for the two dimensional analysis of multilayered structures”,Composite Structures,37, 373–384.
Librescu, L. (1987), “Refined geometrically non-linear theories of anisotropic laminated shells”,Quarterly of Applied Mathematics,55, 1–22.
Sun, C.T. and Chin, H. (1987), “Analysis of asymmetric composite laminates”,American Institute of Aeronautics and Astronautics Journal,26, 714–718.
Carrera, E. (1991), “Postbuckling behaviors of multilayered shells”,Ph. Dissertation, DIASP, Politecnico di Torino.
Chen, H.P. and Shu, J.C. (1992), “Cylindrical bending of unsymmetric composite laminates”,American Institute of Aeronautics and Astronautics Journal,30, 1438–1440.
Carrera, E. (1993), “Nonlinear Response of asymmetrically laminated plates in cylindrical bending”,American Institute of Aeronautics and Astronautics Journal,31, 1353–1357.
Carrera, E. (1994), “Reply by the author to C.T. Sun”,American Journal of Aeronautics and Astronautics,32, 2135–2136.
Cauchy, A.L. (1828), “Sur l'equilibre et le mouvement d'une plaque solide”,Execrises de Matematique,3, 328–355.
Poisson, S.D. (1829), “Memoire sur l'equilibre et le mouvement des corps elastique”,Mem. Acad. Sci.,8, 357.
Kirchhoff, G. (1850), “Über das Gleichgewicht und die Bewegung einer elastischen Scheibe”,J. Angew. Math.,40, 51–88.
Love, A.E.H. (1927),The mathematical theory of elasticity, 4th edition, Cambridge University Press, Cambridge.
Reissner, E. and Stavsky, Y. (1961), “Bending and stretching of certain type of heterogeneous elastic plates”,Journal of Applied Mechanics,9, 402–408.
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.
Reissner, E. (1945), “The effect of transverse shear deformation on the bending of elastic plates”,Journal of Applied Mechanics,12, 69–76.
Mindlin (1951), “Influence of rotatory inertia and shear in flexural motions of isotropic elastic plates”,Journal of Applied Mechanics,18, 1031–1036.
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.
Vlasov, B.F. (1957), “On the equations of Bending of plates”,Dokla Ak. Nauk. Azerbeijanskoi-SSR,3, 955–979.
Reddy, J.N. (1984b), “A simple higher order theories for laminated composites plates”,Journal of Applied Mechanics,52, 745–742.
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.
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.
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.
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.
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.
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.
Touratier, M. (1988), “A refined theory for thick composites plates”,Mechanics Research Communications,15, 229–236.
Touratier, M. (1989), “Un modele simple et efficace em mechanique dees structures composites”,C.R. Adad. Sci. Paris,309, 933–938.
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.
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.
Touratier, M. (1991), “An efficient standard plate theory”, IJES,29, 901–916.
Gaudenzi, P. (1992), “A general formulation of higher order theories for the analysis of laminated plates”,Composite Structures,20, 103–112.
Touratier, M. (1992), “A refined theory of laminated shallow shells”,International Journal of Solids and Structures,29, 1401–1415.
Touratier, M. (1992), “A generalization of shear deformation theories for axisymmetric multilayered shells”,International Journal of Solids and Structures,29, 1379–1399.
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.
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.
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.
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.
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.
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.
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.
Hsu, T. and Wang, J.T. (1971), “Rotationally Symmetric Vibrations of Orthotropic Layered Cylindrical Shells,”Journal of Sound and Vibration,16, 473–487.
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.
Srinivas, S. (1973), “A refined analysis of composite laminates,”Journal of Sound and Vibration,30, 495–507.
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.
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.
Carrera, E. (2000), “A Priori vs a Posteriori Evaluation of Transverse Stresses in Multilayered Orthotropic Plates,”Composite Structures 48, 245–260.
Lekhnitskii, S.G. (1935), “Strength Calculation of Composite Beams”,Vestnik Inzhen. i Tekhnikov, No.9.
Ambartsumian, S.A. (1958), “On a theory of bending of anisotropic plates”,Investiia Akad. Nauk SSSR, Ot. Tekh. Nauk., No 4.
Ambartsumian, S.A. (1958), “On a general theory of anisotropic shells,”PMM,22, No. 2, 226–237.
Ambartsumian, S.A. (1961),Theory of anisotropic shells, Fizmatzig, Moskwa; Translated from Russian, NASA TTF-118, 1964.
Ambartsumian, S.A. (1962), “Contributions to the theory of anisotropic layered shells,”Applied Mechanics Review,15, 245–249.
Ambartsumian, S.A. (1969),Theory of anisotropic plates, Translated from Russian by T. Cheron and Edited by J.E. Ashton Tech. Pub. Co.
