**03**

*Nov*

### Consistent Units in FEA

This post and the pdf doc provide a practical explanation of consistent units in FEA. Many FEA modellers/solvers do not show units within the software – the analyst **must** use consistent units with these. The PDF provides details and a units conversion table.

EnDuraSim_Consistent_Units.pdf

**But if you have limited time and are starting a new model, here is the short summary for common structural / mechanical analysis:**

- What length units are you using? If you have imported geometry from elsewhere, then measure some entities to figure out what length units were used.
- Choose your preferred unit of force.
- Derive ALL other physical units from your chosen Force and Length units (assumes everyone will be using seconds as the standard unit of time!).
- For example, Length = mm, Force = N, then Pressure = Stress = Youngs Mod = N/mm^2 = MPa. F=ma, thus mass MUST be Tonnes because acceleration = mm/sec^2. Thus density MUST be Tonnes/mm^3, eg. 7.8e-9 for a typical steel.
- Similarly, if Length = inch, Force = pounds, then Pressure = Stress = Youngs Mod = lbs/in^2 = psi. F=ma, thus mass MUST be slug-inch (this mass weighs ~386lbf on earth). Thus density MUST be Slug-inch/in^3, eg. 7.3e-4 for a typical steel. Pounds is not a mass for science or engineering, it is a force. Force and mass should never be confused.
- For a mm and Newtons model you could accidentally get away with using kg/mm^3 for density and 9.81 m/sec^2 for a simple gravity analysis, because the “inconsistency errors” cancel to give correct results. But if you then do natural frequency or any dynamics, the answers WILL BE wrong. So… stick with consistent units and maximise the chances of successful analysis / review / subsequent work.

**If you are trying to determine what units have been used in someone else’s “units-free” mode**l, some examples of consistent unit sets are:

- kg, m, sec, Newtons, Pascals, Joules, Watts. Density thus must be kg/m^3 and acceleration in m/sec^2.
- In this system, Steel has a Youngs Mod of ~ 2e11 and its density is ~ 7800 (water ~ 1000). 1g acceleration ~ 9.8.
- kg, mm, sec, milliNewtons (F=ma), kiloPascals (milliNewton/mm^2), Joules (mN.mm), Watts. Density thus must be kg/mm^3 and acceleration in mm/sec^2.
- In this system, Steel has a Youngs Mod of ~ 2e8 and its density is ~ 7.8e-6 (water ~ 1e-6). 1g acceleration ~ 9800.
- Tonne, mm, sec, N (F=ma), MPa (N/mm^2), milliJoules, milliWatts. Density thus must be Tonnes/mm^3 and acceleration in mm/sec^2.
- In this system, Steel has a Youngs Mod of ~ 2e5 and its density is ~ 7.8e-9 (water ~ 1e-9). 1g acceleration ~ 9800.
- slug-inch (mass), inch, sec, pound (force), psi, pound.inch (energy), pound.inch/sec (power). Density thus must be slug/in^3 and acceleration in inch/sec^2.
- In this system, Steel has a Youngs mod of ~ 29000000 and its density is 7.3e-4 (water ~ 9.4 e-5). 1g acceleration ~ 386. Beware of PARAM, WTMASS in Nastran (see pdf for details).

**Caution for metric Femap users:** a fresh Femap install assumes people model in inches, which will cause some metric modelled geometry to be scaled during import. To avoid this and other inconveniences, your first Femap action should be to go to File | Preferences -> Geometry/Model and change the Solid Geometry Scale Factor to Millimeters (or Meters if you use metres).

Understanding consistent units is critical when moving FEA models from one package to another via a text/neutral/universal format such as STEP, Patran or Nastran BDF – or when reviewing another analyst’s work. For those systems where consistent units are required, the attached document provides the details on why you must use Tonnes per cubic mm as density if you like to use Newtons for force and mm for sizing geometry. The pdf doc was first authored by EnDuraSim in 2009, but includes some minor refreshes and a correction in the imperial units section.