User:Eas4200c.f08.wiki.b/HW1

=Basics of Aerospace Structures=

The Finite Element method (FEM) can be used in a wide variety of fields, from various types of engineering, to applied math, and even geology. Aerospace structures is one of the fields where FEM can be used to solve the partial differential equations that govern this particular field.

The structure of an aircraft must be designed with two main goals in mind: it must be light, and it must be strong. More specifically, the structure of an aircraft should have a high stiffness, high strength, and be composed of light weight materials.

Stiffness refers to a Young’s modulus $$\displaystyle E$$, or the slope, in a linear relation between stress $$\displaystyle \sigma$$ and strain $$\displaystyle \epsilon$$, or $$\displaystyle \sigma = E \epsilon$$. Strength refers to a particular stress, such as the yield stress $$\displaystyle \sigma_Y$$, where a material begins to weaken, and the ultimate stress $$\displaystyle \sigma_U$$, where a material fails. Toughness is simply the capacity to endure fracture or damage.

Examples of materials with high stiffness and high strength include steel and titanium alloys, since they have a large Young’s modulus and large ultimate and yield strengths. Glass is an example of a material with high stiffness, but low toughness. It does not withstand much plastic deformation and does not resist fracture well. Plastics and nylon are materials with a low stiffness, and high toughness, as they are they behave oppositely to glass.

Aircraft structures typically have monocoque or semi-monocoque designs to them. The term monocoque refers to a “single shell” design, while semi-monocoque is a shell that is stiffened by a supporting structure. These designs allow aircraft to have low weight, while also remaining strong and resisting bending. The geometry of an aircraft is, of course, also restricted by aerodynamics such as lift and drag on an airfoil.