On Green's function for a three–dimensional exponentially graded elastic solid
On Green's function for a three–dimensional exponentially graded elastic solid
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DOI：
10.1098/rspa.2001.0952
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发表时间：
2002-08
期刊：
影响因子：
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通讯作者：
Paul A. Martin;J. Richardson;Leonard J. Gray;John Berger
中科院分区：
文献类型：
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作者：
Paul A. Martin;J. Richardson;Leonard J. Gray;John Berger
考虑了无界三维各向同性弹性固体中的点力问题。开尔文解决了均匀材料的这个问题。在这里，材料是不均匀的；它是“功能分级的”。具体地说，固体是“指数梯度的”，这意味着LAMé模数在给定的固定方向上呈指数变化。格林函数的解是通过傅里叶变换得到的，它由开尔文解给出的奇异部分加上非奇异余项组成。这个分次项不是以简单的封闭形式得到的，而是修正的贝塞尔函数的有限区间上的单积分和初等函数的有限区域上的重积分的和。对于梯度材料的这一新的基本解的了解使得对于这些具有重要技术意义的非均匀固体的边界积分方法的发展成为可能。
The problem of a point force acting in an unbounded, three–dimensional, isotropic elastic solid is considered. Kelvin solved this problem for homogeneous materials. Here, the material is inhomogeneous; it is ‘functionally graded’. Specifically, the solid is ‘exponentially graded’, which means that the Lamé moduli vary exponentially in a given fixed direction. The solution for the Green's function is obtained by Fourier transforms, and consists of a singular part, given by the Kelvin solution, plus a non–singular remainder. This grading term is not obtained in simple closed form, but as the sum of single integrals over finite intervals of modified Bessel functions, and double integrals over finite regions of elementary functions. Knowledge of this new fundamental solution for graded materials permits the development of boundary–integral methods for these technologically important inhomogeneous solids.