Improved Rectangular Element for Shear Deformable Plates
Publication: Journal of Engineering Mechanics
Volume 118, Issue 2
Abstract
A 40‐degree‐of‐freedom displacement‐type rectangular finite element for shear deformable flat plates is presented. The element includes transverse shear effects, is fully conforming, may be orthotropic, and has a stiffness that may be obtained by closed‐form integration. The element does not appear to lock. Numerical examples for plates with uniform loads and for simply supported and clamped boundary conditions are presented and compared with results from other investigators. These results demonstrate that this element is more flexible than most other finite elements for moderately thick plates. The results also agree well with those from a numerical solution of the three‐dimensional elasticity equations. Convergence to thin‐plate theory is obtained when the length‐to‐thickness ratio is large or when the transverse shear moduli are artificially increased.
Get full access to this article
View all available purchase options and get full access to this article.
References
1.
Abdalla, H., and Hassan, K. (1988). “On the Bergan‐Wang approach for moderately thick plates.” Commun. Appl. Numer. Methods, 4(1), 51–58.
2.
Baldwin, J. T., Razzaque, A., and Irons, B. M. (1973). “Shape function subroutine for an isoparametric thin plate element.” Int. J. Numer. Methods Engrg., 7(4), 431–440.
3.
Bathe, K. J., Brezzi, F., and Cho, S. W. (1989). “The MITC7 and MITC9 plate bending elements.” Comput. Struct., 32(3/4), 797–814.
4.
Batoz, J. L., Bathe, K. J., and Ho, L. W. (1980). “A Study of three‐node triangular plate bending elements.” Int. J. Numer. Methods Engrg., 15(12), 1771–1812.
5.
Bergan, P. G., and Wang, X. (1984). “Quadrilateral plate bending elements with shear deformations.” Comput. Struct., 19(1–2), 25–34.
6.
Bert, C. W. (1984). “A critical evaluation of new plate theories applied to laminated composites.” Compos. Struct., 2(4), 329–347.
7.
Bhashyam, G. R., and Gallagher, R. H. (1984). “An approach to the inclusion of transverse shear deformation in finite element plate bending analysis.” Comput. Struct., 19(1–2), 35–40.
8.
Clough, R. W., and Tocher, J. L. (1965). “Finite element stiffness matrices for analysis of plate bending.” Proc. First Conf. on Matrix Methods in Struct. Mech., J. S. Przemieniecki et al., eds., Air Force Flight Dynamics Laboratory, 515–545.
9.
Cook, R. D. (1972). “Two hybrid elements for analysis of thick, thin and sandwich plates.” Int. J. Numer. Methods Engrg., 5(2), 277–288.
10.
Fricker, A. J. (1985). “An improved three‐noded triangular element for plate bending.” Int. J. Numer. Methods Engrg., 21(1), 105–114.
11.
Gellert, M. (1988). “A new method for derivation of locking‐free plate bending finite elements via mixed/hybrid formulation.” Int. J. Numer. Methods Engrg., 26(5), 1185–1200.
12.
Ghosh, S. K., and Buragohain, D. N. (1985). “Two triangular elements for the analysis of thick, sandwich plates.” Proc. Int. Conf. Computational Mechanics, Pergamon Press, Elmsford, N.Y., 259–268.
13.
Hrabok, M. M., and Hrudey, T. M. (1984). “A review and catalogue of plate bending finite elements.” Comput. Struct., 19(3), 479–495.
14.
Irons, B. M. (1976). “The semi‐loof element.” Finite elements for thin shell and curved members, D. G. Ashwell and R. H. Gallagher, eds., John Wiley and Sons, New York, N.Y., 197–222.
15.
Irons, B. M., and Loikkanen, M. (1983). “An engineers' defence of the patch test.” Int. J. Numer. Methods Engrg., 19(9), 1391–1401.
16.
Kant, T. (1982). “Numerical analysis of thick plates.” Comput. Methods in Appl. Mech. Engrg., 31(1), 1–18.
17.
Kant, T., and Hinton, E. (1980). “Numerical analysis of rectangular Mindlin plates by the segmentation method.” Report C/R/365/80, Univ. of Wales, Swansea, U.K.
18.
Langhaar, H. L. (1962). Energy methods in applied mechanics. John Wiley and Sons, Inc., New York, N.Y., 41–44.
19.
Levinson, M. (1980). “An accurate, simple theory of the statics and dynamics of elastic plates.” Mech. Res. Commun., 7(6), 343–350.
