Week - 1 - Consistency of Units
AIM:
Generally SI unit system is the standard system which is followed world wide. But many industries as per their convenience follow different system of units. LS DYNA don't follow any default system of units. So as per the application, the conversion factors for different system of units is to be find out.
EXPLANATION:
The following table shows the different measurements that need to be converted.
| S.NO | ||
| 1 | Mass | 1 kg |
| 2 | Length | 1 m |
| 3 | Time | 1 s |
| 4 | Force | 1 N |
| 5 | Stress | 1 Pa |
| 6 | Energy | 1 Nm |
| 7 | Density | 1 kg/m3 |
| 8 | Youngs Modulus | 210 GPa |
| 9 | Velocity | 56.33 KMPH |
| 10 | Gravity | 9.8 m/s2 |
First we need to find out the conversion factor from SI unit to gm/mm/ms unit system.
Mass = 1 kg = 1e3 g. So the conversion factor of mass from SI to gm/mm/ms is 1e3.
Length = 1 m = 1e3 mm. The conversion factor of length from SI to gm/mm/ms is 1e3.
Time = 1 s = 1e3 ms. The conversion factor of time from SI to gm/mm/ms is 1e3.
Force = 1 N =1 kg-m/s2 = (1e3 * 1e3)/1e3^2 gm-mm/ms2 = 1 gm-mm/ms2. The conversion factor is 1.
Stress = 1 Pa = 1 kg/m-s2 = 1e3/(1e3*1e3^2) gm/mm-ms2 = 1e-6 gm/mm-ms. The conversion factor is 1e-6.
Energy = 1 N-m = 1 kg-m2/s2 = (1e3*1e3^2)/1e3^2 gm-mm2/ms2 =1e3 gm-mm2/ms2. The conversion factor is 1e3.
Density = 1 kg/m3 = 1e3/1e3^3 gm/mm3 = 1e-6 gm/mm. The conversion factor is 1e-6.
Youngs Modulus = 210*1e9 Pa = 210*1e9*1e-6 gm/mm-ms2 = 210*1e3 gm/mm-ms2. The conversion factor is 1e-6 from SI system to gm/mm/ms system.
Velocity = 56.33 KMPH = 56.33*(5/18) m/s = 15.647 m/s (SI system) = 15.647 mm/ms. The conversion factor is 1 from SI system to gm/mm/ms.
Gravity = 9.8 m/s2 = 9.8*(1e3/1e3^2) mm/ms2 = 9.8e-3 mm/ms2. The conversion factor is 1e-3.
| UNITS |
Mass (1 kg) |
Length (1 m) |
Time (1 s) |
Force (1 N) |
Stress (1 Pa) |
Energy (1 N-m) |
Density (1 kg/m3) |
Youngs Modulus (210e9 Pa) |
Velocity (15.647 m/s) |
Gravity (9.81 m/s2) |
| kg/cm/ms | 1 | 100 | 1000 | 1e-4 | 1e-8 | 1e-2 | 1e-6 | 2100 | 1.5647 | 9.81e-4 |
| kg/cm/s | 1 | 100 | 1 | 1e2 | 1e-2 | 1e4 | 1e-6 | 210e7 | 1564.7 | 981 |
| kg/m/s | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 |
| gm/cm/s | 1000 | 100 | 1 | 1e5 | 10 | 1e7 | 1e-3 | 210e10 | 1564.7 | 981 |
| gm/cm/us | 1000 | 100 | 1e6 | 1e-7 | 1e-11 | 1e-5 | 1e-3 | 210e-2 | 15.647e-4 | 9.81e-10 |
| ton/mm/s | 1e-3 | 1000 | 1 | 1 | 1e-6 | 1e3 | 1e-12 | 210e3 | 15.647e3 | 9.81e3 |
| slug/ft/s | 0.068 | 3.28 | 1 | 0.22 | .02 | 0.73 | 0.0019 | 420e7 | 51.322 | 32.176 |
| kg/mm/s | 1 | 1000 | 1 | 1000 | 1e-3 | 1e6 | 1e-9 | 210e6 | 15.647e3 | 9.81e3 |
| gm/cm/ms | 1000 | 100 | 1000 | 0.1 | 1e-5 | 10 | 1e9 | 210e4 | 15.647e-1 | 9.81e-4 |
| kg/mm/ms | 1 | 1000 | 1000 | 1e-3 | 1e-9 | 1 | 1e-9 | 210 | 15.647 | 9.81e-3 |
RESULT:
The conversion factors from SI system to different system of units are obtained.