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7. Verification & Validation
It is imperative to do some checks to make sure that the numerical results are accurate. Numerical results can either be compared directly to empirical data or they may be compared to theory.
Mesh Refinement
Another, way to verify the solution of a numerical method is to examine the convergence of the solution as the mesh is refined. Generally, the numerical solution should converge to the exact solution as the mesh is refined. In order to refine the mesh, first click on the mesh tab, 
, in the tree outline. Next, expand "Sizing" in "Details of Mesh". The mesh will be refined by adjusting the "Element Size". The length of the beam is 4m so if you want n elements then you will need to set the "Element Size" to (4m/n). For instance, if you wanted 20 elements the "Element Size" should be set to (4m/20)=0.2m . After you have changed the "Element Size" to your preference, click on the solve button, 
, to recalculate the solution with the new mesh.
The table below displays the outputs of the ANSYS simulation for a mesh of 2 elements and a mesh of 10 elements.
|
Total Deformation (m) |
Maximum Bending Stress Pa |
|---|---|---|
Theory Values |
0.005103 |
4.635x10^6 |
2 Element FEA |
0.0051352 |
4.6352x10^6 |
10 Element FEA |
0.0051352 |
4.6352x10^6 |
As one can see from the table above the results do not change as the mesh is refined. The reason that the results do not change is that they have already converged to the answer. The exact solution for the deformation is cubic and for this setup ANSYS uses element BEAM 188 which in turn uses cubic interpolation. Thus, for the simple cantilever beam setup the numerical method converges very quickly.