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

We present a general framework to obtain analytical design sensitivities fo r steady-stare 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 adjoin t methods and are compared to show that the two sensitivity analysis method s yield identical expressions. Both adjoint and direct sensitivities for th e generalized Hele-Shaw system, which models the flow of purely viscous non -Newtonian fluids through thin cavities, are obtained using weak formulatio ns and then discretized for the finite element analysis. These sensitivitie s are used with numerical optimization to design polymer sheeting dies with minimum pressure drop and reduced velocity variation across the die exit. (C) 1998 Published by Elsevier Science S.A. All rights reserved.