This paper presents a micromechanical method to analyze the thermal stresses in a finite plane containing multiple elliptical inclusions. Firstly, the Eshelby’s equivalent inclusion method is employed to solve the elastic fields of a two-dimensional infinite plane containing multiple elliptical inclusions under a uniform temperature change. Both the interior Eshelby’s tensor and the exterior Eshelby’s tensor are employed. Then the boundary of the plane is modeled by continuous distributions of dislocation densities. By combining the two steps, a system of singular integral equations is formulated based on the traction-free boundary condition. Then the thermal stresses of the plane can be obtained by the superposition of the stresses obtained by the Eshelby’s equivalent inclusion method and distributed dislocation method. Additionally, some examples are given to show the effects of the presented method. The effects of the material constants, geometric parameters and fiber packing arrangement on the thermal stresses are also studied.

本文提出了一种微机械方法来分析包含多个椭圆形夹杂物的有限平面中的热应力。首先，采用Eshelby的等效夹杂法求解均匀温度变化下包含多个椭圆形夹杂物的二维无限平面的弹性场。既使用内部Eshelby的张量，也使用外部Eshelby的张量。然后，通过位错密度的连续分布来模拟平面的边界。通过将这两个步骤结合起来，基于无牵引力边界条件，建立了一个奇异积分方程组。然后，可以通过叠加由埃舍尔比的等效包含法和分布位错法获得的应力来获得平面的热应力。另外，给出了一些例子来说明所提出方法的效果。还研究了材料常数，几何参数和纤维堆积方式对热应力的影响。