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http://dx.doi.org/10.12989/sem.2008.29.3.327

Problems with a popular thick plate element and the development of an improved thick plate element  

Cheng, Y.M. (Department of Civil and Structural Engineering, Hong Kong Polytechnic University)
Law, C.W. (Housing Department, Hong Kong SAR Government)
Publication Information
Structural Engineering and Mechanics / v.29, no.3, 2008 , pp. 327-349 More about this Journal
Abstract
Some unreasonable results from the use of a popular thick plate element are discovered from the analysis of a raft foundation and a pile cap in Hong Kong. To overcome the problems, the authors have developed a new shear deformable beam which can be extended to a general quadrilateral shear deformable plate. The behaviour of this new element under several interesting cases is investigated, and it is demonstrated that the new element possesses very high accuracy under different depth/span ratios, and the results from this new element are good even for a coarse mesh.
Keywords
thick plate; shear deformation; finite element;
Citations & Related Records
Times Cited By KSCI : 3  (Citation Analysis)
Times Cited By Web Of Science : 7  (Related Records In Web of Science)
Times Cited By SCOPUS : 1
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1 Wilson, E.L., Taylor, R.L., Doherty, W. and Ghaboussi, J. (1973), "Incompatible displacement models", Numer. Comput. Meth. Struct. Mech., Academic press
2 Zienkiewicz, O.C. and Taylor, R.L. (2000), The Finite Element Method 5th edition, 2, Butterworth-Heinemann
3 Soh, A.K., Cen, S., Long ,Y.Q., Long, Z.F. (2001), "A new twelve DOF quadrilateral element for analysis of thick and thin plates", Euro. J. Mech. A/Solids, 20(2), 299-326   DOI   ScienceOn
4 Szilard, R. (2004), Theory and Applications of Plates Analysis of Plates, John Wiley
5 Timoshenko, S. and Krieger, W. (1959), Theory of Plates and Shells, McGraw-Hill
6 Reismann, H. (1988), Elastic Plates, Theory and Application, John Wiley
7 Tessler, A. and Hughes, T.J.R. (1985), "A three-node Mindlin plate element with improved transverse shear", Comput. Meth. Appl. Mech. Eng.
8 Urugal, A.C. (1999), Stress in Plates and Shells 2nd edition, McGraw-Hill
9 Wang, C.M., Reddy, J.N. and Lee, K.H. (2000), Shear Deformable Beams and Plates, Elsevier
10 Gruttmann, F. and Wagner, W. (2004), "A stabilized one-point integrated quadrilateral Reissner-Mindlin plate element", Int. J. Numer. Meth. Eng., 61, 2273-2295   DOI   ScienceOn
11 Hartmann, F. and Katz, C. (2004), Structural Analysis with Finite Elements, Springer
12 Hughes, T.J.R. (1987), The Finite Element Method, Prentice Hall
13 Ibrahimbegovic, A. (1992), "Plate quadrilateral finite elements with incompatible modes", Commun. Appl. Numer. Meth., 8, 497-504   DOI
14 Ozgan, K. and Daloglu Ayse, T. (2007), "Alternative plate finite elements for the analysis of thick plates on elastic foundations", Struct. Eng. Mech., 26(1), 69-86   DOI   ScienceOn
15 Lyly, M. and Stenbergy, R. (1998), "The stabilized MITC plate bending elements", Computational Mechanics, New Trends and Applications, CINME Press, Barcelona, Spain
16 Onate, E., Zienkiewicz, O.C., Suarez, B. and Taylor, R.L. (1992), "A general methodology for deriving shear constrained Reissner-Mindlin plate element", Int. J. Numer. Meth. Eng., 33, 345-367   DOI
17 Ozdemir, Y.I., Bekiroglu, S. and Ayvaz, Y. (2007), "Shear locking-free analysis of thick plates using Mindlin's theory", Struct. Eng. Mech., 27(3), 311-331   DOI   ScienceOn
18 Reddy, J.N. (2000), Theory and Analysis of Elastic Plates, Taylor and Francis
19 Chen, W.J. and Cheung, Y.K. (2000), "Refined quadrilateral element based on Mindlin/Reissner plate theory", Int. J. Numer. Meth. Eng., 47, 605-627   DOI
20 Computers and Structures Inc. (2002), Sap2000 8.0 User's Manual
21 Abdalla, J.A. and Ibrahim, A.K. (2007), "A geometrically nonlinear thick plate bending element based on mixed formulation and discrete collocation constraints", Struct. Eng. Mech., 26(6), 725-739   DOI   ScienceOn
22 Bathe, K.J. and Dvorkin, E.N. (1985), "A Four node plate bending element based on Mindlin/Ressiner plate theory and mixed interpolation", Int. J. Numer. Meth. Eng., 21, 367-383   DOI   ScienceOn
23 Bathe, K.J., Brezzi, F. and Cho, S.W. (1989), "The MITC7 and MITC9 plate elements", Comput. Struct., 32, 797-814   DOI   ScienceOn
24 Computers and Structures Inc. (2002), Safe 7.0 User's and Verification Manual
25 Batoz, J.L. and Lardeur, P. (1989), "A discrete shear triangular nine D.O.F. element for the analysis of thick to very thin plates", Int. J. Numer. Meth. Eng., 28, 533-560   DOI   ScienceOn
26 Cen, S., Long, Y.Q., Yao, Z.H. and Chiew, S.P. (2006), "Application of the quadrilateral area co-ordinate method: A new element for Mindlin-Reissner plate", Int. J. Numer. Meth. Eng., 66, 1-45   DOI   ScienceOn
27 Chen, W.J. and Cheung, Y.K. (2001), "Refined 9-Dof triangular Mindlin plate elements", Int. J. Numer. Meth. Eng., 51, 1259-1281   DOI   ScienceOn
28 Ibrahimbegovic, A. (1993), "Quadrilateral finite elements for analysis of thick and thin plates", Comput. Meth. Appl. Mech. Eng., 10, 195-209
29 Jirousek, J., Wroblewski, A. and Szybinski, B. (1995), "A new 12 d.o.f. Quadrilateral element for analysis of thick and thin plates", Int. J. Numer. Meth. Eng., 38, 2619-2638   DOI   ScienceOn
30 Katili, I. (1993), "A new discrete Kirchhoff-Mindlin element based on Mindlin-reissner plate theory and assumed shear strain fields - Part I: An extended DKT element for thick-plate bending analysis", Int. J. Numer. Meth. Eng., 36, 1859-1883   DOI   ScienceOn
31 Sheikh, A.H. and Dey, P. (2001), "A new triangular element for the analysis of thick and thin plates", Commun. Numer. Meth. Eng., 17, 667-673   DOI   ScienceOn
32 Sze, K.Y. (2002), "Three-dimensional continuum finite element models for plate/shell analysis", Pro. Struct. Eng. Mater., 4, 400-407   DOI   ScienceOn