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A complex variable meshless method for fracture problems

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Abstract

Based on the moving least-square (MLS) approximation, the complex variable moving least-square approximation (CVMLS) is discussed in this paper. The complex variable moving least-square approximation cannot form ill-conditioned equations, and has greater precision and computational efficiency. Using the analytical solution near the tip of a crack, the trial functions in the complex variable moving least-square approximation are extended, and the corresponding approximation function is obtained. And from the minimum potential energy principle, a complex variable meshless method for fracture problems is presented, and the formulae of the complex variable meshless method are obtained. The complex variable meshless method in this paper has greater precision and computational efficiency than the conventional meshless method. Some examples are given.

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Authors and Affiliations

  1. Shanghai Institute of Applied Mathematics and Mechanics, Shanghai University, Shanghai, 200072, China

    Cheng Yumin

  2. Department of Building Engineering, Xi’an University of Technology, Xi’an, 710048, China

    Li Jiuhong

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  1. Cheng Yumin
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  2. Li Jiuhong
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Correspondence to Cheng Yumin.

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Cheng, Y., Li, J. A complex variable meshless method for fracture problems. SCI CHINA SER G 49, 46–59 (2006). https://doi.org/10.1007/s11433-004-0027-y

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  • DOI: https://doi.org/10.1007/s11433-004-0027-y

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