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A semi-analytical solution for multiple circular inhomogeneities in one of two joined isotropic elastic half-planes

机译：两个连接的各向同性弹性半平面之一中的多个圆形不均匀性的半解析解

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摘要

The paper presents a semi-analytical method for solving the problem of two joined, dissimilar isotropic elastic half-planes, one of which contains a large number of arbitrary located, non-overlapping, perfectly bonded circular elastic inhomogeneities. In general, the inhomogeneities may have different elastic properties and sizes. The analysis is based on a solution of a complex singular integral equation with the unknown tractions at each circular boundary approximated by a truncated complex Fourier series. A system of linear algebraic equations is obtained by using a Taylor series expansion. Apart from round-off, the only errors introduced into the solution are due to truncation of the Fourier series. The resulting semi-analytical method allows one to calculate the elastic fields everywhere in the half-planes and inside the inhomogeneities. Numerical examples are included to demonstrate the effectiveness of the approach.
机译：本文提出了一种半解析方法，用于解决两个相连的，各向同性的各向同性弹性半平面的问题，其中一个半平面包含大量任意定位，不重叠，完美结合的圆形弹性不均匀性。通常，不均匀性可以具有不同的弹性和大小。该分析基于一个复杂奇异积分方程的解，该奇异积分方程的每个圆边界处的牵引力均由截短的复傅立叶级数近似。通过使用泰勒级数展开获得线性代数方程组。除四舍五入外，引入到解决方案中的唯一错误是由于傅立叶级数的截断。所得的半分析方法允许人们计算半平面内和不均匀内部各处的弹性场。包括数值示例，以证明该方法的有效性。

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