Week - 1 - Consistency of Units

Objective:

The objective of this challenge is to convert the given SI unit values of the given quantities to gm/mm/ms units and also to prepare a consistent unit system table for the different unit system. Before converting the given values into the different unit system, the definitions of Fundamental quantities and the derived quantities are established just as a ritual.

Fundamental Quantity: A fundamental quantity is that which is independent of any other quantity (length(m), mass(kg), time(s))

Derived quantity: A quantity which is dependent on Fundamental quantity is called derived quantity (density(kg/m3), acceleration (m/s2), velocity(m/s))

For the convenience the fundamental quantities (mass, length and time are converted to different unit measurement)

1kg => 1e+3 g = 0.001 tonne = 0.06852 slug

1m => 100 cm = 1000 mm = 3.2808 ft

1s => 1000 ms = 1e+6 μs

All parameters are converted to their respective unit system with the SI Unit system as standard. (Kg, m, s)

Calculation of the conversion from SI unit to (g, mm, ms):

FORCE 1N:

1N = 1mass*1acceleration

= 1kg*1 m/s

= (1000g*1000mm)/(1000ms)

= 10 *10 (g*mm)/ms

= 1 (g*mm)/ms

Conversion factor = 1

STRESS 1Pa:

1 Pa = 1N/m²

= {1kg*(1 m/s²)} /m² = 1 kg/ (m*s²)

So, 1 kg/ (m*s²) = 1000g/{1000mm*(1000ms) ²}

= 10^-6 g/(mm*ms²) = Conversion factor = 10^-6

ENERGY 1Nm:

1 J = 1Nm = (1kg*1 m/s²) * m 1 (kg*m² /s²)

Now, 1 (kg*m²/s²) = {1000g * (1000mm)²}/(1000ms)²

= (10⁹ g*mm²) / (10⁶ ms²)

= 10³ (g*mm² / ms²)

Conversion factor = 10³

DENSITY 1Kg/m³:

1Kg/m³ = 1000g/(1000mm)³

= 10^-6 g/mm³

Conversion factor = 10^-6

YOUNG'S Modulus 210GPa:

210GPa = 210e+9 kg/ (m*s²)

Here we already have 1 kg/ (m* s) while calculating the stress

1 kg/ (m*s²) = 1000g/{1000mm*(1000ms)²}

= 10^-6 g/(mm*ms²)

Therefore,

210e+9 kg/(m*s²) = 210e+9 * 10^-6 g/ (mm*ms²)

= 210e+3 g/ (mm*ms²) = 210*10³ g/ (mm*ms²)

Conversion factor = 10³

Velocity 56.33Kmph:

56.33 Kmph = 56.33 * {10⁶ mm/(3600*1000ms)}

= 15.647 mm/ms

Conversion factor = 1

GRAVITY 9.8m/s²:

9.8m/s² = 9.8 * 1000mm/(1000ms)²

= 9.8* 10^-3 mm/ms²

Conversion factor = 10^-3   

Conclusion:

Performed conversion of units as LS-DYNA doesn’t have a default system of units. The user needs to be conversant with converting quantities from one system of units to another so that error won’t occur while performing simulations.