基于等效夹杂法的界面热应力分析

An Interface Thermal Stress Analysis Based on the Equivalent Inclusion Method

本文采用等效夹杂法研究含单个椭圆的夹杂平面在均匀温度变化下的热弹性问题.首先,利用二维椭圆夹杂的Eshelby内部张量和外部张量推导无限大平面下含单个椭圆夹杂的热应力计算公式,并编制成计算机程序;然后,通过典型数值算例证明本文方法的有效性,并与有限元结果进行比较.结果表明,本文方法具有高效率和高精度等优点.最后,使用本文方法分析了夹杂和基体的剪切模量以及椭圆夹杂的长短轴比对热弹性场的影响.

In this paper,the thermoelastic problem of a single elliptical inclusion of infinite matrix under uniform temperature changes was studied using the equivalent inclusion method.Firstly,using the Eshelby internal tensor and external tensor of two-dimensional elliptical inclusions,the thermal stress calculation formula with a single elliptical inclusion in the infinite matrix was derived and programmed.The typical calculation case demonstrates the effectiveness of the method and a comparison with the FEM calculation results was made.The results show that the proposed method has the advantages of being more efficient and more precise.Finally,the effects of the shear modulus of inclusions and matrix and the long and short axis ratio of the elliptical inclusion to the thermoelastic field were studied by adopting the proposed method.