Strain energy density of a circular cavity buried in a semi-infinite slab of functionally graded materials subjected to anti-plane shear waves
Strain energy density of a circular cavity buried in a semi-infinite slab of functionally graded materials subjected to anti-plane shear waves
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DOI：
10.1016/j.ijsolstr.2007.03.024
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发表时间：
2007-10
影响因子：
3.6
通讯作者：
X. Fang;Chao Hu;Wenhu Huang
中科院分区：
文献类型：
--
作者：
X. Fang;Chao Hu;Wenhu Huang
本文提出了一种研究含圆孔的功能梯度材料半无限平板中剪切波的多次散射和应变能密度的理论方法。采用波函数展开法给出了波场的解析解，并通过满足腔体边界条件确定了展开模式系数。采用镜像法满足半无限体的自由边界条件。导出了问题的解析解，并给出了孔洞周围应变能密度因子的数值解。分析了孔洞与半无限板边界的距离、波数和材料的非均匀性参数对应变能密度因子的影响。分析表明，孔洞周围的应变能密度随材料非均匀性参数和入射波数的增大而增大。半无限平板边界对圆孔周围的最大应变能密度和分布有很大影响，且影响随入射波数的增加而增大。当半无限边界与孔洞之间的距离变化时，上、下边界对孔洞周围应变能密度因子分布的影响也被考察。
The paper presents a theoretical method to investigate the multiple scattering of shear waves and strain energy density in a semi-infinite slab of functionally graded materials with a circular cavity. The analytical solutions of wave fields are expressed by employing wave function expansion method and the expanded mode coefficients are determined by satisfying the boundary conditions of the cavity. Image method is used to satisfy the free boundary condition of the semi-infinite structure. The analytical solution of the problem is derived, and the numerical solutions of the strain energy density factors around the cavity are also graphically presented. The effects of the distances between the cavity and the boundaries of the semi-infinite slab, the wave number and the non-homogeneous parameter of materials on strain energy density factors are analyzed. Analyses show that the strain energy density around the cavity increases with increasing non-homogeneous parameter of materials and incident wave number. The boundaries of the semi-infinite slab have great effect on both the maximum strain energy density and the distribution around the circular cavity, and the effect increases with increasing incident wave number. When the distance between the semi-infinite boundary and the cavity varies, the effect of the upper and lower boundaries on the distribution of the strain energy density factors around the cavity is also examined.