Week - 1 - Consistency of Units

1. Kg cm ms

MASS 1kg
LENGTH 1m=1e2 cm
TIME 1s=1e3 ms
FORCE 1N= kg . m/s2=kg.1e2 cm/1e-6 ms2=1e-4 kg.cm/ms2
STRESS 1Pa= N/m2=(1e-4 kg.cm/ms2)/1e4 cm2=1e-8 kg/cm.ms2
ENERGY 1Nm=(1e-4 kg.cm/ms2).1e2 cm=1e-2 kg.cm2/ms2
DENSITY 1Kg/m3=1kg/1e6 cm3 = 1e-6 kg/cm3
YOUNG'S Modulus 210GPa =210 *1e9*1e-8= 2100
Velocity 56.33KMPH = 56.33 * 1e5 cm /(60*60*1e3) ms= 1.56
GRAVITY 9.8m/s2= 9.8 *1e2 cm/ (1e6) ms2=9.81e-4

For the first case, Force in Newtons is calculted by replacing the SI units with the converted units and hence, the conversion factor is calculated. similar is done, with STRESS, ENERGY, DENSITY. For YOUNGS MODULUS, the above conversion factor are multiplied. and these values are direclty fed as inout for the K file of LSdyna and hence, the unit se=ystem for kg-cm and ms is established into the solver.

Similar process is followed for the rest of the units.

2. Kg cm s

MASS 1kg
LENGTH 1m=100 cm
TIME 1s
FORCE 1N= kg.m/s2=1e2 kg. cm/s2
STRESS 1Pa = N/m2=(1e2 kg. cm/s2)/1e4 cm2= 1e-2 kg/cm.s
ENERGY 1Nm=(1e2 kg. cm/s2).(1e2 cm )= 1e4 kg cm2/s2
DENSITY 1Kg/m3= 1e-6 kg/cm3
YOUNG'S Modulus 210GPa=210. 1e9.1e-2=210 e7
Velocity 56.33KMPH= 56.33*1e5 cm/ (60* 60)=1564.72
GRAVITY 9.8m/s2=9.8 . 1e2= 9.8e2

3. gm mm ms

MASS 1kg=1000 gm
LENGTH 1m= 1000 mm
TIME 1s=1000 ms
FORCE 1N= kgm/s2=1e3 gm.1e3 mm/1e6 ms2= 1 gm.mm/ms2
STRESS 1Pa= (1 gm.mm/ms2)/1e6 mm2= 1e-6 gm/ms.mm
ENERGY 1Nm= 1 gm.mm/ms2. 1e3 mm= 1e3 gm. mm2/ms2
DENSITY 1Kg/m3= 1e3 gm/1e9 mm3= 1e-6 gm/mm3
YOUNG'S Modulus 210GPa=210*1e9*1e-6= 210e3
Velocity 56.33KMPH= 56.33 *1e6 mm/(60*60*1e3)= 15.64
GRAVITY 9.8m/s2= 9.8* 1e3 mm/1e6 ms2=9.8 e-3

4. kg m s

MASS 1kg
LENGTH 1m
TIME 1s
FORCE 1N
STRESS 1Pa
ENERGY 1Nm
DENSITY 1Kg/m3
YOUNG'S Modulus 210GPa = 210e9
Velocity 56.33KMPH= 56.33*1e3 m/(60*60)=15.647
GRAVITY 9.8m/s2

5. g cm s

MASS 1kg=1e3 g
LENGTH 1m = 1e2 cm
TIME 1s
FORCE 1N= 1e3 g. 1e2 cm/s2= 1e5 g cm/s2
STRESS 1Pa= (1e5 g cm/s2)/ 1e4 cm2= 1e1 g/cm s2
ENERGY 1Nm= 1e5 g cm/s2. 1e2 cm= 1e7 g. cm2/s2
DENSITY 1Kg/m3= 1e3 g/1e6 cm3= 1e-3 g/cm3
YOUNG'S Modulus 210GPa = 210 * 1e9* 1e1= 210 1e10
Velocity 56.33KMPH = 56.33 . 1e5/(60*60)= 15647.22
GRAVITY 9.8m/s2 = 9.8 . 1e2 cm/s2=9.8e2

6. g cm us

MASS 1kg=1e3 g
LENGTH 1m=1e2 cm
TIME 1s=1e6 us
FORCE 1N= 1e3 g* 1e2 cm/1e12 us2= 1e-7 g cm/us2
STRESS 1Pa= (1e-7 g cm/us2)/(1e4 cm2)= 1e-11 g/us2.cm
ENERGY 1Nm= (1e-7 g cm/us2). 1e2 cm= 1e-5 g cm2/us2
DENSITY 1Kg/m3= 1e3 g/1e6 cm3= 1e-3 g/cm3
YOUNG'S Modulus 210GPa= 210*1e9*1e-11=2.10
Velocity 56.33KMPH= 56.33 *1e5 cm/(60*60*1e6 us)= 1.56 e -3
GRAVITY 9.8m/s2 = 9.8 * 1e2 cm/ 1e12 us= 9.8 e-10

7. g mm s

MASS 1kg= 1e3 g
LENGTH 1m= 1e3 mm
TIME 1s
FORCE 1N= 1e3 g. 1e3 mm/s2= 1e6 g mm/s2
STRESS 1Pa= (1e6 g mm/s2)/1e6 mm2= 1 g/s2 mm
ENERGY 1Nm= (1e6 g mm/s2). 1e3 mm=1e9 g mm2/s2
DENSITY 1Kg/m3= 1e3 g/ 1e9 mm3= 1e-6 g/mm3
YOUNG'S Modulus 210GPa= 210. e9 . 1= 210 e9
Velocity 56.33KMPH= 56.33* 1e6 mm/(60*60)= 15647.222
GRAVITY 9.8m/s2= 9.8 * 1e3 mm/s2= 9.8 e3

8. ton mm s

MASS 1kg=1e-3 ton
LENGTH 1m=1e3 mm
TIME 1s
FORCE 1N= 1e-3 ton. 1e3mm/s2= 1 ton mm/s2
STRESS 1Pa= 1 ton mm/s2 / 1e3 mm2= 1e-3 ton/s2.mm
ENERGY 1Nm= (1 ton mm/s2). 1e3 mm= 1e3 ton mm2/s2
DENSITY 1Kg/m3= 1e-3 ton/1e9 mm3= 1e-12 ton/mm3
YOUNG'S Modulus 210GPa= 210. e9. 1e-3 = 210. e6
Velocity 56.33KMPH= 56.33 1e6 mm/ (60*60)= 15647.22
GRAVITY 9.8m/s2= 9.8 1e3 mm/s2= 9.8*1e3

9. slug ft s

MASS 1kg= 0.0685 slug
LENGTH 1m= 3.28 ft
TIME 1s
FORCE 1N= 0.0685 slug. 3.28 ft/s2= 0.22468 slug. ft/s2
STRESS 1Pa= (0.22468 slug. ft/s2)/ (3.28* 3.28 ft2)= 20.38 e-3 slug/ft.s2
ENERGY 1Nm= (0.22468 slug. ft/s2). 3.28 ft= 0.736688 sluf ft2/s2
DENSITY 1Kg/m3= 0.0685 slug/ 3.28.*3.28*3.28 ft3= 1.94 e-3 slug/ft3
YOUNG'S Modulus 210GPa= 210 * e9* 20.38 e-3= 4279.8 e6
Velocity 56.33KMPH= 56.33 * 1e3* 3.28 ft/ (60*60)= 51.322
GRAVITY 9.8m/s2= 9.8 * 3.28 ft/s2= 32.144

10. kg mm s

MASS 1kg
LENGTH 1m=1e3 mm
TIME 1s
FORCE 1N= 1 kg 1e3 mm/s2= 1e3 kg.mm/s2
STRESS 1Pa=( 1e3 kg.mm/s2 )/1e6 mm2= 1e-3 kg /s2 mm
ENERGY 1Nm= 1e3 kg.mm/s2. 1e3 mm= 1e6 kg. mm2/s2
DENSITY 1Kg/m3= 1kg/ 1e9 mm3= 1e-9 kg/mm3
YOUNG'S Modulus 210GPa= 210 . 1e9. 1e-3= 210 e6
Velocity 56.33KMPH= 56.33 1e6 mm/ (60*60)= 15647.22
GRAVITY 9.8m/s2= 9.8 1e3 mm/s2= 9.8 e3

11. g cm ms

MASS 1kg= 1e3 g
LENGTH 1m= 1e2 cm
TIME 1s= 1e3 ms
FORCE 1N= 1e3 g. 1e2 cm/1e6 ms2= 1e-1 g cm/ms2
STRESS 1Pa= (1e-1 g cm/ms2)/1e4 cm2 = 1e-5 g/ms2. cm
ENERGY 1Nm= (1e-1 g cm/ms2). 1e2 cm= 1e1 g cm2/ms2
DENSITY 1Kg/m3= 1e3 g/ 1e6 cm3= 1e-3 g/cm3
YOUNG'S Modulus 210GPa= 210* 1e9* 1e-5= 210 e4
Velocity 56.33KMPH= 56.33* 1e5/ (60*60*1e3)=1.5647
GRAVITY 9.8m/s2= 9.8*1e2 cm/1e6 ms2= 9.8 1e-4

12. kg mm ms

MASS 1kg
LENGTH 1m= 1e3 mm
TIME 1s=1e3 ms
FORCE 1N= 1 1e3 kg mm/1e6 ms2= 1e-3 kg mm/ms2
STRESS 1Pa= (1e-3 kg mm/ms2). / 1e6 mm2 = 1e-9 kg/mm.ms2
ENERGY 1Nm= (1e-3 kg mm/ms2). 1e3 mm= 1 kg mm2/ms2
DENSITY 1Kg/m3= 1kg/1e9 mm3= 1e-9 kg/mm3
YOUNG'S Modulus 210GPa= 210 e9 * 1e-9 =210
Velocity 56.33KMPH= 56.33 * 1e6 mm/ (60*60*1e3)= 15.647
GRAVITY 9.8m/s2= 9.8 * 1e3mm/1e6 ms2= 9.8e-3