A general upper bound elementary technique (UBET) expression is derived for an axisymmetric triangular element none of which side may be parallel to the axis of symmetry, so that one can devide the deforming region of complex shape more easily by using these non-parallel triangular elements. The UBET technique, therefore, can be applied effectively to the complex shape forging.
The axisymmetric extrusion-forging is analyzed by the UBET technique employing these elements, in particular, for the case of extruding simultaneously through upper and lower orifices with different diameters. Comparison between the theory and experiments were made. The theoretical forging loads are in good agreement with the experimental values if the height-to-diameter ratio is relatively high and if the ratio between the two orifice diameters is small. The extruded length from the theory shows better agreement with that from the experiment as the ratio between the orifices decreases.