Stress Distributions in Cylindrically Aeolotropic Plates

Abstract

Abstract The subject of this paper is the mathematical analysis of the distribution of stress in thin plates of cylindrically aeolotropic material. The plane-stress theory leading to the general solution of this problem under arbitrary boundary conditions is developed in a manner analogous to that used in the corresponding problem involving isotropic materials. The analogy between the plane-stress and plane-strain problems is the same as in the isotropic case, and hence needs no discussion. The following problems are solved: The ring under uniform radial internal and external pressure; the extension of this problem to include the case of the complete disk; the rotating disk; the curved beam bent by end couples; the dislocation problems of the ring; the hydrostatic-stress problem; the force and the couple applied to the vertex of a wedge; and the force applied at a point in the infinite plate. Stresses and displacements are plotted for the first four of the foregoing problems, showing the effect of the degree of anisotropy.