Modelo

AIAA-98-4963
PAPER HELICOPTER - EXPERIMENTAL OPTIMUM ENGINEERING DESIGN CLASSROOM PROBLEM Terry L. Siorek (siorek@BellSouth.net), 5201 SW 18th Street Plantation, FL 33317 Raphael T. Haftka (haftka@ufl.edu) * University of Florida, Gainesville, FL 32611. ** ABSTRACT Experimental Optimum Engineering Design is a new undergraduate/graduate course developed at the University of Florida for combininganalytical optimization techniques and design of experiments methods in product design. The paper describes a design project - the design of a paper helicopter for minimum autorotation speed - and its usage in the course. This project, originally developed for introducing students to basic experimental statistics concepts, turned out to be well suited for combining analytical and experimentaldesign techniques. INTRODUCTION The past few years have seen increasing emphasis on strengthening the design content of engineering curricula (e.g., Mason et al., 1995). The increasing availability of spreadsheet programs, such as Lotus 1-2-3 and Excel, as well as mathematical computation packages, such as Mathematica and Matlab, allows us to introduce design optimization concepts early in thecurriculum. These packages allow students to perform design optimization in low-dimensional design spaces graphically, by exhaustive searches or by formal optimization. However, the increasing power of computational tools available to students accentuates an existing bias in favor of analytical design exercises as compared to design based on building and testing prototypes. In real life the designprocess rarely ends with an analytical design study, or even with the building of a single prototype. Rather, often extensive tests are conducted to explore the performance of prototypes. Several modifications are often built and tested, so that the design process which begins analytically is refined through experiments. There is a need for courses that teach students design techniques that combineanalytical models with experimental refinement of the design. One of us (Haftka), has recently developed an undergraduate/graduate course, Experimental Optimum Engineering Design, to address this need.
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The course begins with optimization formulation, optimality criteria and a short survey of optimization techniques, and continues with design of experiments (DOE) techniques for constructingresponse surface approximations. The course is focused around a project. Students first design based on analysis, continue to build and test the analytical optimum, and finally refine the design experimentally by building and testing a number of designs in the neighborhood of the analytical optimum. The course emphasizes theory for response-surface techniques. These techniques have recently becomepopular also for analytical optimization (e.g., Kaufman et al., 1996). The reasons for this popularity include increasing similarity between numerical simulations and laboratory experiments due to numerical noise, as well as the ease of using response-surface techniques for connecting large and complex analysis software to optimization software (see also Haftka et al., 1998). The course was firstoffered in 1996, and the course project was the shape optimization of a lap joint for connecting two aluminum pieces (Haftka and Jenkins, 1998). This project was first tried out in an Introduction to Engineering sophomore course. It was found that with the aid of spreadsheet programs, such as Lotus 1-2-3 and Microsoft Excel, sophomores could handle well the combined analytical-experimental designproblem, albeit with too little understanding of the underlying techniques. A more thorough testing of the lapjoint project, in the Experimental Optimum Engineering Design course, revealed one flaw in the project. Even though simple strength-of-material formulae were used for the analysis, they proved to be so accurate, that the experimental optimization part did not change the design significantly....