1. Optimal Design for Molded Composite Products and Processes Douglas E. Smith University of Missouri at Columbia NSF/DOE/APC Workshop Future of Modeling in Composites Molding Processes Design and Optimization Group June 9-10, 2004

2. MISSOURI Design and Optimization Research Numerical optimization in polymer processing Employ mathematical programming methodsEmploy mathematical programming methods Easily interfaced with finite element methodsEasily interfaced with finite element methods Process/product metrics enter cost functionProcess/product metrics enter cost function and constraints Efficiency gained with analytical gradientsEfficiency gained with analytical gradients Design Sensitivity Analysis Quantify relationship between designQuantify relationship between design variables and performance measures Finite difference methods often employedFinite difference methods often employed Analytical approaches provide greater accuracy and efficiencyAnalytical approaches provide greater accuracy and efficiencyE.g., where and increasing F b1b1 b2b2 b1b1 b2b2 b1b1 FF F(b)F(b) b2b2

3. MISSOURI Design and Optimization Research Injection molding process design Sheet extrusion die cavity design gate 1 ( b 1 =0.5) gate 2 ( b 2 =0.5) time (sec) 4.64 3.98 3.31 2.65 1.99 1.33 0.66 0.00 2.82 2.41 2.01 1.61 1.21 0.81 0.40 0.00 initial design optimal design gate 1 ( b 1 =0.412) gate 2 ( b 2 =0.733) fill time (sec) 4.75 2.90 (-39%) find: to min: subject to: gate locations, gate pressures fill time injection rate clamp force flow front uniformity find: to min: subject to: die cavity geometry, inlet pressure inlet pressure exit velocity uniformity prescribed exit flow rate initialdesign optimaldesign half-gap (mm)

4. MISSOURI State of the Art Numerous software / algorithms available for numerical optimization –VDoc/DOT, ISight, Hyperopt, LMS Optimus, Dakota, IMSL, Excel, Matlab, IMSL, Minpack, etc…. Structural optimization well established –Sizing, Shape, and Topology Multidisciplinary Design Optimization (MDO) developed for niche applications, e.g., aeroelasticity, automotive body structure, etc… Non-Deterministic Approaches (NDA) address uncertainty in design –Reliability Analysis Methods, Robust Design, Reliability-Based Design, etc… Design Sensitivity Analysis methods developed for numerous manufacturing applications –Polymer injection molding and extrusion, forging, casting, metal extrusion, etc… Optimal design applied to polymer composites –IM, Sheet extrusion, RTM

5. MISSOURI Vision drops (8x) gates (13x) sprue manufacturing materialsdesign The development and implementation of a comprehensive composites design environment that generates the geometric configuration, component materials, and processing schedule for industrial products. Design tool to be based on validated simulations, and address uncertainty in the product’s use, its processing, and models used to assess each, and provide desirable performance over its entire life cycle. Composite Design Attributes Usability Extendibility Durability Dimensional stability Reliability Manufacturability Serviceability Recycle ability Disposability etc…

6. MISSOURI Vision (cont) Integrated product and process design for short fiber reinforced polymer composites Stiffness and strength defined by fiber direction during manufacturingStiffness and strength defined by fiber direction during manufacturing Integrated product and process design yields improved performanceIntegrated product and process design yields improved performance IPPD enabling technologiesIPPD enabling technologies integratednon-integrated mold filling fiber orientation material properties product performance polymer melt flow analysis static stress analysis modal analysis thermal stress analysis mold filling simulation fiber orientation prediction material property calculation mold cooling analysis warpage simulation numerical optimization design sensitivity analysis multidisciplinary design methodologies structural optimization

7. MISSOURI Perceived Gaps Validated models needed for all aspects of composites processing –E.g., strength and stiffness prediction from flow simulation Design sensitivities not developed to level of analyses –Fiber orientation –Mechanical properties from process models –Non-isothermal flow, reactive flow Optimal Design / DSA not available to end user –Design parameterization process appropriate Optimal design applications are task or discipline focused –I.e., Multidisciplinary design methods rarely not applied to composite molding problems Nondeterministic approaches not applied to composite molding problems

8. MISSOURI Future Research Further develop/validate composite molding process/product models Development and application of DSA method for composites molding Development of a user-oriented composites molding design environment –Incorporate multidisciplinary design methodologies –Incorporate design under uncertainty tools –Include process control in optimal process design Application / Validation on industrial scale problems