Ren, J.G. (1986), “A new theory of laminated plates,”Composite Science and Technology,26, 225–239.
Ren, J.G. (1986), “Bending theory of laminated plates,”Composite Science and Technology,27, 225–248.
Whitney, J.M. (1969), “The effects of transverse shear deformation on the bending of laminated plates,”Journal of Composite Materials,3, 534–547.
Rath, B.K. and Das, Y.C. (1973), “Vibration of Layered Shells,”Journal of Sound and Vibration,28, 737–757.
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.
Yu, Y.Y. (1959), “A new theory of elastic sandwich plates. One dimensional case,”Journal of Applied Mechanics,37, 1031–1036.
Chou and Carleone (1973), “Transverse Shear in Laminated Plates Theories,”American Institute of Aeronautics and Astronautics Journal,11, 1333–1336.
Dischiuva, M. (1984), “A refinement of the transverse shear deformation theory for multilayered plates,”Aerotecnica Missili e Spazio,63, 84–92.
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.
Dischiuva, M. (1987), “An improved shear deformation theory for moderately thick multilayered anisotropic shells and plates,”Journal of Applied Mechanics,54, 589–596.
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.
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.
Bhashar, B. and Varadan, T.K. (1989), “Refinement of Higher-Order laminated plate theories”,American Institute of Aeronautics and Astronautics Journal,27, 1830–1831.
Savithri, S. and Varadan, T.K. (1990), “Refinement of Higher-Order laminated plate theories,”American Institute of Aeronautics and Astronautics Journal,28, 1842–1843.
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.
Li, X. and Liu, D. (1994), “Zig-zag theories for composites laminates,”American Institute of Aeronautics and Astronautics Journal,33, 1163–1165.
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.
Touratier, M. (1992), “A generalization of shear deformation theories for axisymmetric multilayered shells,”International Journal of Solids and Structures,29, 1379–1399.
Touratier, M. (1992), “A refined theories for laminated shallow shells,”International Journal of Solids and Structures,29, 1401–1415.
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.
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.
Idlbi, A., Karama, M. and Touratier, M. (1997), “Comparison of various laminated plate theories,”Composite Structures,37, 173–184.
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.
Ossodzow, C., Touratier, M. and Muller, P. (1999), “Deep doubly curved multilayered shell theory,”American Institute of Aeronautics and Astronautics Journal,37, 100–109.
Murakami, H. (1984), “A laminated beam theory with interlayer slip,”Journal of Applied Mechanics,51, 551–559.
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.
Murakami, H. (1986), “Laminated composite plate theory with improved in-plane responses,”Journal of Applied Mechanics,53, 661–666.
Toledano, A. and Murakami, H. (1987), “A composite plate theory for arbitrary laminate configurations,”Journal of Applied Mechanics,54, 181–189.
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.
Murakami, H. and Yamakawa, J. (1996), “Dynamic response of plane anisotropic beams with shear deformation,”ASCE Journal of Engineering Mechanics,123, 1268–1275.
Murakami, H., Reissner, E. and Yamakawa, J. (1996), “Anisotropic beam theories with shear deformation,”Journal of Applied Mechanics,63, 660–668.
Carrera, E. (1998), “Mixed Layer-Wise Models for Multilayered Plates Analysis,”Composite Structures,43, 57–70.
Carrera, E. (1998), “Evaluation of Layer-Wise Mixed Theories for Laminated Plates Analysis,”American Institute of Aeronautics and Astronautics Journal,26, 830–839.
Carrera, E. (1998), “Layer-Wise Mixed Models for Accurate Vibration Analysis of Multilayered Plates,”Journal of Applied Mechanics,65, 820–828.
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.
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.
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.
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.
Carrera, E. (1999), “Transverse Normal Stress Effects in Multilayered Plates,”Journal of Applied Mechanics,66, 1004–1012.
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.
Messina, A. (2000), “Two generalized higher order theories in free vibration studies of multilayered plates,”Journal of Sound and Vibration,242, 125–150.
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.
Jing, H. and Tzeng, K.G. (1993b), “Refined Shear Deformation Theory of Laminated Shells,”American Institute of Aeronautics and Astronautics Journal,31, 765–773.
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.
Reissner, E. (1950), “On variational theorem in elasticity,”Journal of Mathematics & Physics,20, 90.
Zenkour, A.M. (1998), “Vibration of axisymmetric shear deformable cross-ply laminated cylindrical shells-a variational approach,”Composite Structures,36, 219–231.
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.
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.
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.
Fettahlioglu, O.A. and Steele, C.R. (1974), “Asymptotic Solutions for Orthotropic Non-homogeneous Shells of Reution”,Journal of Applied Mechanics,41, 753–758.
Berdichevsky, V.L. (1979), “Variational-Asymptotic Method of Shell Theory Construction”,PMM,43, 664–667.
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.
