复合材料裂纹中心受增加载荷作用下的动态问题

Dynamic problems on crack center of composite materials subjected to increasing loads

利用已建立的复合材料桥连的动态裂纹模型,将桥连处纤维用载荷代替。当裂纹扩展时,其纤维必将连续地开裂。通过复变函数论的方法,可以很容易地将所讨论的问题转化为Remann-Hilbert问题,而后一问题可以用通常的Muskhelishvili方法进行求解,并可以相当简单地得到问题的闭合解。采用自相似函数的途径,求得了扩展裂纹的坐标原点分别受到增加载荷Px/t、Pt3/x2作用下位移、应力和动态应力强度因子的解析解的一般表达式。利用这些解并采用叠加原理,就可以求得任意复杂问题的解。

By application of the built dynamic crack model of bridge in composite materials, bridging fiber section is substituted by loads. When a crack propagates, its fibers must break continuously. By the approaches of the theory of complex functions, the problems dealt with can be facilely translated into Remann-Hilbert problems which are solved by the usual Muskhelishvili＇s measure, and their closed solutions are acquired rather simple according to this technique. The general representations of analytical solutions on the displacements, stresses and dynamic stress intensity factors under the action of increasing loads Px/t, Pt3/x2situated at the origin of the coordinates of propagation crack, respectively, is attained by the methods of self-similar functions. After those analytical solutions are utilized by superposition theorem, the solutions to arbitrarily completed problems can be readily obtained.