Application of the symbolic mathematics system to the finite element program. Evaluation of the stiffness matrix of a 4-node isoparametric element.

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  • 数式処理のＦＥＭプログラムへの応用　　４節点アイソパラメトリック要素の剛性マトリックスの数式処理による評価
  • スウシキ ショリ ノ FEM プログラム ヘ ノ オウヨウ 4 セッテン アイ

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Abstract

The stiffness matrix of a 4-nodes isoparametric element for the two dimensional finite element analysis is evaluated using the symbolic mathematics system, called REDUCE. The results are compared with those obtained by numerical integration. It is shown that these exist some differences between the numerical values of the stiffness matrix by symbolic and numerical integration. The differences become smaller due to the increase of the integration points in the numerical integration, which means that the results obtained by symbolic integration give accurate values. The stiffness matrix in elastic-plastic state is also evaluated using symbolic mathematics, and it is shown that the numerical results agree with those obtained by numerical integration. It is pointed out that it is possible to decease the CPU time by using the symbolic mathematics system.

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