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Applied Mathematics and Mechanics (English Edition) ›› 2004, Vol. 25 ›› Issue (3): 252-256.

• 论文 • 上一篇    下一篇

MATHEMATICAL PROBLEMS IN THE INTEGRAL-TRANSFORMATION METHOD OF DYNAMIC CRACK

边文凤1, 王彪2, 贾宝贤1   

  1. 1. Automobile Institute, Harbin Institute of Technology, Weihai, Shandong 264209, P.R.China;
    2. Center for Composite Materials and Electro-Optics Research Center, Harbin Institute of Technology, Harbin 150001, P.R.China
  • 收稿日期:2002-10-29 修回日期:2003-10-20 出版日期:2004-03-18 发布日期:2004-03-18

MATHEMATICAL PROBLEMS IN THE INTEGRAL-TRANSFORMATION METHOD OF DYNAMIC CRACK

BIAN Wen-feng1, WANG Biao2, JIA Bao-xian1   

  1. 1. Automobile Institute, Harbin Institute of Technology, Weihai, Shandong 264209, P.R.China;
    2. Center for Composite Materials and Electro-Optics Research Center, Harbin Institute of Technology, Harbin 150001, P.R.China
  • Received:2002-10-29 Revised:2003-10-20 Online:2004-03-18 Published:2004-03-18

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摘要： In the investigation on fracture mechanics,the potential function was introduced, and the moving differential equation was constructed. By making Laplace and Fourier transformation as well as sine and cosine transformation to moving differential equations and various responses, the dual equation which is constructed from boundary conditions lastly was solved. This method of investigating dynamic crack has become a more systematic one that is used widely. Some problems are encountered when the dynamic crack is studied. After the large investigation on the problems, it is discovered that during the process of mathematic derivation, the method is short of precision, and the derived results in this method are accidental and have no credibility.A model for example is taken to explain the problems existing in initial deriving process of the integral-transformation method of dynamic crack.

Abstract: In the investigation on fracture mechanics,the potential function was introduced, and the moving differential equation was constructed. By making Laplace and Fourier transformation as well as sine and cosine transformation to moving differential equations and various responses, the dual equation which is constructed from boundary conditions lastly was solved. This method of investigating dynamic crack has become a more systematic one that is used widely. Some problems are encountered when the dynamic crack is studied. After the large investigation on the problems, it is discovered that during the process of mathematic derivation, the method is short of precision, and the derived results in this method are accidental and have no credibility.A model for example is taken to explain the problems existing in initial deriving process of the integral-transformation method of dynamic crack.

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