UPPER-BOUND ELEMENTAL TECHNIQUE (UBET) WITH CONVEX CIRCULAR PARALLELEPIPED AND CONVEX SPHERICAL ELEMENTS FOR 3-DIMENSIONAL FORGING ANALYSIS

In this study, two kinematically admissible velocity fields are derive d for the proposed three-dimensional convex circular parallelepiped an d convex spherical UBET elements. Those elements are applied to three- dimensional closed-die forging having convex curve surfaces; the capab ility of the proposed elements is then demonstrated. From the derived velocity fields, the upper-bound loads on the upper die and the veloci ty field are determined by minimizing the total energy consumption wit h respect to some chosen parameters. Also, experiments of two closed-d ie forgings are performed with commercial pure lead billets at the amb ient temperature. The theoretical predictions of the forming load corr elated well with the experimental results. The results in this study c onfirm that the elements proposed in this work can effectively be used to predict the forming load accurately in three-dimensional closed-di e forging with convex curve surfaces. (C) 1997 Elsevier Science Ltd. A ll rights reserved.