Understanding FEA Numbers

Two times zero is still zero and half of infinity is still infinity. If you want to develop good engineering judgement you need to understand the profound meaning of this perspective on zero and infinity. When dealing with very small numbers, it makes no difference in the greater scheme of things whether the number is doubled or not. The number will still be a small number and needs to be interpreted that way.

Similarly when dealing with large numbers, even if you half the number you still are left with a large number. For all numbers in between you can use relative comparisons , however, for small and large numbers, one needs to understand that relative comparisons may not hold true.

Consider an FEA example where you are looking at stress in a model. In a certain region the stress should theoretically be close to zero. However one FEA software says the stress is 1 MPA, while another says it is 2 MPA. Does this mean the second software is producing results with 50% error ? No , it means both softwares are outputting very small numbers which are close to zero and therefore the SAME number.

Now consider you are probing stresses near a sigularity in the model, such as a sharp corner. Theoretical results say the stress should be infinity as you refine the mesh. Software A says it is 6000 MPa, while software B shows 3000 MPa. Again does this mean software B has 50% error? No, it means both softwares are outputting very large numbers which correlate to the trend of infinite stress and are therefore the SAME number.

Too many engineers only focus on the absolute numbers when comparing FEA results. Good engineering judgement involves looking at relative differences and also seeing how large or small the numbers are when making comparisons. Another way of thinking of this is in terms of order of magnitude. Small or very large numbers within the same order of magnitude are essentially the same number for all practical purposes. This is not only true in FEA but all life in general.