Forging is a metal forming process that transforms a simple shape of a workpiece to a predetermined complex shape through the application of compressive forces. Generally, the final forging components have complex intricate shapes. In this case, the simple workpiece is deformed through a number of intermediate shapes of dies to avoid problems such as fold over, cracks, and improper die fill. The design problem of these intermediate shapes is characterized by continually changing contact boundary conditions, large displacements and nonlinear material behavior. In the design of forging processes, finite element based metal forming simulations are providing a good diagnostic information such as forging loads, final shapes, stresses, strains as well as detailed localized information on the state of material. The design cycle can be enhanced further if design sensitivity information is available which could be used in an optimization. The commercial 3D simulations software is a black box and it is an impediment for incorporating analytical sensitivity equations. To overcome this difficulty, in this research, we investigate the analytical continuum-based sensitivity analysis method. This is developed for three-dimensional preform and die shape design, using boundary integral and material derivative formulations. Sensitivity derivation starts by obtaining an identity integral for nonlinear deformation process. Then the adjoint problem is introduced to obtain an explicit expression for the sensitivity of an objective and constraint functions. Initially, the applicability of sensitivity analysis is demonstrated through a steady-state extrusion process. Further,an extension of the methodology to transient non-steady state forging processes is proposed.
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