Sensitivity analysis for the design of profile extrusion dies

This paper proposes a procedure for design sensitivity analysis using the direct differentiation method which can be easily included into a finite element code. By a reformulation of the governing equations, it is shown that the derivatives necessary to evaluate the sensitivity of a given performance measure corresponding to the current design configuration can be obtained through a post-processing step by the same finite element solver used to solve the discrete state equations. The procedure is illustrated for some examples with known analytical expression of the sensitivity and then applied to several practical problems in the design of an extrusion process.