How the FEM Cell Simulation Works!

"The mesh itself is done on 3 dimensional lattice space. However, for the data analysis purpose only the surface nodes and elements get extracted. Once this is done, radial vectors are constructed each of them having equal angular distant from each other covering 360 degrees. Along these lines, interpolated displacement fields are integrated. The result of these integrations represent radial displacements."

In the figure above, red lines represent the paths of integration and blue lines are the mesh that we are integrating. Since a position at which the integration lines cross with the surface mesh lines are random, I had to take into account several different cases when I was developing the code. That is, given that the mesh is done by tetrahedral element types, a face of an element that is exposed to the surface will always be a triangle. The question is, how many cases are there in positioning the outer (and inner) elliptical cell boundary and a triangle with an integration line crossing it? Many. The code is completed, but I still don't know how many cases I counted, but roughly there are five cases followed by 3-4 subcases under them.

The above figure well shows the internal mechanism of the code as it not only shows the mesh of the cell but the path of integration lines. The mesh also features a higher mesh density inside the cell boundaries then other regions to increase FEM efficiency. This is also noticeable in the picture above. However, when the above picture was generated, the virtual cell boundary was translated to the left by a cell radius so that when plotted this variation in mesh density can be seen well within the boundary.

No comments: