Browse > Article
http://dx.doi.org/10.12989/sem.2008.28.5.603

A laminated composite plate finite element a-priori corrected for locking  

Filho, Joao Elias Abdalla (Programa de POs-Graduacgo em Engenharia Mecanica, Pontificia Univ Catolica do Parana (PUCPR) Rua Imaculada Conceicao)
Belo, Ivan Moura (Programa de POs-Graduacao em Engenharia Mecanica, Pontificia Univ Catolica do Parana (PUCPR) Rua Imaculada Conceicao)
Pereira, Michele Schunemann (Programa de POs-Graduacao em Engenharia Mecanica, Pontificia Univ Catolica do Parana (PUCPR) Rua Imaculada Conceicao)
Publication Information
Structural Engineering and Mechanics / v.28, no.5, 2008 , pp. 603-633 More about this Journal
Abstract
A four-node plate finite element for the analysis of laminated composites which is developed using strain gradient notation is presented. The element is based on a first-order shear deformation theory and on the equivalent lamina assumption. Strains and stresses can be calculated at different points through the thickness of the plate. They are averaged values due to the equivalent lamina assumption. A shear correction factor is used as the transverse shear strain is taken to be constant over the plate thickness while its actual variation is parabolic. Strain gradient notation, which is physically interpretable, allows for the detailed a-priori analysis of the finite element model. The polynomial expansions are inspected and spurious terms responsible for modeling errors are identified in the shear strains polynomial expansions. The element is corrected by simply removing the spurious terms from the shear strains expansions. The element is implemented into a FORTRAN finite element code in two versions; namely, with and without spurious terms. Results are compared to show the effects of the spurious terms on the solutions. It is also shown that a refined mesh composed of corrected elements provides solutions which approximate very well the analytical solutions, validating the procedure.
Keywords
laminated composites; plates; finite elements; locking; strain gradient notation; parasitic shear;
Citations & Related Records

