含多个椭圆夹杂圆板的热弹性分析  

THERMO-ELASTIC ANALYSIS OF A CIRCULAR PLATE CONTAINING MULTIPLE ELLIPTICAL INCLUSIONS

作　　者：戴明[1] 孙慧玉[1] 

机构地区：[1]南京航空航天大学机械结构力学及控制国家重点实验室,南京210016

出　　处：《工程力学》2013年第6期47-53,共7页Engineering Mechanics

基　　金：国家自然科学基金项目(10972101)

摘　　要：基于Muskhelishvili数学弹性力学理论,研究了含多个椭圆夹杂平面圆板在稳态温度场下的热弹性问题。首先,借助保角变换、Faber级数和Fourier级数等工具,推导出了基体和夹杂复势函数的级数解。然后,在一个夹杂退化为孔的算例中,得出了非均匀稳态温度场下孔边的热应力,并与有限元结果对比。最后,通过几组算例,讨论了夹杂的材料常数、几何参数对夹杂/基体界面热应力的影响。结果表明:该文方法具有收敛性好、精度高等优点。Based on the complex potential method for isotropic plane problems, the thermo-elastic problem of a circular plate containing multiple elliptical inclusions subjected to a steady-state temperature field is investigated. Firstly, a series solution to the thermo-elastic problem is derived with the aid of conformal mappings, Faber series and Fourier series. Then the thermal stresses in one numerical case where inclusions are degenerated to holes are calculated and compared with those by the finite element method. Finally, the effects of geometric and material parameters of elliptical inclusions on interfacial thermal stresses are investigated through other numerical cases. It is shown that the solution presented in the paper has many advantages such as a good convergence and high accuracy.

关 键 词：热应力 椭圆夹杂 复变函数 Faber级数 保角变换 

分 类 号：O343.6[理学—固体力学]