Abstract

We consider the equations of nonlinear elasticity assuming that the components of the deformation vector depend only on the two space coordinates each of which has the two corresponding coordinates. Some system of the three differential equations for three tangent components of the stress tensor is obtained in result of this study. This system can be used to describe the elastic torsion of a parallelepiped around the three orthogonal axes. We show that the solution of this problem, in stresses, depends on the three arbitrary functions each of which depends only on the two space variables.

中文翻译：

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关于围绕三轴的弹性扭转

摘要

我们考虑非线性弹性方程，假设变形矢量的分量仅取决于两个空间坐标，每个空间坐标具有两个对应的坐标。研究结果得到了应力张量三个正切分量的三个微分方程组。该系统可用于描述围绕三个正交轴的平行六面体的弹性扭转。我们表明，在压力下，此问题的解决方案取决于三个任意函数，每个函数仅取决于两个空间变量。