Abstract

The Lamè system on the plane is considered for the displacement vector in a general anisotropic medium. Cases of explicit calculation of the roots of its characteristic equation are indicated. It is proved that this system cannot be written in the complex form of a single equation. An integral representation of general solution of the Lamè system is received in the class of continuous functions in a closed domain. The kernel and co-kernel of this representation are described. In orthotropic and isotropic an elastic medium, their explicit expression is given in terms of elastic modulus. Applications to the solution of two main boundary value problems of the theory of elasticity are also indicated.

中文翻译：

---

平面各向异性介质中拉梅系统的解

摘要

平面上的拉梅系统被认为是一般各向异性介质中的位移矢量。给出了显式计算其特征方程根的情况。证明该系统不能写成单个方程的复数形式。在封闭域中的连续函数类中接收拉梅系统的一般解的积分表示。描述了这种表示的内核和协同内核。在正交各向异性和各向同性的弹性介质中，它们的显式表达式是根据弹性模量给出的。还指出了解决弹性理论的两个主要边界值问题的应用。