功能梯度材料在机械、光电、核能、生物工程领域的应用非常广泛.但由于生产技术及工作环境等方面的原因,功能梯度材料内部常常产生各种形式的裂纹并最终导致材料破坏,这将会给材料所处的整个系统带来巨大损失.因此研究功能梯度材料的断裂问题对于该种材料的设计,制备和合理、安全的应用具有极大的促进作用.本文在压电材料线性宏观理论下,研究了功能梯度压电带中偏心裂纹对SH波的散射问题.借助于积分变换方法,在电非渗透型边界条件的情况下,将所考虑的问题转化为奇异积分方程,运用Gauss-Chebyshev数值积分方法对奇异积分方程进行了数值求解,进而得到了裂纹尖端的应力和电位移强度因子.%Functionally graded materials (FGMs) have been used in many fields, such as machinery, photoelectron, nuclear energy and biomedical imaging. But due to the reasons of limited technology, working condition and some other factors, various cracks always arise in real FGMs. Therefore, it is significantly meaningful to study the crack problems of FGMs. In this paper, the scattering of SH wave on eccentric crack problems of the functionally graded piezoelectric strip is investigated on the basis of linear macroscopic theory of piezoelectric materials. By employing the integral transform method, the problem in consideration is transformed into a system of singular integral equations of the first kind under impermeable boundary conditions. The singular integral equations for impermeable cracks are numerically solved by using the Gauss-Chebyshev integration method. Stress intensity factors at crack tips are thus obtained.
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