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

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.