Week - 1 - Consistency of Units
Aim = To convert the given measurements from SI unit system to given different system of units.
Objective = As LS-DYNA doesn't have a default system of units. We need to input material properties and physical dimensions according to a consistent system of units as per our choice. To use LS-DYNA in different circumstances, user has to be conversant with converting quantities from one system of units to another.
Calculations =
Force (F)=Mass (m)*Acceleration (a)
or
Mass (m)= Force (f)/Acceleration (a)
- Force=Mass*Length/Time^2=kg*m/sec^2
- Mass=Force*Time^2/Length=N*Sec^2/m
- Stress=Mass*1/Length*Time^2
- Energy=Mass*Length^2/Time^2
- Mass=1kg, 1kg=1000 gm; CF=10^3
- Length=1m, 1m=100cm, 1cm=1000mm; CF=10^3
- Time=1Sec, 1Sec=1000 ms; CF=10^3
- Force=1N, 1N=1kgm/s^2= 1gm mm/ms^2; CF=10^0
- Stress= 1pa, 1pa=1N/m^2= 10^-6 gm/(mm ms)2); CF=10^-6
- Energy=1Nm, 10^3 (gm mm^2)/ms^2; CF=10^3
- Density=1kg/m^3, 10^-6 g/mm^3; CF=10^-6
- Young's Modulus, E=210 Gpa, 210*10^3 gm/mm ms^2; CF=10^-6
- Velocity= 56.33 kmph, 15.64 m/s, 15.64 mm/ms; CF=10^0
- Gravity=9.8 m/s^2, 9.8*10^-3 mm/ms^2; CF=10^-3
CF=Conversion Factor= CF is a number which we have to multiply with a quantity in one unit system to convert it in another unit system.
| Sr. No. | Unit System | Mass 1 kg | CF | Length 1 m | CF | Time 1 Sec | CF | Force 1 N | CF | Stress 1Pa | CF | Energy 1 Nm | CF | Density 1kg/m^3 | CF | Young's Modulus 210 GPa | CF | Velocity 56.33 kmph | CF | Gravity 9.8 m/s^2 | CF |
| 1. | kg cm ms | 1 | 10^0 | 1 | 10^2 | 1 | 10^3 | 1 | 10^-4 | 1 | 10^-8 | 1 | 10^-2 | 1 | 10^-6 | 210x10^0 | 10^-8 | 1.564 | 10^-1 | 9.8x10^-4 | 10^-4 |
| 2. | kg cm s | 1 | 10^0 | 1 | 10^2 | 1 | 10^3 | 1 | 10^2 | 1 | 10^-2 | 1 | 10^4 | 1 | 10^-6 | 210x10^7 | 10^-2 | 1564 | 10^2 | 9.8x10^2 | 10^2 |
| 3. | gm mm ms | 1 | 10^3 | 1 | 10^3 | 1 | 10^3 | 1 | 10^0 | 1 | 10^-6 | 1 | 10^3 | 1 | 10^-6 | 210x10^3 | 10^-6 | 15.64 | 10^0 | 9.8 | 10^-3 |
| 4. | kg m s | 1 | 10^0 | 1 | 10^0 | 1 | 10^0 | 1 | 10^0 | 1 | 10^0 | 1 | 10^0 | 1 | 10^0 | 210x10^9 | 10^9 | 15.64 | 10^0 | 9.8 | 10^0 |
| 5. | g cm s | 1 | 10^3 | 1 | 10^2 | 1 | 10^0 | 1 | 10^5 | 1 | 10^1 | 1 | 10^7 | 1 | 10^-3 | 210x10^10 | 10^1 | 1564 | 10^2 | 9.8x10^2 | 10^2 |
| 6. | g cm us | 1 | 10^3 | 1 | 10^2 | 1 | 10^6 | 1 | 10^-7 | 1 | 10^-11 | 1 | 10^-5 | 1 | 10^-3 | 210x10^-2 | 10^-11 | 15.64x10^-4 | 10^-4 | 9.8x10^-10 | 10^-10 |
| 7. | g mm s | 1 | 10^3 | 1 | 10^3 | 1 | 10^0 | 1 | 10^6 | 1 | 10^0 | 1 | 10^9 | 1 | 10^-6 | 210x10^9 | 10^0 | 15.64x10^3 | 10^3 | 9.8x10^3 | 10^3 |
| 8. | tonn mm s | 1 | 10^-3 | 1 | 10^3 | 1 | 10^0 | 1 | 10^0 | 1 | 10^-6 | 1 | 10^3 | 1 | 10^-12 | 210x10^3 | 10^-6 | 15.64x10^3 | 10^3 | 9.8x10^3 | 10^3 |
| 9. | slug ft s | 0.06852 | 0.06851 | 3.2808 | 3.2808 | 1 | 10^0 | 0.2248 | 0.2248 | 0.0208 | 0.0208 | 0.7375 | 0.7375 | 0.00194 | 0.00194 | 4.385 | 2.088x10^7 | 5.01793 | 3.2x10^-1 | 3.2152 | 3.2*10^0 |
| 10. | kg mm s | 1 | 10^0 | 1 | 10^3 | 1 | 10^0 | 1 | 10^3 | 1 | 10^-3 | 1 | 10^6 | 1 | 10^-9 | 210x10^6 | 10^-3 | 15.64x10^3 | 10^3 | 9.8x10^3 | 10^3 |
| 11. | g cm ms | 1 | 10^3 | 1 | 10^2 | 1 | 10^3 | 1 | 10^2 | 1 | 10^-2 | 1 | 10^4 | 1 | 10^-3 | 210x10^-7 | 10^-16 | 1.564 | 10^-1 | 9.8x10^-4 | 10^-4 |
| 12. | kg mm ms | 1 | 10^0 | 1 | 10^3 | 1 | 10^3 | 1 | 10^-3 | 1 | 10^-9 | 1 | 10^0 | 1 | 10^-9 | 210 | 10^-9 | 15.64 | 10^0 | 9.8x10^-3 | 10^-3 |
Learning Outcome: LS-DYNA is not having a unit system. I learned about the process of converting quantities in one unit system to other unit system.