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Closed Form Integration of Element Stiffness Matrices Using a Computer Algebra System
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| Organization: | Dept. of Mechanical Engineering, University of Strathclyde |
| Organization: | University of Strathclyde, Glasgow, Scotland |
| Organization: | University of Strathclyde, Glasgow, Scotland |
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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.
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