5 - Boundary–Value Problems: Cylindrical Coordinates

Summary

The representation of the stress and strain tensors and the formulation of the boundary-value problem of linear elasticity in cylindrical coordinates is considered. The Cauchy equations of equilibrium, expressed in terms of stresses, the strain–displacement relations, the compatibility equations, the generalized Hooke's law, and the Navier equations of equilibrium, expressed in terms of displacements, are all cast in cylindrical coordinates. The axisymmetric boundary-value problem of a pressurized hollow cylinder with either open or closed ends is formulated and solved. The results are used to obtain the elastic fields for a pressurized circular hole in an infinite medium, and to solve a cylindrical shrink-fit problem. A pressurized hollow sphere and a spherical shrink-fit problem are also considered to illustrate the solution procedure in the case of problems with spherical symmetry.