Week - 1 - Consistency of Units
OBJECTIVE:
To convert the given SI Unit measurements into other system of units mentioned below.
SI Unit measurements:
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
System of units to which the measurements are to be converted:
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
Calculation for conversion of measurements from SI units to gm/mm/ms unit system:
Mass:
1 Kg = 1000 gm
Conversion Factor: `10^3`
Length:
1m = 1000 mm
Conversion Factor: `10^3`
Time:
1 s = 1000 ms
Conversion Factor: `10^3`
Force:
1 N = 1 Kg * 1 m/`s^2`
= (1000 gm * 1000 mm)/`(1000 ms)^2`
= 1 (gm*mm)/`ms^2`
Conversion Factor: 1
Stress:
1 Pa = 1 N/`m^2`
= 1 (Kg * m/`s^2`)/`m^2`
= 1 Kg/(m*`s^2`)
= 1000 gm/(1000 mm * (1000 ms * 1000 ms))
= `10^-6` gm/(mm*`ms^2`)
Conversion Factor: `10^-6`
Energy:
1 Nm = 1 (Kg * m/`s^2`)*m
= (1000 gm * (1000 mm *1000 mm))/(1000 ms * 1000 ms)
= `10^3` (gm*`mm^2`)/`ms^2`
Conversion Factor: `10^3`
Density:
1 Kg/`m^3` = 1000 gm/(1000 mm * 1000 mm * 1000 mm)
= `10^-6` gm/`mm^3`
Conversion Factor: `10^-6`
Young’s Modulus:
210GPa = 210*`10^9` Pa
= 210*`10^9` N/`m^2`
= 210*`10^9` (Kg * m/`s^2`)/`m^2`
= 210*`10^9` [1000 gm/(1000 mm * (1000 ms * 1000 ms))]
= 210*`10^9` [`10^-6` gm/(mm*`ms^2`)]
= 210*`10^3` gm/(mm*`ms^2`)
Conversion Factor: `10^3`
Velocity:
1 KMPH = `10^6` mm/(3600 * 1000) ms …………….{1 Km = `10^6` mm}; {1 hr = 3600*1000 ms}
= 10/36 mm/ms
= 0.2777 mm/ms
Therefore, 56.33 KMPH = 56 * 0.2777 mm/ms
= 15.64 mm/ms
Conversion Factor: 0.2777
Gravity:
9.8 m/`s^2`= 9.8 (1000 mm/(1000 ms *1000 ms))
= 9.8*`10^-3` mm/`ms^2`
Conversion Factor: `10^-3`
Conversion from SI Units to other system of units mentioned:
| Unit System | Mass | Length | Time | Force | Stress | Energy | Density | Young's Modulus | Velocity | Gravity |
| Kg cm ms | 1 Kg | `10^2` cm | `10^3` ms | `10^-4` kg*cm/`ms^2` | `10^-8` kg/(cm*`ms^2`) | `10^-2` kg*`cm^2`/`ms^2` | `10^-6` kg/`cm^3` | 2100 kg/(cm*`ms^2`) | 1.5647 cm/ms | 9.8*`10^-4` cm/`ms^2` |
| Kg cm s | 1 Kg | `10^2` cm | 1 s | `10^2` kg*cm/`s^2` | `10^-2` kg/(cm*`s^2`) | `10^4` kg*`cm^2`/`s^2` | `10^-6` kg/`cm^3` | 210e+7 kg/(cm*`s^2`) | 1564.7 cm/s | 9.8*`10^2` cm/`s^2` |
| kg m s | 1 Kg | 1 m | 1 s | 1 kg*m/`s^2` | 1 kg/(m*`s^2`) | 1 kg*`m^2`/`s^2` | 1 kg/`m^3` | 210e+9 kg/(m*`s^2`) | 15.647 m/s | 9.8 m/`s^2` |
| g cm s | `10^3` g | `10^2` cm | 1 s | `10^5` g*cm/`s^2` | 10 g/(cm*`s^2`) | `10^7` g*`cm^2`/`s^2` | `10^-3` g/`cm^3` | 210e+10 g/(cm*`s^2`) | 1564.7 cm/s | 9.8*`10^2` cm/`s^2` |
| g cm `mu`s | `10^3` g | `10^2` cm | `10^6` `mu`s | `10^-7` g*cm/`mus^2` | `10^-11` g/(cm*`mus^2`) | `10^-5` g*`cm^2`/`mus^2` | `10^-3` g/`cm^3` | 2.10 g/(cm*`mus^2`) | 15.647*`10^-4` cm/`mu`s | 9.8*`10^-10` cm/`mus^2` |
| g mm s | `10^3` g | `10^3` mm | 1 s | `10^6` g*mm/`s^2` | 1 g/(mm*`s^2`) | `10^9` g*`mm^2`/`s^2` | `10^-6` g/`mm^3` | 2.10e+11 g/(mm*`s^2`) | 15647 mm/s | 9.8*`10^3` mm/`s^2` |
| ton mm s | `10^-3` ton | `10^3` mm | 1 s | 1 ton*mm/`s^2` | `10^-6` ton/(mm*`s^2`) | `10^3` ton*`mm^2`/`s^2` | `10^-12` ton/`mm^3` | 210e+3 ton/(mm*`s^2`) | 15647 mm/s | 9.8*`10^3` mm/`s^2` |
| slug ft s | 0.068 slug | 3.28 ft | 1 s | 0.2246 slug*ft/`s^2` | 0.0208 slug/(ft*`s^2`) | 0.7366 slug*`ft^2`/`s^2` | 1.93*`10^-3` slug/`ft^3` | 4.368e+9 slug/(ft*`s^2`) | 51.322 ft/s | 32.144 ft/`s^2` |
| kg mm s | 1 Kg | `10^3` mm | 1 s | `10^3` kg*mm/`s^2` | `10^-3` kg/(mm*`s^2`) | `10^6` kg*`mm^2`/`s^2` | `10^-9` kg/`mm^3 | 210e+6 kg/(mm*`s^2`) | 15647 mm/s | 9.8*`10^3` mm/`s^2` |
| g cm ms | `10^3` g | `10^2` cm | `10^3` ms | `10^-1` g*cm/`ms^2` | `10^-5` g/(cm*`ms^2`) | 10 g*`cm^2`/`ms^2` | `10^-3` g/`cm^3` | 210e+4 g/(cm*`ms^2`) | 1.5647 cm/ms | 9.8*`10^-4` cm/`ms^2` |
| kg mm ms | 1 Kg | `10^3` mm | `10^3` ms | `10^-3` kg*mm/`ms^2` | `10^-9` kg/(mm*`ms^2`) | 1 kg*`mm^2`/`ms^2` | `10^-9` kg/`mm^3 | 210 kg/(mm*`ms^2`) | 15.647 mm/ms | 9.8*`10^-3` mm/`ms^2` |
CONCLUSION:
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 has to be conversant with converting quantities from one system of units to another.