Week - 1 - Consistency of Units

LS-DYNA doesn't have a default system of units. User needs to input material properties and physical dimensions according to a consistent system of units as per their choice. This warrants that to use LS-DYNA in different circumstances, users has to be conversant with converting quantities from one system of units to another.

Value of the following measurements are given as follows:

MASS 1kg
LENGTH 1m
TIME 1s
FORCE 1N
STRESS 1Pa
ENERGY 1Nm
DENSITY 1Kg/m3
YOUNG'S Modulus 210GPa
Velocity 56.33KMPH
GRAVITY 9.8m/s2

Now, here are a few system of units:

Kg cm ms

Kg cm s

gm mm ms

kg m s

g cm s

g cm us

g mm s

ton mm s

slug ft s

kg mm s

g cm ms

kg mm ms

Detailed Calculation:

Here we will see conversion of above measurements with conversion factor.

• Detailed calculation for conversion from SI unit to gm/mm/ms unit system can be as given below

MASS: 1kg = 1000 gm. Conversion factor -1*1000 =10³

LENGTH: 1m = 1000 mm. Conversion factor=1*1000 = 10³

TIME:1s = 1000 ms, Conversion factor =1*1000 =10³

FORCE: 1N - 1 (Kg*m) /S²

=1 (1000 gm*1000 mm)/(1000 ms)²

= (1 gm*mm)/ ms²

Conversion factor=1

STRESS: 1Pa = 1N/m² = {(1 Kg* m) /S²)/m²

= {(1000gm * 1000mm) /1000000 ms²}/1000000mm² ={(10⁶ gm mm)/ 10⁶ ms²)/10⁶ mm²

=(1 gm mm)/ms² /10⁶ mm²

=(10-⁶* gm)/mm*ms²

Conversion factor 10-⁶ (10^-6)

ENERGY: 1Nm {1 (Kg * m)/S²

={1 (1000 gm*1000 mm) / (1000 ms)² }* 1000mm

={1 (10⁶ gm*mm) / (10⁶ ms)² * 10³ mm

=1{(gm* mm) / ms²}* 10² mm

=1{(gm* mm) / ms² )* 10³mm

= 10³(gm * mm²) / ms²

Conversion factor =10³

DENSITY: 1Kg/m³ = 1000 gm/ (1000mm)³

=1000 gm/10⁹ mm³

=10-⁶ gm / 10 mm³

=10-⁶gm /mm³

Conversion factor =10-⁶ (10^-6)

YOUNG'S Modulus: 210GPA =210* 1000 N/mm²

={210* 1000 (Kg *m) /S²}mm²

={210* 1000 (1000gm *1000 mm) / (1000 ms)²}/ mm² ={210 * 1000 (1 gm *mm) /ms²) / mm²

={210 * 10³ gm *mm) /mm²* ms²

={210 * 10³ gm/mm * ms²

Conversion factor =10³

VELOCITY: 56.33KMPH = (56.33 * 1000 m) / H

= (56.33 * 106 mm) / 3600 * 1000 s

= (56.33 * 10 mm) / 36 * 10 ms

= 15.6472 mm/ ms

GRAVITY: 9.8m/s² = 9.8 (1000mm) / (1000 ms)²

= 9.8 (10³ mm) / 10⁶ms²

= 9.8 *10-³mm /ms

=Conversion factor =10-³ (10^-3)

Conclusion:

As we know that LS Dyna has no own unit system, so we have to convert each units as per requirements.

We can convert units with help of conversion factor very easy and fast.

So above conversion should always keep in mind and when ever we need ,we must convert units with help of conversion factor.