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):
|
SI Unit system (kg, m, s) |
Value |
Conversion to (g, mm, ms) |
|
MASS |
1 Kg |
1000 g |
|
LENGTH |
1 m |
1000 mm |
|
TIME |
1 s |
1000 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.