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.
Berdichevsky, V.L. and Misyura, V. (1992), “Effect of Accuracy Loss in Classical Shell Theory”,Journal of Applied Mechanics,59, S217-S223.
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.
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.
Wang, S. and Tarn, J. (1994), “A three-dimensional analysis of anisotropic inhomogeneous laminated plates”,International Journal of Solids and Structures,31, 497–415.
Satyrin, V.G. and Hodges, D.H. (1996), “On asymptotically correct linear laminated plate theory”,International Journal of Solids and Structures,33, 3649–3671.
Satyrin, V.G. (1997), “Derivation of Plate Theory Accounting Asymptotically Correct Shear Deformation”,Journal of Applied Mechanics,64, 905–915.
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.
Antona, E. and Frulla, G. (2001), “Cicala's asymptotic approach to the linear shell theory”,Composite Structures,52, 13–26.
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.
Green, A.E. and Naghdi, P.M. (1982), “A theory of laminated composite plates”,Journal of Applied Mathematics,29, 1–23.
Sun, C.T., Achenbach, J.D. and Herrmann (1968), “Continuum theory for a laminated medium”,Journal of Applied Mechanics, 467–475.
Grot, R.A. (1972), “A Continuum model for curvilinear laminated composites”,International Journal of Solids and Structures,8, 439–462.
Epstein, M. and Glockner, P.G. (1977), “Nonlinear analysis of multilayred shells”,International Journal of Solids and Structures,13, 1081–1089.
Esptein, M. and Glockner, P.G. (1979), “Multilayerd shells and directed surfaces”,International Journal of Engineering Sciences,17, 553–562.
Noor, A.K. and Rarig, P.L. (1974), “Three-Dimensional solutions of laminated cylinders”,Computer Methods in Applied Mechanics and Engineering,3, 319–334.
Malik, M. (1994), “Differential quadrature method in computational mechanics: new development and applications”,Ph.D. dissertation, University of Oklahoma, Oklahoma.
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.
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.
Davi, G. (1996), “Stress field in general composite laminates”,American Institute of Aeronautics and Astronautics Journal,34, 2604–2608.
Davi, G. and Milazzo, A. (1999), “Bending Stress fields in composite laminate beams by a boundary integral formulation”,Composite Structures,71, 267–276.
Milazzo, A. (2000), “Interlaminar Stress in Laminated Composite Beam-Type Structures Under Shear/Bending”,American Institute of Aeronautics and Astronautics Journal,38, 687–694.
Noor, A.K. and Burton, W.S. (1989a), “Stress and Free Vibration Analyses of Multilayered Composite Plates”,Composite Structures,11, 183–204.
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.
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.
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.
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.
Zienkiwicz, O.C. (1986),The finite element method, Mc Graw-Hill, London.
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.
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.
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.
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.
Noor, A.K. (1972), “Finite Element Analysis of Anisotropic Plates”,American Institute of Aeronautics and Astronautics Journal,11, 289–307.
Mantegazza, P. and Borri, M. (1974), “Elementi finiti per l'analisi di di pannelli anisotropi”,Aerotecnica Missili e Spazio,53, 181–191.
Noor, A.K. and Mathers, M.D. (1977), “Finite Element Analysis of Anisotropic Plates”,International Journal for Numerical Methods in Engineering,11, 289–370.
Panda, S.C. and Natarayan, (1979), “Finite Element Analysis of Laminated Composites Plates”,International Journal for Numerical Methods in Engineering,14, 69–79.
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.
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.
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.
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.
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.
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.
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.
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.
Briossilis, D. (1992), “TheC 0 structural finite elements reformulated”,International Journal for Numerical Methods in Engineering,35, 541–561.
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.
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.
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.
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.
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.
Brank, B. and Carrera, E. (2000), “A Family of Shear-Deformable Shell Finite Elements for Composite Structures”,Computer & Structures,76, 297–297.
Auricchio, F., Lovadina and Sacco, E. (2000), “Finite element for laminated plates”,AIMETA GIMC Conference 195–209, Brescia, Nov. 13–15.
Seide, P. and Chaudhury, R.A. (1987), “Triangular finite elements for thick laminated shells”,International Journal for Numerical Methods in Engineering,27, 1747–1755.
Kant, T., Owen, D.R.J. and Zienkiewicz O.C. (1982), “Refined higher orderC 0 plate bending element”,Computer & Structures,15, 177–183.
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.
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.
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.
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.
Tessler, A. (1991), “A Higher-order plate theory with ideal finite element suitability”,Computer Methods in Applied Mechanics and Engineering,85, 183–205.
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.
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.
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.
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.
Bhaskar, K. and Varadan, T.K. (1991), “A Higher-order Theory for bending analysis of laminated shells of reution”,Computer & Structures,40, 815–819.
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.
