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What is Finite Elemental Analysis?

Finite Element Analysis is used to solve various engineering problems by using mathematical models.

What kind of problems are we can solve?

We can solve all this problems.
·         Structural strength design
·         Structural interaction with fluid flows
·         Analysis of Shock (underwater & in materials)
·         Acoustics
·         Thermal analysis
·         Vibrations
·         Crash simulations
·         Fluid flows
·         Electrical analyses
·         Mass diffusion
·         Buckling problems
·         Dynamic analyses
·         Electromagnetic evaluations
·         Metal forming
·         Coupled analyses

How this problems are solved using FEA?

In FEA there are three major steps.
  • Pre-processing
  • Solving
  • Post-processing


 Pre-processing

Pre-processing has three steps. 
  • Geometry modeling
  • Meshing
  • Applying Boundary condition

          FEA starts with generating the Geometry. By geometry, I mean a model of our part or assembly which we want to analyse, e.g. a shaft, a beam, disc brake or any other component we want to analyse.

Then this whole geometry is converted into the small elements. These elements are assumed to be rigid and do not deform but they can be displaced using force. See this image to understand.

Here consider first line as a beam.
Some force would be applied to this beam, when is will be in service, at point 2 in downward direction and we want to check how this beam will deform or simply, bend.

So we make a CAD model of this beam in computer. Then we make this whole single model to small elements. Here in this case there are three elements, 1-2, 2-3 and 3-4.

Now as I said before this individual elements can’t deform but can be displaced. You can see this in the 3rd line.

This is very basic case to understand the FEA, in actual practice we make this element very small. So that deformation looks like perfect curve.

As we all know, all solids are made of molecules. Now in working condition after applying load if we can find the exact location of every molecule, we can have perfect idea of how that part would behave in actual application. But, there are billions of molecules, even in small component and you can never find the exact location data of every molecule.

In FEA, we imaging a group of molecules as an element and we find location of whole element. This makes problem slightly less complicated, and we can solve this mathematically.

All elements are connected to each other to create a whole part. The point, where two element, connects with each other are called nodes. Point 1,2,3 and 4 are nodes.

This process of converting part into small elements and creating nodes is called mesh generation or meshing.

After meshing, we apply various constraints and forces. Like in above example, we can fix the beam at point 1. So elements at point 1 will not change its place in the space. Then we apply some force at point 4 in 2nd line. During application of the force we specify the magnitude and direction of this force.

This forces and constraints are called boundary conditions.

This whole process of meshing and applying boundary conditions is called Pre-processing.

Solving

After pre-processing, we can solve the model. The process of solving is done by computer programs now a days. It is automated. In solving, computer generate equation based on geometry and applied boundary conditions, using solid mechanics or any other theory based on the problem, and then this equations are solved using matrix. Various methods of solving matrix like, Gaussian Elimination, Cramer’s rule or inversion of matrix are used.

 Post-Processing

After solving, we get the solution. In our beam case, we can get deformation at every node (basically we can get the value by which that node displace in the space) or stress at each node.

Now, we had a small model with only 4 nodes and 3 elements. So we get the 4 displacement values here on 4 node, and at node 1 it is zero because it is fixed. We can easily read and understand this. But in real applications, we get thousands of nodes, and So, thousands of values of stress and strains. Now, if we get the excel file of this data, it is not possible to read that values and understand. So, various programs are available, which read this data and place that nodes in space as they are deformed. So we can visually see the displacement. These program are very advance and they use color codes, which make it very easy to understand.


This is very simple explanation of how FEA works.
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