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An exact element method for plane problem

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Abstract

In this paper, based on the step reduction method [1] and exact analytic method [2] a new method—exact element method for constructing finite element, is presented. Since the new method doesn't need the variational principle, it can be applied to solve non-positive and positive definite partial differential equations with arbitrary variable coefficient. By this method, a quadrilateral noncompatible element with 8 degrees of freedom is derived for the solution of plane problem. Since Jacobi's transformation is not applied, the present element may degenerate into a triangle element. It is convenient to use the element in engineering. In this paper, the convergence is proved. Numerical examples are given at the end of this paper, which indicate satisfactory results of stress and displacements can be obtained and have higher numerical precision in nodes.

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References

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Authors and Affiliations

  1. Lanzhou University, Lanzhou

    Yeh Kai-yuan

  2. Anhui Architectural Industry College, Hefei

    Ji Zhen-yi

Authors
  1. Yeh Kai-yuan
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  2. Ji Zhen-yi
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Kai-yuan, Y., Zhen-yi, J. An exact element method for plane problem. Appl Math Mech 11, 413–420 (1990). https://doi.org/10.1007/BF02016371

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  • DOI: https://doi.org/10.1007/BF02016371

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