Elastic Wave Propagation in a Class of Cracked, Functionally Graded Materials by BIEM
Elastic Wave Propagation in a Class of Cracked, Functionally Graded Materials by BIEM
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BIEM 在一类裂纹功能梯度材料中的弹性波传播
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发表时间：
2006
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通讯作者：
G. Manolis
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作者：
P. Dineva;T. Rangelov;G. Manolis
本文研究了弹性参数为单一空间坐标指数函数的裂纹功能梯度材料（FGM）中的弹性波传播。假定当材料被时谐入射波扫过时，平面应变条件保持不变。FGM的泊松比固定为0.25，而剪切模量和密度曲线均成比例变化。更具体地说，FGM的剪切模量为μ (x)=μ 0 exp (2ax2)，其中μ 0是被认为是各向同性、均匀材料背景的参考值。求解方法是边界积分方程法（BIEM），该方法的一个重要组成部分是无限非齐次平面的格林函数。本文用泛函变换的方法导出了该解的封闭形式及其空间导数和小参数的渐近形式。最后，采用二次型边界元建立了非超奇异牵引型BIEM，并辅以处理裂纹尖端的特殊边缘型单元。该方法首先针对基准问题进行了验证，然后用于研究入射波、时谐压力波(P)和垂直极化剪切波（SV）作用下无限延伸FGM裂纹周围的波散射。参数化研究表明，裂纹尖端的远场位移和近场应力强度因子对这种不均匀性都很敏感，这与参考均匀材料情况的结果相比较
Elastic wave propagation in cracked, functionally graded materials (FGM) with elastic parameters that are exponential functions of a single spatial co-ordinate is studied in this work. Conditions of plane strain are assumed to hold as the material is swept by time-harmonic, incident waves. The FGM has a fixed Poisson’s ratio of 0.25, while both shear modulus and density profiles vary proportionally to each other. More specifically, the shear modulus of the FGM is given as μ (x)=μ 0 exp (2ax2), where μ 0 is a reference value for what is considered to be the isotropic, homogeneous material background. The method of solution is the boundary integral equation method (BIEM), an essential component of which is the Green’s function for the infinite inhomogeneous plane. This solution is derived here in closed-form, along with its spatial derivatives and the asymptotic form for small argument, using functional transformation methods. Finally, a non-hypersingular, traction-type BIEM is developed employing quadratic boundary elements, supplemented with special edge-type elements for handling crack tips. The proposed methodology is first validated against benchmark problems and then used to study wave scattering around a crack in an infinitely extending FGM under incident, time-harmonic pressure (P) and vertically polarized shear (SV) waves. The parametric study demonstrates that both far field displacements and near field stress intensity factors at the crack-tips are sensitive to this type of inhomogeneity, as gauged against results obtained for the reference homogeneous material case