Structural Analysis in Aircraft
Using the Finite Element Method

In order to build an aircraft which will hold up under all expected loads, the engineer must understand how each component in the aircraft is loaded and how much load it can withstand. This can be done with extensive testing, or with detailed analysis - but usually a combination of both.

The complexity of even the earliest airframes was such that analysis of them was very complex and difficult. Except for preliminary calculations, designs were finalized only after rigorous testing programs. As engineering methods have improved over the years, complex structures can be analyzed before expensive prototypes are built, giving better estimates of performance, and saving development time and cost.

An excellent engineering tool now in use is called Finite Element Analysis (FEA). It is used to predict stresses and strains in complex and oddly shaped components, to predict fluid flow conditions around objects such as an aircraft fuselage, a wing foil or an engine turbine blade, and to predict heat transfer through gasses and materials. FEA can be used for other applications as well.

Figure 1a

FEA consists of breaking the problem into many small, simple pieces and solving all of the pieces together. This requires solving thousands of equations simultaneously. Only the development of the digital computer has allowed FEA to become a practical tool.

Figure 1b

Figures 1a and 1b show a simple Finite Element (FE) model and the predicted deflections (multiplied by a scaling factor for better viewing) caused by a typical load. The outer surface of the model is covered with a grid of rectangles. Each rectangle is the outer surface of an element. This particular model consists of 1,560 elements which produces 8,568 separate equations. The complete model takes into account the geometry of the component, the materials used, the loading conditions and constraints and any other pertinent factors.

Figure 2

Figure 2 shows stress predictions in another FE model. Again, the grid on the surface shows the individual elements. The elements in this model are triangular in shape. The different colors represent different stress levels. The results predict higher stress levels near the holes than away from them.

Proper use of FEA allows a part to be "tested" before it is made. If an analysis shows a problem area in a component, the area can be redesigned. Successive iterations such as this allow a part to be modified as necessary to achieve a minimum weight while providing adequate strength.