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Explicit integration of the stiffness matrix of a four-noded-plane-elasticity finite element

✍ Scribed by Videla, L. ;Cerrolaza, M. ;Aparicio, N.

Publisher
John Wiley and Sons
Year
1996
Tongue
English
Weight
720 KB
Volume
12
Category
Article
ISSN
1069-8299

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✦ Synopsis

The paper deals with the symbolic integration of a 4-noded isoparametric finite element for plane elasticity. An efficient approach to generate explicit formulas for computing the elementary stiffness matrix is discussed. The procedure is based on the use of the Derive symbolic manipulation code as well as in a posteriori manipulation of the expressions obtained. The accuracy of the results is tested in extremely distorted and geometrically ill-conditioned elements. Three practical engineering models are presented and the accuracy of the results is discussed. A computer time comparison between both numerical and symbolic integration approaches is also included, showing that relevant CPU savings are obtained when applying symbolic integration.

πŸ“œ SIMILAR VOLUMES

Exact integration of the stiffness matri
Exact integration of the stiffness matrix of an 8-node plane elastic finite element by symbolic computation
✍ L. Videla; T. Baloa; D.V. Griffiths; M. Cerrolaza πŸ“‚ Article πŸ“… 2007 πŸ› John Wiley and Sons 🌐 English βš– 378 KB

## Abstract Computer algebra systems (CAS) are powerful tools for obtaining analytical expressions for many engineering applications in both academic and industrial environments. CAS have been used in this paper to generate exact expressions for the stiffness matrix of an 8‐node plane elastic finit