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.
Reddy, J.N. (1993), “An evaluation of equivalent single layer and layer-wise theories of composite laminates”,Composite Structures,25, 21–35.
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.
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.
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.
Sacco, E. (1992), “A consistent model for first-order moderate rotation plate-theory”,International Journal for Numerical Methods in Engineering,35, 2049–2066.
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.
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.
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.
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.
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.
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.
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.
Krätzig, W.B. (1971), “Allgemeine Schalentheorie beliebiger Werkstoffe und Verformungen”,Ingeniere Archieve,40, 311–326.
Pietraszkiewicz (1983), “Lagrangian description and incremental formulation in the non-linear theory of thin shells”,International Journal of Non-linear Mechanics,19, 115–140.
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.
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.
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.
Basar, Y. (1993), “Finite-rotation theories for composite laminates”,Acta Mechanica,98, 159–176.
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.
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.
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.
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.
Auricchio, F. and Sacco, E. (1999), “MITC finite elements for laminated composites plates”,International Journal for Numerical Methods in Engineering,50, 707–738.
Ren, J.G. and Owen, D.R.J. (1989), “Vibration and buckling of laminated plates”,International Journal of Solids and Structures,25, 95–106.
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.
Dischiuva, M. (1993), “A general quadrilater, multilayered plate element with continuous interlaminar stresses”,Composite Structures,47, 91–105.
Dischiuva, M. (1995), “A third order triangular multilayered plate elements with continuous interlaminar stresses”,International Journal for Numerical Methods in Engineering,38, 1–26.
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.
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.
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.
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.
Ganapathy, M., Patel, B.P., Sambandan and Touratier, M. (1999), “Dynamic instability analysis of circular conical shells”,Composite Structures,46, 59–64.
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.
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.
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.
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.
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.
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.
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.
Iscsro, U. (1998), “Eight node zig-zag element for deflection and analysis of plate with general lay up”,Composites Part B, 425–441.
Averill, R.C. (1994), “Static and dynamic response of moderately thick laminated beams with damage”,Composite Engineering,4, 381–395.
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.
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.
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.
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.
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.
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.
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.
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.
Carrera, E. and Krause, H. (1998), “An investigation on nonlinear dynamics of multilayered plates accounting forC /0 z requirements”,Computer & Structures,69, 463–486.
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.
Carrera, E. and Parisch, H. (1998), “Evaluation of geometrical nonlinear effects of thin and moderately thick multilayered composite shells”,Composite Structures,40, 11–24.
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.
Carrera, E. and Demasi, L. (2000), “An assessment of Multilayered Finite Plate Element in view of the fulfillment of theC 0 z -Requirements”,AIMETA GIMC Conference, 340–348, Brescia, Nov. 13–15.
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. I
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.
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.
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.
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.
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.
Bathe, K.J. and Bolourichi, S. (1980), “A geometric and material nonlinear plate and shell elements”,Composite Structures,11, 23–48.
Chang, T.Y. and Sawimiphakdi, K. (1981), “Large deformation analysis of laminated shells by finite element method”,Composite Structures,13, 331–340.
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.
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.
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.
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.
Epstein, M. and Huttelmeier, H.P. (1983), “A finite element formulation for multilayered and thick plates”,Computer & Structures,16, 645–650.
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.
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.
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.
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.
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.
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.
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.
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.
Szabo, B.A. (1986), “Estimation and control of error based onp convergence”,International Journal for Numerical Methods in Engineering,33, 503–535.
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.
Merk, K.J. (1988), “Hierarchische, kontinuumbasiert Shalenelemente höhere Ordnung”, PhD, Institute für Statik und Dynamik, University of Stuttgart.
Liu, J.H. and Surana, K.S. (1994), “Piecewise hierarchical p-version axisymmetric shell element for laminated composites”,Computer & Structures,50, 367–381.
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.
Mote, C.D. (1971), “Global-Local finite element”,International Journal for Numerical Methods in Engineering,3, 565–574.
Pagano, N.J. and Soni, R.S. (1983), “Global-Local laminate variational model”,International Journal of Solids and Structures,19, 207–228.
Noor, A.K. (1986), “Global-Local methodologies and their application to non-linear analysis”,Finite Element Analysis and Design,2, 333–346.
Pian, T.H.H. (1964), “Derivation of element stiffness matrices by assumed stress distributions”,American Institute of Aeronautics and Astronautics Journal, 1333–1336.
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).
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.
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.
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.
Spilker, R.L. (1980), “A hybrid/stress formulation for thick multilayer laminates”, MIT ASRL TR 181-2.
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.
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.
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.
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.
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.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Carrera, E. Theories and finite elements for multilayered, anisotropic, composite plates and shells. ARCO 9, 87–140 (2002). https://doi.org/10.1007/BF02736649
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF02736649