Week - 1 - Consistency of units

WEEK 1

AIM:

Convert the given units to required conversion as per Ls-dyna standards.

Value of the following measurements are given as follows:

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

units:
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

purpose

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.

Conversion (from SI units to gm/mm/ms unts)

MASS 1kg = 1000g conversion factor: 10³
LENGTH 1m = 1000mm conversion factor: 10³
TIME 1s = 1000ms conversion factor: 10³
FORCE 1N = 1kgm/s²

conversion factor: (1000g*1000mm)/(1000ms)²

⁼ 10⁺⁶*10^-6(g*mm)/ms²

=1(g*mm)/ms²

STRESS 1Pa = 1N/m² = 1{(kg*m)/s²}/m² = 1kg/(ms²)

=1000g/(1000 mm *(1000 ms)²)

= 10^-6 g/mm/ms²

conversion factor: 10^-6
ENERGY 1Nm B = 1J = (1Kg*1m/s²)*m

= (1kg m²/s²)

=1000g*(1000mm)²/(1000ms)²

=10³ (g*mm²/ms²)

conversion factor: 10³
DENSITY 1Kg/m3 = 1kg/m³

= 1000g/(1000mm)³

=10^-6 g/mm³

=10^-6

YOUNG'S Modulus 210GPa = 210 e+09 kg/(m*s²)

=210e+09*10^-6g/(mm* ms²)

=210*10³g/(mm*ms²)

conversion factor: 10³
Velocity 56.33KMPH = 56.33*-(10⁶mm/3600*1000ms)

=15.647mm/ms

conversion factor: 5/18

GRAVITY 9.8m/s2 = 9.8* 1000MM/(1000ms)²

= 9.8*10^-3 mm/ms²

conversion factor: 10^-3

Table unit system

Unit system	mass	length	time	Force	Stress	Energy
SI units	1kg	1m	1s	1N	1Pa	1J=1Nm
Kg cm ms	1kg	102cm	103ms	1kg*cm/ms2	10 kg/(cm*ms2)	10-2 kg*cm2/ms2
Kg cm s	1kg	102cm	1s	10 -4 kg(cm/s2)	10 -8 kg/(cm*ms2)	104 Kg*cm2/s2
g mm ms	103g	103mm	103ms	1g(mm/ms2)	10 -2 g/(mm*ms2)	103 g*mm2/ms2
kg m s	1kg	1m	1s	1kg(m/s2)	1kg/(m*s2)	1Kg*m2/s2
g cm s	103g	102cm	1s	105 g(cm/s2)	10g/(cm*s2)	107g*cm2/s2
g cm us	103g	102cm	10 6ms	10 -7 g(cm/us2)	g/(cm*us2)	10-5 g*cm2/us2
g mm s	103g	103mm	1s	106 g*mm/s2	1g/(mm*s2)	106 g*mm2/s2
ton mm s	10-3ton	103mm	1s	1ton*mm/s2	10-6 ton/(mm*s2)	103 ton*mm2/s2
slug ft s	0.068slug	3.28ft	1s	0.2246 slug*ft/s2	0.0208 slug/(ft*s2)	0.7366 slug*ft2/s2
kg mm s	1kg	103mm	1s	103 Kg*mm/s2	10 -3 kg/(mm*s2)	106 kg*mm2/s2
g cm ms	103g	102cm	103ms	10-1 g*cm/ms2	10-5 g/(cm*ms2)	10 g*cm2/ms2
kg mm ms	1kg	103mm	103ms	10-3 kg*mm/ms2	10 -9 kg/(mm*ms2)	1 K g*mm2/Ms2

Result

The given SI unit is converted into gm/mm/ms and tabulated in the above table.