On the evaluation of the upper-bound approach to problems of rigid-plastic deformation under non-standard conditions

Abstract

The upper-bound theorem constitutes for rigid-plastic materials an important tool for setting up analytical or numerical solutions to technological problems, the finite element method being one special application. It is known that neither the shape of the free surfaces of the considered body nor the values of the yield limit may be varied when the free parameters of the solution, e.g. the nodal velocities, are being optimized. In the present paper the variation of discontinuity interfaces of the assumed velocity field or of the field of strain rates is investigated. It is then shown that additional terms appear in the derivatives of the upper-bound functional. For illustration, and as an example of application, the free surface of the strip in the plane strain drawing process is calculated behind and in front of the dies, assuming an elementary velocity field.