双周期分布圆形弹性夹杂平面热弹性问题

THE PLANE THERMOELASTIC PROBLEM OF DOUBLY-PERIODIC ARRAYS OF CIRCULAR ELASTIC INCLUSIONS

研究了含双周期分布圆形弹性夹杂的无限弹性平面在均匀拉伸和均匀温变下的弹性响应问题.运用Isida的区域单元法和复势函数的级数展开技术,将问题转化为线性方程组的求解.数值结果表明:相邻夹杂间距过大或过小都不利于减小界面应力,当相邻夹杂中心间距与夹杂半径之比为2.2～2.8时,界面剪切应力与环向应力的极大值最小;比值为2.5～3.5时,界面最大径向应力值最小;并且该比值范围不随两相材料弹性模量之比和热膨胀系数之比而变化.

The elastic response of doubly-periodic arrays of circular elastic inclusions under the coupled action of uniformly mechanical loads and temperature loads is investigated. By applying the method of region unite established by Isida and the technique of series expansion, the problem can be reduced to a set of linear algebraic equations. The numerical results indicate that there exists an adequate distance between inclusions that can reduce the interracial stresses. The maximum values of interracial shear and tangential stresses are least when the ratio of the interval of adjacent inclusions to radius of the inclusion changes from 2.2 to 2.8. The interracial radial stresses reach the minimum when this ratio is from 2.5 to 3.5. And the ranges don＇t change with the variation of the elastic modular and the thermal expansion coefficient ratio of two-phase materials.