One Formula Generates Nth Order Shape Functions
Publication: Journal of Engineering Mechanics
Volume 110, Issue 4
Abstract
The paper presents a generalized Lagrangian interpolation formula which generates polynomial shape functions of any desired order. Examples are given to show that polynomial shape functions can be generated for simple one to three dimensional elements commonly used in finite element analysis. The higher order functions are of interest in problems where large strain gradients may be expected and are frequently used in isolated ``super elements'' as in stress intensity calculations. Computational advantages exist due to better matching of the physical phenomena being modeled and consequent reduction in number of elements for a given level of accuracy. The formula presented facilitates selection of appropriate polynomials to represent shape functions associated with a given element type and physical problem.
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References
1.
Argyris, J. H., “Triangular Elements with Linearly Varying Strain for the Matrix Displacement Method,” J. Roy. Aero. Soc. Tech. Note, 69, 1965, pp. 711–713.
2.
Davis, P. J., Interpolation and Approximation, Blaisdell Publishing Company, New York, 1963.
3.
Hamming, R. W., “Numerical Methods for Scientists and Engineers,” 2nd edition, McGraw‐Hill Company, 1973.
4.
Veubeke, B. F., “Displacement and Equilibrium Models in the Finite Element Method,” Chapter 9 of Stress Analysis, O. C. Zienkiewicz and G. S. Holister, eds., John Wiley and Sons, 1965.
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Zienkiewicz, O. C., “The Finite Element Method,” the 3rd, expanded and revised edition of The Finite Element Method in Engineering Science, McGraw‐Hill Company, 1977, pp. 148–177, p. 157.
Information & Authors
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Published In
Journal of Engineering Mechanics
Volume 110 • Issue 4 • April 1984
Pages: 640 - 647
Copyright
Copyright © 1984 ASCE.
History
Published online: Apr 1, 1984
Published in print: Apr 1984
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