Optimal design for polymer extrusion. Part I: Sensitivity analysis for nonlinear steady-state systems Original Research Article

We present a general framework to obtain analytical design sensitivities for steady-state nonlinear systems where special emphasis is given to design variables that define prescribed boundary conditions. The sensitivities are derived for a general response functional using both the direct and adjoint methods and are compared to show that the two sensitivity analysis methods yield identical expressions. Both adjoint and direct sensitivities for the generalized Hele-Shaw system, which models the flow of purely viscous non-Newtonian fluids through thin cavities, are obtained using weak formulations and then discretized for the finite element analysis. These sensitivities are used with numerical optimization to design polymer sheeting dies with minimum pressure drop and reduced velocity variation across the die exit.