SHAPE SENSITIVITY ANALYSIS FOR STEADY METAL-FORMING PROCESSES

This paper develops a numerical technique for determining the shape sensitivity parameters in steady metal- forming processes such as drawing and rolling. The adjoint method is applied to the discrete non-linear system of equations in the finite element model in order to determine the discrete matrix of sensitivity parameters. In this work, two specific cases are considered. The first case involves determining the sensitivity of the process power requirement to the process geometry and the second case involves determining the sensitivity of the internal state variable distribution in the final product to the process geometry. The process geometry is assumed to be characterized by a finite number of shape parameters. The internal state variable distribution in this case represents the resistance to plastic flow and is considered to be related to the quality of the final product. Numerical examples for a simple drawing process are presented to demonstrate the efficiency of the algorithm.