Search

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. [ABSTRACT FROM AUTHOR]

This paper addresses an axisymmetric quasi-static contact problem on both thermal and mechanical interactions of a circular punch and a nonhomogeneous elastic half-space whose mechanical and thermophysical properties are assumed to be arbitrary functions of the depth coordinate. To solve the formulated boundary value problem, the technique of Hankel’s integral transformation is used. Using the bilateral asymptotic method, an approximate analytical–numerical solution is constructed for the heat flux, boundary displacements of the half-space, and contact stress under the punch. Numerical implementation is performed for different dependences of the material properties on the depth of the half-space. [ABSTRACT FROM AUTHOR]