Optimal design for polymer extrusion. Part II: Sensitivity analysis for weakly-coupled nonlinear steady-state systems

The die design methodology presented in Part I is extended to include perfo rmance measures that are functions of material residence time. We solve a h yperbolic differential equation using the velocity field computed from the Hele-Shaw pressure analysis to evaluate the material residence time in poly mer melts. The residence time governing equation lacks natural diffusion, t herefore, we employ the streamline upwind Petrov-Galerkin (SUPG) finite ele ment method to compute a spatially stable residence rime field. In the desi gn problem, we derive design sensitivities for steady-stale nonlinear weakl y-coupled systems and include design variables that parameterize essential boundary conditions. Design sensitivities are derived via the direct differ entiation and adjoint methods. Special consideration is given to the SUPG w eighting function since it is a function of the design. To demonstrate the methodology, sheet extrusion dies are designed to simultaneously minimize t he exit velocity variation and the exit residence time variation. (C) 1998 Published by Elsevier Science S.A. All rights reserved.