热载荷作用下平面裂纹问题的奇异积分方程与边界无法  

Singular Integral Equations and Boundary Element Method of Cracks in Thermally Stressed Planar Solids

作　　者：徐春晖[1] 秦大验 华云龙[1] 

机构地区：[1]中国农业大学基础科学部,北京100083

出　　处：《应用数学和力学》2000年第4期357-364,共8页Applied Mathematics and Mechanics

基　　金：国家自然科学基金!(19672010)

摘　　要：从边界积分方程出发，导出了二维裂纹体热传导问题及热弹性问题的积分方程组，继而使用奇异积分方程与边界元相结合的方法，为其建立了相应的数值求解方法．此外，利用奇异积分方程的主部分析法，严格地证明了裂纹尖端温度梯度场的１／ｒ～（１／ｒ）奇异性，并且给出了奇性温度梯度场的精确解．最后．对一些典型例子，做了数值计算．Using the method of the boundary integral equation, a set of singular integral equations of the heat transfer problems and the thermo-elastic problems of a crack embedded in a two-dimensional finite body is derived, and then its numerical method is proposed by the numerical method of the for sin- gular integral equations combined with boundary element method. Moreover, the singular nature of temperature gradient field near the crack front is proved by the main-part analysis method of the the singular integral equation, and the singular temperature gradients are exactly obtained.Finally, several typical examples are calculated.

关 键 词：奇异积分方程 边界元 热载荷 平面裂纹问题 

分 类 号：O346.1[理学—固体力学]