含有裂纹和夹杂的复合柱体的扭转

本文根据Saint-Venant扭转理论,提出了一种能用于扭转分析的线夹杂模型,并得到了它的基本解,进而将此解与的单层势函数解及单裂纹基本解结合,对同时带有裂纹和夹杂的复合柱体的扭转作了讨论,最后将问题归为解一组混合型积分方程,并建议了数值解法。文中通过问题的退化,证明本文提出的夹杂模型在数学和力学上都是正确的,最后作了若干数值例子的计算,其结果令人满意。

TORSION OF COMPOSITE CYLINDER WITH CRACK AND INCLUSION

According to the theory of Saint-Venant's torsion, a fundamental solutionof a linear inclusion model proposed in this paper is obtained, which will be useful to the torsion problem. Using the obtained solution together with the Muskhelishvili's potential solution of single layer and the fundamental solution of a single crack, the torsion problem of a composite-cylinder with crack and inclusion is studied. Finally, the problem is reduced to solving a set of mixed-type integral equations and at the same time the numerical method of solution is also proposed. Through degeneration of the problem, the correctness of the inclusion model is verified from the physical point of view. At the end, several numerical examples are calculated and the results are satisfactory.