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II. OVERVIEW AND STRATEGY

I. CHAPTER ROADMAP

Figure 16.1 illustrates a roadmap for studying solution methods. One route on this roadmap takes us through basic optimization principles through practical solutions and product applications. The alternative route adds more theoretical understanding to these principles and describes more advanced optimization techniques. Let's begin by considering an overview and strategy for numerical modeling.

II. OVERVIEW AND STRATEGY

As we transition from conceptual design, or early embodiment, the goal is to refine a model of our design concept(s). This model should represent a physical understanding of the product. As an example, consider the simple retail can food container as a product concept. For equal amounts of material, pressure loading, and all other conditions, why are can geometries different? Some cans are short; some cans are tall (long).

Figure 16.2 shows a canned food container (soup or soda) and a graphical representation of its basic parametric model. Assuming a focus metric for the design is the cost of material to produce the can, we seek to specify the can's height, radius, and thickness. These variables can form a simple representative model of the product, when a relationship is developed to estimate cost. Let's assume that a minimum thickness is predetermined for the manufacturing processes of the can. Let's also consider minimization of surface area as an equivalent metric for cost.

What are appropriate choices of the can height and radius to minimize surface area? When creating a food product, we are constrained to include a certain volume in the can. Such a constraint will limit the minimum surface area we can obtain. Thus, we might state a model for the can product as a set of two simultaneous equations:

While Equation (16.1) represents a simple model of the can product, we are still faced with the task of solving it: choosing the can radius and height given the volume of food product, C. How can we systematically represent and solve such a decision-making problem in product design, especially as the number of variables and equations becomes large?

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Date: 2016-01-14; view: 641


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