In the following, we will give some examples of finite element applications. The range of applications of finite elements is too large to list, but to provide an idea of its versatility we list the following:

a. stress and thermal analyses of industrial parts such as electronic chips, electric devices, valves, pipes, pressure vessels, automotive engines and aircraft;
b. seismic analysis of dams, power plants, cities and high-rise buildings;
c. crash analysis of cars, trains and aircraft;
d. fluid flow analysis of coolant ponds, pollutants and contaminants, and air in ventilation systems;
e. electromagnetic analysis of antennas, transistors and aircraft signatures;
f. analysis of surgical procedures such as plastic surgery, jaw reconstruction, correction of scoliosis and many others.

This is a very short list that is just intended to give you an idea of the breadth of application areas for the method. New areas of application are constantly emerging. Thus, in the past few years, the medial community has become very excited with the possibilities of predictive, patient-specific medicine.

One approach in predictive medicine aims to use medical imaging and monitoring data to construct a model of a part of an individual’s anatomy and physiology. The model is then used to predict the patient’s response to alternative treatments, such as surgical procedures.

For example, Figure 1.3(a) shows a hand wound and a finite element model. The finite element model can be used to plan the surgical procedure to optimize the stitches.

Heart models, such as shownin Figure 1.3(b), are still primarily topics of research, but it is envisaged that they will be used to design valve replacements and many other surgical procedures. Another area in which finite elements have been used for a long time is in the design of prosthesis, such as shown in Figure 1.3(c).

Most prosthesis designs are still generic, i.e. a single prosthesis is designed for all patients with some variations in sizes. However, with predictive medicine, it will be possible to analyze characteristics of a particular patient such as gait, bone structure and musculature and custom-design an optimal prosthesis.

FEA of structural components has substantially reduced design cycle times and enhanced overall product quality. For example in the auto industry, linearFEAis used for acoustic analysis to reduce interior noise, for analysis of vibrations, for improving comfort, for optimizing the stiffness of the chassis and for increasing the fatigue life of suspension components, design of the engine so that temperatures and stresses are acceptable, and many other tasks.

NonlinearFEAis used for crash analysis with both models of the car and occupants; a finite element model for crash analysis is shown in Figure 1.4(a) and a finite element model for stiffness prediction is shown in Figure 1.4(c). Notice the tremendous detail in the latter; these models still require hundreds of man-hours to develop. The payoff for such a modeling is that the number of prototypes required in the design process can be reduced significantly.

Figure 1.4(b) shows a finite element model of an aircraft. In the design of aircraft, it is imperative that the stresses incurred from thousands of loads, some very rare, some repetitive, do not lead to catastrophic failure or fatigue failure. Prior to the availability of FEA, such a design relied heavily on an evolutionary process (basing new designs on old designs), as tests for all of the loads are not practical.With FEA, it has become possible to make much larger changes in airframe design, such as the shift to composites.

In a completely different vein, finite elements also play a large role in environmental decision making and hazard mitigation. Forexample, Figure 1.5 is a visualization of the dispersal of a chemical aerosol in the middle of Atlanta obtained by FEA; the aerosol concentration is depicted by color, with the highest concentration in red.

Note that the complex topography of this area due the high-rise buildings, which is crucial to determining the dispersal, can be treated in great detail by this analysis. Other areas of hazard mitigation in which FEA offers great possibilities are the modeling of earthquakes and seismic building response, which is being used to improve their seismic resistance, the modeling of wind effects on structures and the dispersal of heat from power plant discharges.

The advection–diffusion equation can also be used to model drug dispersal in the human body. Of course, the application of these equations to these different topics involves extensive modeling, which is the value added by engineers with experience and knowledge, and constitutes the topic of validation.

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