线夹杂的力学模型及其界面应力分析

采用材料力学的直杆和梁的变形假定，对平面线夹杂问题提出了一种能同时考虑夹杂两侧法向应力和剪应力间断的新的力学模型，然后通过集中力作用的Ｋｅｌｖｉｎ解答，求得了单夹杂问题的基本解。文中还导出了夹杂两侧的界面应力公式。最后对夹杂端点的应力强度因子及界面应力作了计算，结果令人满意

The Mechanical Model of a Linear Inclusion and Analysis of Interface Stresses

By using the hypothesis of the deformation of the straight bar and beam in mechanics of materials and taking account of the discontinuities of the normal stress and the shearing stress on the sides of the inclusion, a new mechanical model for a linear inclusion is presented. Then the fundamental solution of a single inclusion is obtained by the help of the Kelvin solution of concentrate force or the method of complex potentials. After that the problem is reduced to solve a set of uncoupled singular integral equations, which can be solved numerically. Next, the expressions of the interface stress on the sides of the inclusion are also derived here. At the end of this paper, the stress intensity factors at the inclusion tips and the interface stresses are calculated and the numerical results are satisfactory.