Stiffness Matrices of Isoparametric Four-Node Finite Elements by Exact Analytical Integration
Publication: Journal of Aerospace Engineering
Volume 21, Issue 2
Abstract
Explicit algebraic expressions needed to compute element stiffness matrices using procedural (FORTRAN) and object oriented computer programs are presented. Numerical illustrations for a convex quadrilateral and a triangle with a side node are included. The wide controversy due to conventional element level approximate numerical quadrature within the computational square domain in and coordinates is completely resolved here by the closed form analytical integration within the physical element, in and coordinates.
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Acknowledgments
The research was supported by the following grants from the National Science Foundation: “Concave Finite Element Shape Functions” NSFCMS-0202232. “Workshop for Scientists and Engineers on Structural Deformations at the Historic Site of Angkor, in Cambodia” NSFOISE-0456406, and “US-France Cooperative Research: Engineering Shape Calculation for Surgery, Biology and Anthropology” NSFINT-0233570.
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Information & Authors
Information
Published In
Journal of Aerospace Engineering
Volume 21 • Issue 2 • April 2008
Pages: 45 - 50
Copyright
© 2008 ASCE.
History
Received: Mar 31, 2005
Accepted: Sep 2, 2006
Published online: Apr 1, 2008
Published in print: Apr 2008
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