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The perturbation finite element method for solving problems with nonlinear materials

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Abstract

The perturbation method is one of the effective methods for solving problems in nonlinear continuum mechanics. It has been developed on the basis of the linear analytical solutions for the original problems. If a simple analytical solution cannot be obtained, we would encounter difficulties in applying this method to solving certain complicated nonlinear problems. The finite element method appears to be in its turn a very useful means for solving nonlinear problems, but generally it takes too much time in computation. In the present paper a mixed approach, namely, the perturbation finite element method, is introduced, which incorporates the advantages of the two above-mentioned methods and enables us to solve more complicated nonlinear problems with great saving in computing time.

Problems in the elastoplastic region have been discussed and a numerical solution for a plate with a central hole under tension is given in this paper.

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Authors and Affiliations

  1. Qinghua University, Beijing

    Xie Zhi-cheng, Wang Rei-wu, Yang Xue-zhong & Chien Zhen-dong

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  1. Xie Zhi-cheng
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  2. Wang Rei-wu
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  3. Yang Xue-zhong
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  4. Chien Zhen-dong
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Communicated by Chien Wei-zang.

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Zhi-cheng, X., Rei-wu, W., Xue-zhong, Y. et al. The perturbation finite element method for solving problems with nonlinear materials. Appl Math Mech 4, 127–140 (1983). https://doi.org/10.1007/BF01896720

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  • DOI: https://doi.org/10.1007/BF01896720

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