Week - 1 - Consistency of Units
AIM:
Inorder to use LS-DYNA which doesn't follow a default unit system, all input values such as physical or material properties should be converted ta convenient sustem od units. As a practice, we are converting the given quantities from SI unit to different system of units.
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/s⊃2;
SAMPLE CALCULATIONS:
As an example the above Quantities are converted from kg,m,s to gm,mm,ms.
Given,
- Mass= 1kg= 1000g
- Length= 1m=1000mm
- Time= 1s= 1000ms
- Force= 1N= `1kg*m/s^2`= `(1000g*1000mm)/(1000ms)^2`= `1g*(mm)/(ms^2)`
- Stress= 1Pa= 1N/m⊃2;= `(1kg*m/s^2) /(1m^2)`= `(1000g*1000mm)/((1000ms)^2*(1000mm)^2)`= `10^-6 g/(mm*ms^2)`
- Energy= 1Nm= `1(kg*m/s^2)*m`= `((1000g*1000mm)/(1000ms)^2)*1000mm`= `1000g*(mm^2)/(ms^2)`
- Density= 1kg/m⊃3;= `(1000g)/(1000mm)^3`= `10^-6g/(mm^3)`
- Young's Modulus= 210GPa= `210xx10^9Pa`= `210xx10^9N/m^2`= `(210xx10^9kg*m/s^2) /(m^2)`= `210xx10^9*(1000g*1000mm)/((1000ms)^2*(1000mm)^2)`= `210xx10^3 g/(mm^6*ms^2)`
- Velocity= 56.33kmph= `56.33xx(1000m)/(3600s)`= `56.33xx(1000*1000mm)/(3600*1000ms)`= `15.6472(mm)/(ms)`
- Gravity= 9.8m/s⊃2;= `9.8xx((1000mm)/(1000ms)^2)`= `9.8xx10^-3(mm)/(ms^2)`
UNIT SYSTEM CONVERSION:
| UNIT SYSTEM | MASS (1kg) | LENGTH (1m) | TIME (1s) | FORCE (1N) | STRESS (1Pa) | ENERGY (1Nm) | DENSITY (1kg/m⊃;3;) | YOUNG'S MODULUS (210GPa) | VELOCITY (56.33Kmph) | GRAVITY (9.8m/s) |
| kg cm ms | 1kg | 100cm | 1000ms | 1e-04 kg*cm/ms2 | 1e-08 kg/cm*ms2 | 0.01 kg*cm⊃2;/ms⊃2; | 1e-06 kg/cm3 | 2100 kg/cm*ms2 | 1.56472 cm/ms | 9.8 cm/ms⊃2; |
| kg cm s | 1kg | 100cm | 1s | 100 kg*cm/s2 | 0.01 kg/cm*s2 | 10000 kg*cm⊃2;/s⊃2; | 1e-06 kg/cm3 | 2.1e+09 kg/cm*s2 | 1.56472e+03 cm/s | 9.8e+02 cm/s⊃2; |
| g mm ms | 1000g | 1000mm | 1000ms | 1 g*cm/ms2 | 1e-06 g/mm*ms2 | 1000 g*mm⊃2;/ms⊃2; | 1e-06 g/mm3 | 2.1e+05 g/mm*ms2 | 1.56472e+01 mm/ms | 9.8e-03 mm/ms⊃2; |
| g cm s | 1000g | 100cm | 1s | 1e+05 g*cm/s2 | 10 g/cm*s2 |
1e+07 g*cm⊃2;/s⊃2; |
1e-03 g/cm3 | 2.1e+12 g/cm*s2 | 1.56472e+03 cm/s | 9.8e+02 cm/s⊃2; |
| g cm μs | 1000g | 100cm | 1e+06 µs | 1e-07 g*cm/µs2 | 1e-11 g/cm*µs2 | 1e-05 g*cm⊃2;/µs⊃2; | 1e-03 g/cm3 | 1 g/cm*µs2 | 1.56472e-03 cm/µs | 9.8e-10 cm/µs⊃2; |
| g mm s | 1000g | 1000mm | 1s | 1e+06 g*mm/s2 | 1 g/mm*s2 | 1e+09 g*mm⊃2;/s⊃2; | 1e-06 g/mm3 | 2.1e+11 g/mm*s2 | 1.56472e+04 mm/s | 9.8e+03 mm/s⊃2; |
| ton mm s | 1e-03 ton | 1000mm | 1s | 1 ton*mm/s2 | 1e-06 ton/mm*s2 | 1000 ton*mm⊃2;/s⊃2; | 1e-12 ton/mm3 | 2.1e+05 ton/mm*s2 | 1.56472e+04 mm/s | 9.8e+03 mm/s⊃2; |
| slug ft s | 6.852e-02 slug | 3.28 ft | 1s | 0.2247 slug*ft/s2 | 0.02089 slug/ft*s2 | 0.737 slug*ft⊃2;/s⊃2; | 1.941e-03 slug/ft3 | 4.386e+09 slug/ft*s2 | 5.1322e+01 ft/s | 32.137 ft/s⊃2; |
| kg mm s | 1kg | 1000mm | 1s | 1000 kg*cm/ms2 | 1e-03 kg/mm*s2 | 1e+06 kg*cm⊃2;/ms⊃2; | 1e-09 kg/mm3 | 2.1e+08 kg/mm*s2 | 1.56472e+04 mm/s | 9.8e+03 mm/s⊃2; |
| g cm ms | 1000g | 100cm | 1000ms | 0.1 g*cm/ms2 | 1e-05 g/cm*ms2 | 10 g*cm⊃2;/ms⊃2; | 1e-03 g/cm3 | 2.1e+06 g/cm*ms2 | 1.56472 cm/ms | 9.8e-04 cm/ms⊃2; |
| kg mm ms | 1kg | 1000mm | 1000ms | 1e-03 kg*cm/ms2 | 1e-09 kg/mm*ms2 | 1 kg*mm⊃2;/ms⊃2; | 1e-09 kg/mm3 | 210 kg/mm*ms2 | 1.56472e+01 mm/ms | 9.8e-03 mm/ms⊃2; |
Conclusion:
The conversion of SI unit to convenient system of units can be followed using above table as reference.