On certain two-dimensional applications of the couple stress theory

Abstract The two-dimensional problem of equilibrium of a perfectly elastic body with couple-stresses is considered. The general form of solution of the problem in the case of an orthotropic medium is given in Section 1. Section 2 shows that there exists a close analogy between the equations governing the behavior of a plane rectangular lattice composed of rigidly interconnected elastic beams, and the general set of equations of the two-dimensional couple-stress theory for certain orthotropic bodies. Section 3 contains two problems which demonstrate the effects of couple-stresses upon the behavior of stresses and displacements in the vicinity of a circular inclusion and a circular hole in an infinite elastic plane.