Week - 1 - Consistency of Units

Consistency of Units

AIM:

The Main aim of this project is to convert the given measurements into convert quantities from one system of units to another.

Procedures:

The Young's Modulus of steel is 210GPa which is input as 210e+9 in LS-DYNA as per SI unit system. However, if you use kg/mm/ms unit system, the input quantity will be 210. Thus, the conversion factor is 10^-9.

Similar to the above one the values of the units below will also be converted accordingly.

Given 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 systems 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

Calculations:

The values are given in SI unit system.

For example, the given values will be converted to the following,

1. MASS 1kg

1 Kilogram = 1000 grams
= 1000000 milligrams
= 0.001ton
= 0.0685218 slug

Converting factor:

For Gram 10³

For Milligrams 10⁶

For Ton 10^-3

2. LENGTH 1m
   1 Meter = 100 centimeters
   =1000 millimeters
   = 0.0006213712 mile
   = 0.001 kilometers
   = 3.28084 feet

Converting Factor:

For Centimeter 10²

For Millimeter 10³

For Mile multiply the length value by 1/1609

For Kilometer 10^-3

For Inches multiply the length value by 39.37

For Feet multiply the length value by 3.281

3. TIME 1s
   1 Seconds = 1/60 minutes
   = 1/3600 hours
   = 1000000 microseconds

Converting Factor:

For Minutes 0.0166667

For Hours 0.0002777778

For Microseconds 10⁶

4. FORCE 1N
   1N = 1kilograms* 1 meter/seconds²

= (1000 grams * 1000 millimeters) / (1000 milliseconds²

= (10⁶*10^-6) (grams millimeters / milliseconds²

= 1 grams millimeters /milliseconds²

Converting Factor:

For 1 g mm/ms² = 1

For kgf 1 newton = 0.1019716213 kilogram-force

5. STRESS 1Pa
   1Pa = 1N/m²

= (1 Kilograms (1meter /seconds²)) / meter²

= 1 Kilograms / (meter seconds²)

= 1000 grams / (1000 millimeters (1000 milliseconds²))

=10^-6 grams / (millimeters milliseconds²)

Converting Factor: 10³

6. ENERGY 1Nm
   1 Nm= 1J=1Kg (1m/s²) m

=1 (kg m²/ s²)

= ((1000 g (1000mm)) / (1000 ms²))

=10^-6 g/ (mm ms²)

Converting Factor: 10³

7. DENSITY 1Kg/m3
   1Kg/m³ =1000g/(1000mm³)

= 10^-6 g/mm

Converting Factor: 10^-6

8. YOUNG'S Modulus 210GPa
   210GPa=210e+9kg/ (m s²)

=210e+9*10^-6 g / (mm m s²)

=210e+3 g / (mm m s²)

=210*10³ g / (mm m s²)

Converting Factor: 10³

9. Velocity 56.33KMPH
   33Kmph = 56.33 * ((10⁶mm)/3600*1000ms))

=15.647 mm/ms

Converting Factor: 5/18

10. GRAVITY 9.8m/s2

9.8m/s² = 9.8*1000 mm / (1000ms²)

= 9.8*10-3 mm/ms²

Converting Factor: 10^-3

Table:

This table is made for 1 units in the conversion,

Units	Length	Mass	Time	Force	Stress	Energy
	1m	1kg	1s	1N=1kg m/s2	1Pa = 1kg/(m s2)	1J=1 Nm= 1 Kg m2/s2
kg m s	1m	1Kg	1s	1N	1Pa	1J
kg cm ms	102cm	1Kg	103ms	10-4	10-8	10-2
kg cm s	102cm	1Kg	1s	102	10-2	104
g mm ms	103mm	103g	103ms	1	10-6	103
g cm s	102cm	103g	1s	105	10	107
g cm μs	102cm	103g	106μs	10-7	10-11	10-5
g mm s	103mm	103g	1s	106	1	109
ton mm s	103mm	10-3ton	1s	1	10-6	103
slug ft s	3.28 ft	0.068 slug	1s	0.2246	0.0208	0.7366
kg mm s	103mm	1Kg	1s	103	10-3	106
g cm ms	102cm	1000g	103ms	10-1	10-5	10
kg mm ms	103mm	1Kg	103ms	10-3	10-9	1

Conclusion:

Since 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 have to be conversant with converting quantities from one system of units to another.

Thus, the conversion of the Units is done in this report.