About Elastic Torsion around Three Axes

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.