MATHEMATICAL PROBLEMS IN THE INTEGRAL-TRANSFORMATION METHOD OF DYNAMIC CRACK

• Published in: Applied mathematics and mechanics Vol. 25; no. 3; pp. 252 - 256
• Main Author: 边文凤 王彪 贾宝贤
• Format: Journal Article
• Language: English
• Published: Dordrecht Springer Nature B.V 01.03.2004; Automobile Institute, Harbin Institute of Technology,Weihai, Shandong 264209, P.R.China%Center for Composite Materials and Electro-Optics Research Center,Harbin Institute of Technology, Harbin 150001, P.R.China
• Edition: English ed.
• Subjects: Boundary conditions; Differential equations; Fourier transforms; Fracture mechanics; Mathematical problems; Trigonometric functions; 二元方程; 傅立叶变换; 势能函数; 固体力学; 拉普拉斯变换; 断裂力学; dynamic crack; integral transform; dual equation; potential function
• ISSN: 0253-4827; 1573-2754
• DOI: 10.1007/bf02437327

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.