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A Computer Algebra Based Finite Element Development Environment

Chee Kiang Yew
Organization: Dept. of Mechanical Engineering, University of Strathclyde
J. T. Boyle
Organization: University of Strathclyde, Glasgow, Scotland
D. Mackenzie
Organization: University of Strathclyde, Glasgow, Scotland
Journal / Anthology

Advances in Engineering Software
Year: 2001
Volume: 32
Issue: 12
Page range: 913-925

A finite element development environment based on the technical computing program Mathematica is described. The environment is used to automatically program standard element formulations and develop new elemets with novel features. Source code can also be exported in a format compatible with commercial finite element program user-element facilities. The development environment is demonstrated for three mixed Petrov-Galerkinplane stress elements: a standard formulation, an advanced formulation incorporating rotational degrees of freedom, and a standard fomulation in which the stiffness matrix is integrated analytically, before being exported as ANSYS user elements. The results presented illustrate the accuracy of the standard mixed formulation element and the engancement of performance when rotational degrees of freedom are added. Further, the analytically integrated element shows that computational requirements can be greatly reduced when analytical integration schemes are used in the formation.

*Engineering > Finite Element Methods

computer algebra, finite element method, Petrov-Galerkin plane stress elements
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