Three-dimensional Analogue of Kolosov–Muskhelishvili Formulae
Three-dimensional Analogue of Kolosov–Muskhelishvili Formulae
复制标题
Kolosov-Muskhelishvili 公式的三维模拟
DOI：
10.1007/978-3-319-42529-0_11
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发表时间：
2016
影响因子：
3.8
通讯作者：
Y. Grigor’ev
中科院分区：
文献类型：
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作者：
Y. Grigor’ev
在平面弹性力学中，Kolosov-Muskhelishvili公式是应用全纯复函数理论的一种有效方法。对于三维情况，可以使用一元Clifford函数或四元数减变量的正则四元数函数。这些函数是Moisil-Theodresco系统的解。在最近的文章中，得到了三维Kolosov-Muskhelishvili公式的一些变体，但仅适用于星形区域。对于应用来说，拥有适用于更广泛类别的域的这些公式是非常重要的。利用调和本原函数的概念，提出了边界光滑的任意单连通区域上的广义Kolosov-Muskhelishvili公式。证明的方法是基于一个关于从给定的标量部分重构正则函数的新定理。
In the plane elasticity an effective method of using the holomorphic complex function theory is based on Kolosov–Muskhelishvili formulae. For a three-dimensional case monogenic Clifford functions or regular quaternion functions of a reduced quaternion variable are used. Such functions are solutions of the Moisil–Theodoresco system. In recent papers some variants of three-dimensional Kolosov–Muskhelishvili formulae are obtained but only for star-shaped regions. For applications it is very important to have these formulae for a wider class of domains. We propose the generalized Kolosov– Muskhelishvili formulae in arbitrary simply connected domains with a smooth boundary not only star-shaped, where a notion of harmonic primitive function is used. The method of proving is based on a new theorem about reconstruction of a regular function from a given scalar part.