Properties of the stress vector in the conditions of plane stress

Abstract

The plane state of stress for some deformable body is analysed in this paper. Besides, linear operator is used as mathematical mean. Liner operator is actually a mixed second-order tensor. However, the application of liner operator allows the analysis of stress with the methods of vector algebra. It is demonstrated that, because of the symmetry of linear operator in the plane state of stress,the two principal directions of stress exist which linear operator leaves alone. Further, the intensities and the locations of the principal normal stresses are expressed relative to cartesian coordinate system very simple.