2.2. Subsidiary Design Equations

Equations expressing other functional requirements or constraints that must also be met but are not part of the main goal.

Subsidiary Design Equations (SDEs) refer to additional equations that address other important requirements that aren't the main optimization goal. While the primary design equation focuses on achieving the main objective—like minimizing weight or cost—SDEs ensure that other necessary constraints such as strength, manufacturability, and safety are also taken into account. These represent conditions that the design must satisfy to be deemed acceptable.

Think of designing a smartphone. The main goal might be to minimize the weight for portability. However, the subsidiary equations will ensure that the phone is also durable enough to withstand drops (strength constraints), thin enough to fit comfortably in a pocket (dimensional constraints), and uses materials that are safe for the user (safety constraints).

Typically include stress limits, deflection criteria, manufacturability, or safety factors in mechanical designs.

SDEs play a crucial role in mechanical design by defining limits on various parameters. For instance, they may include criteria related to how much stress a component can handle before failing, how much it can deflect under load, and ensuring that it can be manufactured with the available techniques. By integrating these constraints, designers ensure that products are not only optimized for performance but also practical and safe in real-world applications.

Imagine if you were designing a bridge. You want to make it light and cost-effective (primary goal), but you also have to make sure it can handle certain weights (stress limits) and doesn't sway too much in the wind (deflection criteria). If the design fails to meet these subsidiary criteria, the bridge might end up being unsafe, regardless of how well it meets the primary design objectives.

SDEs act as side conditions or relationships linking materials, geometry, and performance.

While the Primary Design Equation (PDE) outlines the central goal of the design process, the Subsidiary Design Equations establish crucial relationships that connect various aspects of the design, such as the materials used or the geometric shapes adopted. This interrelation ensures that when a design is optimized toward its main goal, it concurrently adheres to vital performance and safety standards as dictated by the SDEs.

Think of a recipe for a cake. The main goal may be to create the tastiest cake (the PDE), but there are specific conditions like the baking time, the temperature of the oven, and the proportions of ingredients that must be followed (the SDEs). If you ignore the SDEs, you might find your delicious cake is burnt or undercooked.

In practice, the primary equation defines the optimization goal, while subsidiary equations handle additional constraints that the design must satisfy for feasibility and acceptance.

In real-world applications, when engineers embark on design optimization, they first establish their primary goals utilizing the PDE. After that, they must incorporate SDEs to satisfy engineering standards and specifications. This ensures that the final design not only meets the intended objectives but is also practically viable and safe for end-use. Without considering SDEs, a design may look good on paper but fail to perform or be implementable in reality.

When building a vehicle, the main goal might be to achieve the highest fuel efficiency (PDE). However, engineers will need to ensure that the vehicle adheres to safety standards (SDE), can withstand accidents, and is comfortable for passengers. If they only focus on fuel efficiency without considering these additional aspects, the vehicle could become unsafe or uncomfortable, leading to poor acceptance in the market.

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