7 - Two–Dimensional Problems in Polar Coordinates

Summary

Two-dimensional problems of plane stress and plane strain in polar coordinates, both axisymmetric and non-axisymmetric, are considered. Among axisymmetric problems, the bending of a curved beam by two end couples and the problem of a pressurized hollow disk or cylinder are analyzed. Among non-axisymmetric problems, solutions are derived for problems of bending of a curved cantilever beam by a vertical force, loading of a circular hole in an infinite medium,concentrated vertical and tangential forces at the boundary of a half-plane, and a semi-elliptical pressure distribution over the boundary of a half-space. The problems of diametral compression of a circular disk (Michell problem), stretching of a large plate weakened by a small circular hole (Kirsch problem), stretching of a large plate strengthened by a small circular inhomogeneity, and spinning of a circular disk are also analyzed and discussed. The chapter ends with an analysis of the stress field near a crack tip under symmetric and antisymmetric remote loadings, the stress and displacement fields around an edge dislocation in an infinite medium, and around a concentrated force in an infinite plate.