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Application of the symbolic mathematics system to the finite element program

Evaluation of the stiffness matrix of a 4-nodes isoparametric element

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Abstract

The stiffness matrix of a 4-nodes insoparametric element for the two dimensional finite element analysis is evaluated using the symbolic mathematics systems, called REDUCE. The results are compared with those obtained by numerical integration. It is shown that there exist some differences between the numerical values of the stiffness matrix by symbolic and numerical integrations. The differences become smaller as the integration points of the numerical integration increases, 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 results agree with those obtained by numerical integration. It is pointed out that there is a possibility to decrease the CPU time by using the symbolic mathematics system.

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References

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Authors and Affiliations

  1. Dep. of Mechanical Engineering, Faculty of Science and Technology, Science University of Tokyo, Noda, 278, Chiba, Japan

    M. Kikuchi

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  1. M. Kikuchi
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Kikuchi, M. Application of the symbolic mathematics system to the finite element program. Computational Mechanics 5, 41–47 (1989). https://doi.org/10.1007/BF01046878

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  • DOI: https://doi.org/10.1007/BF01046878

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