The bending behaviour of isotropic and laminated composite and sandwich plates has been analysed using two new C° assumed strain quadrilateral finite element formulations based on a refined form of Reddy's higher-order theory. The assumed strain approach ensures that there are no parasitic spurious zero energy modes and no shear locking. The element performances are evaluated on some standard plate tests involving closed-form solutions and experimental results. All results indicate that the present elements have satisfactory convergence properties, accuracy in the results and freedom from any major defects.
BoseP.ReddyJ. N.Analysis of composite plates using various plate theories. Part 1—formulation and analytical solutionsStruct. Engng and Mechanics, 1998, 6 (6), 583–612.
2.
BoseP.ReddyJ. N.Analysis of composite plates using various plate theories. Part 2—finite element model and numerical resultsStruct. Engng and Mechanics, 1998, 6 (7), 727–746.
3.
VlachoutsisS.Shear correction factors for plates and shellsInt. J. Numer. Meth. Engng, 1992, 33 (7), 1537–1552.
4.
ReddyJ. N.A simple higher-order theory for laminated composite platesTrans. ASME, J. Appl. Mechanics, 1984, 51 (4), 745–752.
5.
RohwerK.Application of higher-order theories to the bending analysis of layered composite platesInt. J. Solids Structs, 1992, 29 (1), 105–119.
6.
BarutA.MadenciE.HeinrichJ.TesslerA.Analysis of thick sandwich construction by a {3–2} order theoryInt. J. Solids Structs, 2001, 38, 6063–6077.
7.
NoorA. K.BurtonW. S.BertC. W.Computational models for sandwich panels and shellsTrans. ASME, Appl. Mechanics Rev., 1996, 49 (3), 155–199.
8.
PlantemaF. J.Sandwich Construction: The Bending and Buckling of Sandwich Beams, Plates and Shells, 1966 (John Wiley, New York).
9.
AllenH. G.Analysis and Design of Structural Sandwich Panels, 1969 (Pergamon Press, Oxford).
10.
ZenkertD.An Introduction to Sandwich Construction, 1995 (EMAS Publications, West Midlands).
11.
VinsonJ. R.The Behaviour of Sandwich Structures of Isotropic and Composite Materials, 1999 (Technomic, USA).
12.
MeunierM.ShenoiR. A.Free vibration analysis of composite sandwich platesProc. Instn Mech. Engrs, Part C: J. Mechanical Engineering Science, 1999, 213 (C7), 715–727.
13.
MeunierM.ShenoiR. A.Dynamic analysis of composite sandwich plates with damping modelled using high-order shear deformation theoryComposite Structs, 2001, 54, 243–254.
AzarJ. J.Bending theory for multilayer orthotropic sandwich platesAm. Inst. Aeronaut. Astronaut. J., 19686 (11), 2166–2169.
16.
KanematsuH. H.HiranoY.lyamaH.Bending and vibration of CFRP-faced rectangular sandwich platesComposite Structs, 1988, 10, 145–163.
17.
PaganoN. J.Exact solutions for rectangular bidirectional composites and sandwich platesJ. Composite Mater., 1970, 4, 20–34.
18.
SrinivasS.RaoA. K.Bending, vibration and buckling of simply supported thick orthotropic rectangular plates and laminatesInt. J. Solids Structs, 1970, 6, 1463–1481.
19.
YangH. T. Y.SaigalS.MasudA.KapaniaR. K.A survey of recent shell finite elementsInt. J. Numer. Meth. Engng, 2000, 47 (1–3), 101–127.
20.
KhatuaT. P.SheungY. K.Triangular element for multi-layer sandwich platesJ. Engng Mechanics, ASCE, 1972, 98, 1225–1238.
21.
KhatuaT. P.CheungY. K.Bending and vibration of multi-layer sandwich beams and platesInt. J. Numer. Meth. Engng, 1973, 6, 11–24.
22.
NayakA. K.MoyS. S.J.ShenoiR. A.Damping prediction of sandwich plates using the finite element method. In 2nd International Conference onTheoretical, Applied, Computational and Experimental Mechanics (ICTACEM 2001), IIT Kharagpur, India, 2001, paper 104, pp.1–12.
23.
MawenyaA. S.DaviesJ. D.Finite element bending analysis of multi-layer platesInt. J. Numer. Meth. Engng, 1974, 8, 215–225.
24.
BatheK. J.DvorkinE. N.A four-node plate bending element based on Mindlin/Reissner plate theory and a mixed interpolationInt. J. Numer. Meth. Engng, 1985, 21, 367–383.
25.
HuangH. C.HintonE.A nine node Lagrangian Mindlin plate element with enhanced shear interpolationEngng Computations, 1984, 1, 369–379.
26.
HintonE.HuangH. C.A family of quadrilateral Mindlin plate elements with substitute shear strain fieldsComputers and Structs, 1986, 23 (3), 409–431.
27.
SimoJ. C.HughesT. J. R.On the variational foundations of assumed strain methodsTrans. ASME, J. Appl. Mechanics, 1986, 53, 51–54.
28.
OwenD. R.J.LiZ. H.A refined analysis of laminated plates by finite element displacement methods. I. Fundamentals and static analysisComputers and Structs, 1987, 26 (6), 907–914.
29.
ReddyJ. N.RobbinsD. H.JrTheories and computational models for composite laminatesTrans. ASME, Appl. Mechanics Rev., 1994, 47 (6), 147–169.
30.
Di SciuvaM.An improved shear deformation theory for moderately thick multilayered anisotropic shells and platesTrans. ASME, J. Appl. Mechanics, 1987, 54, 589–596.
31.
IcardiU.Eight-noded zig-zag element for deflection and stress analysis of plates with general lay-upComposites Part B: Engng, 1998, 29 (4), 425–441.
32.
RenJ. G.HintonE.The finite element analysis of homogeneous and laminated composite plates using a simple higher-order theoryCommuns in Appl. Numer. Meth., 1986, 2 (2), 217–228.
33.
AverillR. C.ReddyJ. N.An assessment of four noded plate finite elements based on a generalized third order theoryInt. J. Numer. Meth. Engng, 1992, 33, 1553–1572.
34.
NayakA. K.MoyS. S.J.ShenoiR. A.Free vibration analysis of composite sandwich plates based on Reddy's higher order theoryComposites Part B: Engng, 2002, 33, 505–519.
35.
NayakA. K.ShenoiR. A.MoyS. S. J.Damping prediction of composite sandwich plates using assumed strain plate bending elements based on Reddy's higher-order theory. In 43rd AIAA/ASME/ASCE/AHS Conference onStructures, Structural Dynamics and Materials, Denver, Colorado, April 2002, paper 1243, pp. 1–11.
36.
NayakA. K.ShenoiR. A.MoyS. S. J.Analysis of damped composite sandwich plates using plate bending elements with substitute shear strain fields based on Reddy's higher-order theoryProc. Instn Mech. Engrs, Part C: J. Mechanical Engineering Science, 2002, 216 (C5), 591–606.
37.
CawleyP.AdamsR. D.The predicted and experimental natural modes of free-free CFRP platesJ. Composite Mater., 1978, 12, 336–347.
38.
LeeF. J.FanY. J.Bending and vibration analysis of composite sandwich platesComputers and Structs, 1996, 60 (1), 103–112.
