## What is Finite Element Analysis or the Finite Element Method?

written by: kkaarthic • edited by: Lamar Stonecypher • updated: 12/27/2010

This article is written to give a basic insight on what Finite Element Analysis (FEA) or Finite Element Method (FEM) means. There is a lot of hype about the areas of application for which FEA can be applied. This article should throw some light on what exactly FEA means.

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FEA- Finite Element Analysis as the name suggests is the methodology we apply to analyse a complex body. A best example for a complex body would be everything we see in day to day life from a toothbrush to the motor car we use. The only difference being the toothbrush is a single component whereas the motor car is composed by a lot of these single components.

You may ask why one should analyse a simple toothbrush. For an answer, consider if the toothbrush broke into two pieces when you applied pressure to clean your teeth. Though this example may seem to be very simple, it is very much required for the proper usage of anything without causing any damage. Now just think about the millions of articles you tend to use in your day to day life; FEA is an area which will help to understand these complex components with ease.

How can FEA help us to do this?

FEA is a mathematical computation method in which:

• A complex entity is broken up into continuous simple geometric shapes called Elements.
• Elements can be simple geometric shapes like cube pyramids for 3–dimensional objects and as squares or triangles for 2–dimensional shapes.
• They are broken into simple geometric shapes because we know the formulas pertaining to each of these sections like volume, area, etc
• Each Element in interconnected with its neighbor in all directions by means of Nodes.
• Any load applied to this single element is distributed to its neighbor correspondingly based on its geometrical features.
• Just visualize a train moving in the distance. At a far view we see the train as a single line moving, but as we move closer we visualize the engine and the compartments as separate entities. Here the engine and compartments are separate elements interconnected to each other by the links (or nodes in FEA terms). The effect caused by the engine (the first element) caused the compartments (consecutive elements) to move or follow it.
• The material properties of the complex entity or object are applied to the whole of these elements.

FEA is an area utilizing all the aspects of mathematics and engineering. Since we can break a complex entity or object into small elements, the use of the computational facilities is very much required to ease the job and arrive at a result quickly. Further FEA helps us in knowing the outcome of a product during its design stage itself, thus saving a lot of money and time that would be wasted if a prototype needs to me made specifically for the testing purpose.

We will look further into the applications of FEA and the more detailed methodologies used in FEA in my further articles.