Transition Plate‐Bending Elements for Compatible Mesh Gradation
Publication: Journal of Engineering Mechanics
Volume 118, Issue 3
Abstract
In this paper, a new approach to the development of the transition plate‐bending elements with variable midside nodes is presented. These elements will facilitate abrupt changes in mesh refinement between domains consisting of quadrilateral elements. For compatible mesh gradation, special shape functions with slope discontinuity at midside nodes are used. The transition elements are formulated based on the Mindlin‐Reissner plate theory to take shear deformation into account. To evaluate the proper element stiffness pertinent to shear, the substitute shear strain polynomials in Cartesian coordinates are constructed. A modified Gaussian integration is adopted to eliminate the slope discontinuity problem in the element domain. Some numerical examples are presented that illustrate the validity and effectiveness of these transition elements for the efficient analysis of plate‐bending problems.
Get full access to this article
View all available purchase options and get full access to this article.
References
1.
Atkinson, K. (1978). An introduction to numerical analysis. John Wiley & Sons, New York, N.Y.
2.
Babuska, I., Zienkiewicz, O. C, Gago, J., and Oliveira, E. R. de A., eds. (1986). Accuracy estimates and adpative refinements in finite element computations. John Wiley & Sons, New York, N.Y.
3.
Bathe, K. J. (1982). Finite element procedures in engineering analysis. Prentice‐Hall, Englewood Cliffs, N.J.
4.
Bathe, K. J., and Dvorkin, E. N. (1985). “A four‐node plate bending element based on Mindlin/Reissner plate theory and a mixed interpolation.” Int. J. Numer. Methods Engrg., 21, 367–383.
5.
Burnett, D. S. (1987). Finite element analysis—from concepts to applications. Addison‐Wesley Publishing Co., Massachusetts.
6.
Choi, D. K., and Park, Y. M. (1989). “Nonconforming transition plate bending elements with variable midside nodes.” Comput. Struct., 32(2), 295–304.
7.
Choi, C. K., and Park, Y. M. (1991). “An adaptive ^‐refinement using transition element for plate bending problems.” Submitted to Int. J. Numer. Methods Engrg.
8.
Choi, C. K., and Schnobrich, W. C. (1973). “Use of nonconforming modes in the finite element analysis of plates and shells.” Civil Engrg. Studies, Structural Research Series No. 401, Dept. of Civil Eng., Univ. of Illinois, Urbana, 111.
9.
Cook, R. D. (1981). Concepts and applications of finite element analysis. 2d Ed., John Wiley & Sons, New York, N.Y.
10.
Donea, J., and Lamain, L. G. (1987). “A modified representation of transverse hear in C° quadrilateral plate elements.” Comput. Methods Appl. Mech. And Engrg., 63, 183–207.
11.
Gupta, A. K. (1978). “A finite element for transition from a fine to a coarse grid.” Int. J. Numer. Methods Engrg., 12, 35–45.
12.
Hinton, E., and Huang, H. C. (1986). “A family of quadrilateral Mindlin plate elements with substitute shear strain fields.” Comput. Struct., 23, 409–431.
13.
Hughes, J. R., Cohen, M., and Haroun, M. (1978). “Reduced and selective integration techniques in the finite element analysis.” Nuclear Engrg. Des., 46, 203–222.
14.
Lasry, D., and Belytschko, T. (1987). “Transverse shear oscillations in four‐node quadrilateral plate elements.” Comput. Struct., 27, 393–398.
15.
Levit, I., Nour‐Omid, B., Stanley, G., and Swenson, L. (1989). “An adaptive mesh refinement strategy for analysis of shell structures.” Computational structural mechanics and multidisciplinary optimziation, pp. 19–26.
16.
Noor, A. K., and Babuska, I. (1987). “Quality assessment and control of finite element solutions.” Finite Element Anal. Des., 3, 1–26.
17.
Pugh, E. D. L., Hinton, E., and Zienkiewicz, O. C. (1987). “A study of quadrilateral plate bending elements with reduced integration.” Int. J. Numer. Methods Engrg., 12, 1059–1079.
18.
Ridlon, S. (1987). “Modeling guidelines.” Finite element idealization—for linear elastic static and dynamic analysis of structures in engineering practice, C. Meyer, ed., ASCE, New York, N.Y.
19.
Timoshenko, S. P., and Woinowsky‐Krieger, S. (1959). Theory of plates and shells. 2d ed., McGraw‐Hill, London, U.K.
20.
Utku, S., and Melosh, K. J. (1984). “Solution errors in finite element analysis.” Comput. Struct., 18(3), 379–393.
21.
Zienkiewicz, O. C., Taylor, R. L., and Too, J. M. (1971). “Reduced integration technique in general analysis of plates and shells.” Int. J. Numer. Methods Engrg., 3, 275–290.
Information & Authors
Information
Published In
Journal of Engineering Mechanics
Volume 118 • Issue 3 • March 1992
Pages: 462 - 480
Copyright
Copyright © 1992 ASCE.
History
Published online: Mar 1, 1992
Published in print: Mar 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.