20.
MacNeal, R. H. (1982). “Derivation of element stiffness matrices by assumed strain distributions.” Nucl. Engrg. Des., 70(1), 3–12.
21.
Mindlin, R. D. (1951). “Influence of rotatory inertia and shear on flexural motions of isotropic, elastic plastes.” J. Appl. Mech., 18(1), 31–38.
22.
Murthy, M. V. V. (1981). “An improved transverse shear deformation theory for laminated anisotropic plates.” NASA TP‐1903, Langley Res. Ctr., Hampton, Va.
23.
Park, K. C., and Stanley, G. M. (1988). “Strain interpolating for a 4‐node ANS shell element.” Computational mechanics '88, S. N. Atluri and G. Yagawa, eds., Vol. 1, Springer‐Verlag, New York, N.Y., 26.i.1–26.i.4.
24.
Pryor, C. W., Jr., Barker, R. M., and Frederick, D. (1970). “Finite element bending analysis of Reissner plates.” J. Engrg. Mech. Div., ASCE, 96(6), 967–983.
25.
Pugh, E. D. L., Hinton, E., and Zienkiewicz, O. C. (1978). “A study of quadrilateral plate bending elements with ‘reduced’ integration.” Int. J. Numer. Methods Engrg., 12(7), 1059–1079.
26.
Rao, G. V., Venkataramana, J., and Raju, I. S. (1974). “A high precision triangular plate bending element for the analysis of thick plates.” Nuc. Engrg. Des., 30(3), 408–412.
27.
Reissner, E. (1945). “The effect of transverse shear deformation on the bending of elastic plates.” J. Appl. Mech., 12(2), A69–A77.
28.
Saleeb, A. F., and Chang, T. Y. (1987). “An efficient quadrilateral element for plate bending analysis.” Int. J. numer. Methods Engrg., 24(6), 1123–1155.
29.
Salerno, V. L., and Goldberg, M. A. (1960). “Effect of shear deformations on the bending of rectangular plates.” J. Appl. Mech., 27(1), 54–58.
30.
Spilker, R. L., and Munir, N. I. (1980). “The hybrid‐stress model for thin plates.” Int. J. Numer. Methods Engrg., 15(8), 1239–1260.
31.
Srinivas, S., and Rao, A. K. (1973). “Flexure of thick rectangular plates.” J. Appl. Mech., trans. ASME, 39(1), 298–299.
32.
Timoshenko, S. P., and Woinowsky‐Krieger, S. (1959). Theory of plates and shells. Second Ed., McGraw‐Hill, New York, N.Y.
33.
Voyiadjis, G. Z., Baluch, M. H., and Chi, W. K. (1985). “Effects of shear and normal strain on plate bending.” J. Engrg. Mech., ASCE, 111(9) 1130–1143.
34.
Voyiadjis, G. Z., and Pecquet, R. W., Jr. (1987). “Isotropic plate elements with shear and normal strain deformations.” Int. J. Numer. Methods Engrg., 24(9), 1671–1695.
35.
Wempner, G., Talaslidis, D., and Hwang, C.‐M. (1982). “A simple and efficient approximation of shells via finite quadrilateral elements.” J. Appl. Mech., 49(1), 115–120.
36.
Whitney, J. M., and Pagano, N. J. (1970). “Shear deformation in heterogeneous anisotropic plates.” J. Appl. Mech., 37(4), 1031–1036.
37.
Yuan, F. G., and Miller, R. E. (1988). “A rectangular finite element for moderately thick flat plates.” Comput. Struct., 30(6), 1375–1387.
38.
Yuan, F. G., and Miller, R. E. (1989). “A cubic triangular finite element for flat plates with shear.” Int. J. Numer. Methods in Engrg., 28(1), 109–126.
39.
Zienkiewicz, O. C. (1977). The finite element method. McGraw‐Hill, London, England.
40.
Zienkiewicz, O. C., and Hinton, E. (1976). “Reduced integration function smoothing and non‐conformity in finite element analysis (with special reference to thick plate).” J. Franklin Inst., 302(5/6), 443–461.
Information & Authors
Information
Published In
Journal of Engineering Mechanics
Volume 118 • Issue 2 • February 1992
Pages: 312 - 328
Copyright
Copyright © 1992 ASCE.
History
Published online: Feb 1, 1992
Published in print: Feb 1992
Authors
Metrics & Citations
Metrics
Citations
Download citation
If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.