De. Smith et al., Optimal design for polymer extrusion. Part II: Sensitivity analysis for weakly-coupled nonlinear steady-state systems, COMPUT METH, 167(3-4), 1998, pp. 303-323
Citations number
28
Categorie Soggetti
Mechanical Engineering
Journal title
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
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
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