Some Problems of Orthotropic Plane Stress

Abstract

Abstract Many plane-stress problems in isotropic elasticity are solved conveniently by considering the Airy stress functions in the form of Fourier series (periodic loading) or Fourier integrals (nonperiodic loading) of harmonic and biharmonic functions. The object of this paper is to show how many of these solutions can be extended to the case where the material is orthotropic. For illustrative purposes, the following seven problems are solved: (a) Half plane subjected to normal loading; (b) wedge subjected to axial loading; (c) half plane subjected to a normal force applied through a rigid punch; (d) half plane subjected to tangential loading; (e) wedge subjected to transverse loading; (f) force applied at a point in an infinite plane; and (g) analysis of deep beams.