Versatile Variable-Node Flat-Shell Element
Publication: Journal of Engineering Mechanics
Volume 122, Issue 5
Abstract
A variable-node flat shell element is presented. The element has a variable number of midside nodes and each node has a drilling freedom. The element has been developed basically by combining a membrane element with drilling degrees of freedom and a plate bending element. Thus, the element possesses six degrees of freedom per node that, in addition to improvement of the element behavior, permit an easy connection to other six-degrees-of-freedom per node elements. By introducing the variable-node elements that have physical midside nodes, some difficulties associated with connecting the different layer patterns in the common adaptive h -refinement on quadrilateral mesh, such as imposing displacement constraints on irregular nodes to enforce the interelement compatibility can be easily overcome. Detailed numerical studies show the excellent performance of the new shell elements developed in this study.
Get full access to this article
View all available purchase options and get full access to this article.
References
1.
Allman, D. J.(1984). “A compatible triangular element including vertex rotations for plane elasticity problems.”Comp. Struct., 19, 1–8.
2.
Allman, D. J.(1988). “A quadrilateral finite element including vertex rotations for plane elasticity problems.”Int. J. Numer. Methods Engrg., 26, 717–739.
3.
Ashell, D. J., and Sabir, L. B.(1972). “A new cylindrical shell finite element based on simple independent strain functions.”Int. J. Mech. and Sci., 14, 171–183.
4.
Bathe, K. J. (1983). Finite element procedures in engineering analysis . Prentice-Hall, Englewood Cliffs, N.J.
5.
Calladine, C. R. (1983). Theory of shell structures . Cambridge University Press, Cambridge, England.
6.
Choi, C. K., and Lee, N. H.(1993). “Three dimensional transition solid elements for mesh gradation.”Struct. Engrg. & Mech., 1, 61–74.
7.
Choi, C. K., and Lee, W. H.(1995). “Transition membrane elements with drilling freedom for local mesh refinements.”Struct. Engrg. & Mech., 3(1), 75–89.
8.
Choi, C. K., and Park, Y. M.(1989). “Nonconforming transition plate bending elements with variable mid-side nodes.”Comp. and Struct., 32(2), 295–304.
9.
Choi, C. K., and Park, Y. M. (1992). “An adaptive h -refinement using transition element for plate bending problems.”Int. J. Numer. Methods Engrg., 35, 145–163.
10.
Choi, C. K., and Park, Y. M.(1992). “Transition plate bending elements for compatible mesh gradation.”J. Engrg. Mech., ASCE, 118(2), 462–480.
11.
Choi, C. K., Park, Y. M., Seo, J. W., and Lee, W. H. (1989). “Transition elements in plate/shell problems.”Proc., Fourth Int. Conf. and Exhibition on Civ. and Struct. Engrg. Comp. (CIVIL-COMP 89), CIVIL-COMP Press, Edinburgh, England.
12.
Clough, R. W., and Felippa, C. A. (1982). “A refined quadrilateral element for analysis of plate bending.”SAP 6 Theoretical Manual, Univ. of California, Los Angeles, USA.
13.
Donea, J., and Lamain, L. G.(1987). “A modified representation of transverse shear in C0 quadrilateral plate elements.”Comp. Methods in Appl. Mech. and Engrg., 63, 183–207.
14.
Gupta, A. K.(1978). “A finite element for transition from a fine to a coarse grid.”Int. J. Numer. Methods Engrg., 12, 35–45.
15.
Hughes, T. J. R., and Brezzi, F.(1989). “On drilling degrees of freedom.”Comp. Methods Appl. Mech. Engrg., 72, 105–121.
16.
Ibrahimbegovic, A.(1990). “A novel membrane finite element with an enhanced displacement interpolation.”Finite Elements in Analysis and Des., 7, 167–179.
17.
Ibrahimbegovic, A., Taylor, R. L., and Wilson, E. L.(1990). “A robust quadrilateral membrane finite element with drilling degrees of freedom.”Int. J. Numer. Methods Engrg., 30, 445–457.
18.
Reissner, E.(1965). “A note on variational principles in elasticity.”Int. J. Solids Struct., 1, 93–95.
19.
Wilson, E. L.(1974). “The static condensation algorithm.”Int. J. Numer. Methods Engrg., 8, 199–203.
20.
Wilson, E. L., and Ibrahimbegovic, A.(1990). “Use of incompatible displacement modes for the calculation of element stiffnesses or stresses.”Finite Element in Analysis and Des., 7, 229–241.
21.
Zienkiewicz, O. C., and Taylor, R. L. (1989). The finite element method: Basic formulation and linear problems, Vol. I, McGraw-Hill, London, England.
22.
Zienkiewicz, O. C., and Zhu, J. Z.(1992). “The superconvergent patch recovery and a posteriori error estimates. Part 1: The recovery technique.”Int. J. Numer. Methods Engrg., 33, 1331–1364.
23.
Zienkiewicz, O. C., and Zhu, J. Z.(1992). “The superconvergent patch recovery and a posteriori error estimates. Part 2: Error estimates and adaptivity.”Int. J. Numer. Methods Engrg., 33, 1365–1382.
Information & Authors
Information
Published In
Journal of Engineering Mechanics
Volume 122 • Issue 5 • May 1996
Pages: 432 - 441
Copyright
Copyright © 1996 American Society of Civil Engineers.
History
Published online: Jan 19, 1996
Published in print: May 1, 1996
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.