Stress systems in aeolotropic plates. VII

Abstract

The paper is divided into three parts. In Part I a general method of solution is given for problems of stress distributions in isotropic and aeolotropic plates containing a hole of a fairly general shape when the boundary values of the displacements are prescribed, but applications for aeolotropic plates are at present limited to circular and elliptical holes. Part II is concerned with distributions of stress in aeolotropic plates containing a single circular discontinuity or hole when the boundary conditions at the edge of the circle are of a mixed type, i.e. they involve both the displacements and the stresses. A set of fundamental stress functions is obtained which are used to investigate stresses due to bolts and knots in stressed planks, and the work is illustrated numerically for a specimen of spruce wood. In Part III a general method of solution is given for problems of stress distributions in aeolotropic plates which contain any number of circular holes of varying sizes distributed in any manner. The solution is applied to the problem of two circular holes in a tension member, and a few numerical results are given for spruce.