An Upper Bound Solution for the Compression of an Orthotropic Cylinder

The upper bound theorem is used in conjunction with Hill’s quadratic yield criterion for determining the force required to upset a solid cylinder. The kinematically admissible velocity field accounts for the singular behavior of the real velocity field in the vicinity of the friction surface if the maximum friction law is adopted. The regime of sticking is also taken into consideration. The effect of this regime on the upper bound limit load is revealed. In particular, the kinematically admissible velocity field that includes the regime of sticking may result in a lower upper bound than that with no sticking. The boundary value problem is classified by a great number of geometric and material parameters. Therefore, a systematic parametric analysis of the effect of these parameters on the compression force is practically impossible. An advantage of the solution found is that it provides a quick estimate of this force for any given set of parameters.

FREE VIBRATION OF AN ORTHOTROPIC HOLLOW BODY OF REVOLUTION

A method is developed to determine the natural frequencies of vibration of an orthotropic hollow body of revolution of constant thickness but of arbitrary smooth meridian. Equations are derived using the linear three-dimensional theory of elasticity, and a numerical solution is obtained using the differential quadrature method. The geometric generality of the solution is attained by delaying definition of local geometric parameters until the solution stage. Validation is by comparison with previously published results, including results for a hollow orthotropic cylinder. Sample results are given for orthotropic hollow cylinders and spherical segments, and conclusions are drawn.