# An Introduction to the Finite Element Method

This article provides an introduction to the Finite Element Method or the Finite Element Analysis( FEA). This is the method which is used in engineering to simulate the behavior of many mechanical systems and to test the mechanical systems.

Finite Element Analysis of FEA is a discipline, which is recent and crosses the boundaries of various disciplines. These disciplines include physics, mathematics, engineering as well as computer science. The method of FEA or Finite Element analysis has a wide range of applications and also has an extensive utilization in the thermal, structural as well as fluid analysis related areas. There are three important phases comprised in the Finite Element Analysis. The details of the phases are as follows:

1. Pre Processing Phase : In this phase, the analyst produces a finite element mesh to divide the geometry of the subject into small parts for the mathematical analysis. Material properties and the boundary conditions are also imparted to the model in this phase only.
2. Solution : This is the second phase of the Finite Element analysis. In this phase the computer program forms the matrix equations of the model and then solve for various primary quantities.
3. Post Processing : This is the final stage of the Finite Element Analysis. In this phase the validity of the solution is checked by the analysts and the value of primary quantities like stresses and displacement are examined. Some additional quantities like the specialized stresses and error indicators are also examined in this phase.

### Benefits of FEA

There are some very important benefits of FEA over the conventional solution methods.
• The new design concept can be modeled in this analysis domain and then based on the results, the design can be modified. Thus, at times the failure can be anticipated and changes in the design are made. With the investment of a few dollars, the validity of designs under the operating conditions can be tested and modifications can be made in the original design.
• In FEA, the detailed CAD model is first developed and then the FEA can analyze the operating conditions on the design in detail and it will thus save the time and money by decreasing the number of prototypes that are required. A product, which is existing and is experiencing some problems in operation, can be analyzed and subsequently improved and thus, the engineering change can be quickened and reduction in the cost is achieved.
• For performing the FEA, affordable computer workstations can be utilized and there is a lot of professional assistance available both in paid as well as free format.Apart from these advantages, there are some limitations also, involved with the use of FEA. Firstly, it will require a set of computer hardware, to perform the FEA, which will have a fixed cost. Also, the testing of the products can be reduced, but this process cannot completely eliminate the need of testing. Also a user, who is inexperienced, can arrive at wrong results and can lead to wrong decisions, which are very expensive.

### Conclusion

In order to gain the optimum output of the FEA, an experienced person must be chosen who is having an experience not only in the fields of fluids or elasticity, but also knows and is proficient in mathematics and computers.Thus, in this article, we have seen that FEA, is a method which, when used properly can save a lot of time and money in the manufacturing world.