Times Cited By Web Of Science : 0  (Related Records In Web of Science)
Times Cited By SCOPUS : 0
연도 인용수 순위
  • Reference
1 Aagaah, M.R., Mahinfalah, M. and Jazar, G.N. (2003), "Linear static analysis and finite element modeling for laminated composite plates using third order shear deformation theory", Comp. Struct., 62, 27-39   DOI   ScienceOn
2 Bathe, K.J. and Dvorkin, E. (1985), "A four-node plate bending element based on Mindlin/Reissner plate theory and a mixed interpolation", Int. J. Numer. Meth. Eng., 21, 367-383   DOI   ScienceOn
3 Bose, P. and Reddy, J.N. (1998), "Analysis of composite plates using various plate theories, Part 1: Formulation and analytical solutions", Struct. Eng. Mech., 6(6), 583-612   DOI   ScienceOn
4 Bose, P. and Reddy, J.N. (1998), "Analysis of composite plates using various plate theories, Part 2: Finite element model and numerical results", Struct. Eng. Mech., 6(7), 727-746   DOI   ScienceOn
5 Dow, J.O. and Abdalla, $F^{\circ}$ JE (1994), "Qualitative errors in laminated composite plate models", Int. J. Numer. Meth. Eng., 37, 1215-1230   DOI   ScienceOn
6 Dow, J.O. and Byrd, D.E. (1988), "The identification and elimination of artificial stiffening errors in finite elements", Int. J. Numer. Meth. Eng., 26, 743-762   DOI   ScienceOn
7 Dow, J.O. and Byrd, D.E. (1990), "Error estimation procedure for plate bending elements", AIAA J., 28, 685-693   DOI
8 Dow, J.O., Ho, T.H. and Cabiness, H.D. (1985), "A generalized finite element evaluation procedure", J. Struct. Eng., ASCE, 111(2), 435-452   DOI   ScienceOn
9 Hughes, T.J.R., Cohen, M. and Haroun, M. (1978), "Reduced and selective integration techniques in finite element analysis of plates", Nuclear Eng. Des., 46, 203-222   DOI   ScienceOn
10 Hughes, T.J.R., Taylor, R.L. and Kanoknukulchai, W. (1977), "A simple and efficient finite element for plate bending", Int. J. Numer. Meth. Eng., 11, 1529-1543   DOI   ScienceOn
11 Sheikh, A.H. and Chakrabarti, A. (2003), "A new plate bending element based on higher-order shear deformation theory for the analysis of composite plates", Finite Elem. Anal. Design, 39, 883-903   DOI   ScienceOn
12 Dow, J.O. and Huyer, S.A. (1989), "Continuum models of space station structures", J. Aerospace Eng., ASCE, 2(4), 212-230
13 Abdalla, $F^{\circ}$ JE Qualitative and Discretization Error Analysis of Laminated Composite Plate Models. Ph.D. Dissertation (1992), University of Colorado, Boulder, CO.
14 Abdalla, $F^{\circ}$ JE and Dow, J.O. (1994), "An error analysis approach for laminated composite plate finite element models", Comput. Struct., 52(4), 611-616   DOI   ScienceOn
15 Ahamad, S., Irons, B.M. and Zienkiewicz, O.C. (1970), "Analysis of thick and thin shell structures by curved finite elements", Int. J. Numer. Meth. Eng., 2, 419-451   DOI
16 Lo, K.H., Cristensen, R.M. and Wu, E.M. (1977), "A high-order theory of plate deformation, Part 1: Homogeneous plates", J. Appl. Mech., 44(4), 663-668   DOI
17 Lo, K.H., Cristensen, R.M. and Wu, E.M. (1977), "A high-order theory of plate deformation, Part 2: Laminated plates", J. Appl. Mech., 44(4), 669-676   DOI
18 Ghugal, Y.M. and Shimpi, R.P. (2002), "A review of refined shear deformation theories of isotropic and anisotropic laminated plates", J. Reinf. Plast. Comp., 21(9), 775-805   DOI   ScienceOn
19 Dow, J.O., Feng, C.C., Su, S.Z. and Bodley, C.S. (1985), "An equivalent continuum representation of structures composed of repeated elements", AIAA J., 23, 1564-1569   DOI   ScienceOn
20 Brank, B. and Carrera, E. (2000), "A family of shear-deformable shell finite elements for composite structures", Comput. Strucut., 76, 287-297   DOI   ScienceOn
21 Botello, S., Onate, E. and Canet, J.M. (1999), "A layer-wise triangle for analysis of laminated composite plates and shells", Comput. Strucut., 70, 635-646   DOI   ScienceOn
22 Dow, J.O. (1999), A Unified Approach to the Finite Element Method and Error Analysis Procedures, Academic Press, San Diego, CA
23 Prathap, G. (1997), "A field-consistency approach to plate elements", Struct. Eng. Mech., 5(6), 853-865   DOI   ScienceOn
24 Reddy, J.N. (2004), Mechanics of Laminated Composite Plates and Shells: Theory and Analysis, 2nd ed., CRC Press, Boca Raton, FL
25 Singh, G. and Rao, G.V. (1995), "A discussion on simple third-order theories and elasticity approaches for flexure of laminated plates", Struct. Eng. Mech., 3(2), 121-133   DOI   ScienceOn
26 Reddy, J.N. (1989), "On refined computational models of composite laminates", Int. J. Numer. Meth. Eng., 27, 361-382   DOI
27 Reddy, J.N. and Averill, R.C. (1991), "Advances in the modelling of laminated plates", Comput. Syst. Eng., 2(5/6), 541-555   DOI   ScienceOn
28 Reddy, J.N. and Wang, C.M. (2000), "An overview of the relationships between solutions of the classical and shear deformation plate theories", Comp. Sci. Tech., 60, 2327-2335   DOI   ScienceOn
29 Zienkiewicz, O.C., Taylor, R.L. and Too, J.M. (1971), "Reduced integration technique in general analysis of plates and shells", Int. J. Numer. Meth. Eng., 3, 275-290   DOI