Mathematical Problems in the Integral-Transformation Method of Dynamic Crack
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摘要: 引入势函数，形成运动微分方程，对运动微分方程和各种响应进行Laplace变换及Fourier正弦、余弦变换，最后求解由边界条件形成的对偶方程——这种研究动态裂纹的方法已经被广泛使用并成为比较系统的方法．以一种模型为例，对其推演过程进行了研究，最后发现：此方法在数学推演时，存在着不严密的问题，推演结果带有偶然性，不具可信性．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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Key words:
- potential function /
- integral transform /
- dynamic crack /
- dual equation
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