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Closed Form Integration of Element Stiffness Matrices Using a Computer Algebra System

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

Computers & Structures
Year: 1995
Volume: 56
Issue: 4
Page range: 529-539

A symbolic algebra package, Mathematica, is used to investigate the analytical integration of the mixed finite element stiffness matrices. Two mixed finite elements of the Hellinger-Reissner type are examined in this study; the computing effort in the generation of the stiffness matrices with an analytical integration process is reduced, while accuracy is improved. Relative computing efforts required to generate element stiffness matrices both analytically and numerically are compared. A beam bending test is used to compare the relative performance of various displacement and mixed finite elements with severe element distortion. The analytical integration scheme can be applied to general two- and three-dimensional mixed finite elements with careful simplification of integrands to avoid excessive growth in the symbolic expressions.

*Engineering > Mechanical and Structural Engineering