Consistency of units

Objective: To obtain the input value and conversion factor for the measurements in accordance with the provided unit systems.

Procedure

Physical quantity: A physical quantity is a quantity that can be measured i.e. a physical quantity is properly defined, has proper units, and its value can be measured by an instrument. Physical quantities are classified as fundamental and derived quantities.

Fundamental Quantities: Fundamental quantities are those that are defined directly by the process of measurement only. They are not defined in terms of other quantities; their units are not defined in terms of other units. In mechanics we treat length, mass and time as basic or fundamental quantities.

Derived Units: The units of all other physical quantities, which can be obtained from fundamental units, are called derived unit.

1kg=1000gm=.001tonne=0.06852slug

1m=100cm=1000mm=3.28084ft

1s=1000ms=106µs

Conversion from SI unit to gm/mm/ms

SI unit gm/mm/ms

Mass-1kg 1000gm

Length-1m 1000mm

Time-1sec 1000ms

Force

1N= mass*acceleration

=Kg-m/s²

=1000g*1000mm/(1000)²ms²

=1gmm/ms²

Conversion Factor=1

Stress

1Pa=1N/m²=1kg/m-s²

=1000g/(1000mm)*(1000)²ms²

=10^-6g/mm*ms²

Conversion Factor=10^-6

Energy

1J=1N-m=1kg*m²/s²

=1000g*(1000)²mm²/(1000)²ms²

=10³gmm²/ms²

Conversion Factor=10³

Density

1kg/m³=(1000)g/(1000)³mm³

=10^-6g/mm³

Conversion Factor=10^-6

Youngs Modulus

210GPa=210*10⁹kg/m-s²

=210*10⁹*(1000) g/(1000) mm*(1000)²ms²

=210*10³g/mm*ms²

Conversion Factor=10³

Velocity

56.33Kmph=56.33*{10⁶mm/(3600*1000ms)}

=15.647mm/ms

Conversion Factor=1

Gravity

9.8m/s²=9.8*(1000)mm/(1000)²ms²

=10^-3mm/ms²

Conversion Factor=10^-3

	Mass	Length	Time	Force	Stress	Energy	Density	Young’s Modulus	Velocity 56.33kmph	Gravity
Kg m s	1kg	1m	1s	1N= 1kg*m/s2	1Pa= 1kg/ms2	1J=1Nm= 1kg*m2/s2	1kg/ m3	210Gpa=210* 109kg/ms2	15.647m/s	9.8m/ s2
Kg cm ms	1kg	102cm	103ms	10-4 kg*cm/ ms2	10-8 kg/cm*ms2	10-2 kg* cm2/ms2	10-6 kg/cm3	2100kg/cm*ms2	1.5647 cm/ms	9.8* 10-4 cm/ ms2
Kg cm s	1kg	102cm	1s	102kg*cm/s2	10-2 kg/cm*s2	104 kg*cm2/ s2	10-6 Kg/ cm3	210*107kg/cm* s2	1564.7 cm/s	9.8* 102cm/s2
gm mm ms	103gm	103mm	103ms	1gm*mm/ms2	10-6 gm/mm*ms2	103 gm*mm2/ms2	10-6 gm/mm3	210*103gm/mm*ms2	15.647mm/ms	9.8* 10-3 mm/ms2
gm cm s	103 gm	102cm	1s	105gm* cm/s2	10 gm/cm*s2	107 gm* cm2/ s2	10-3 gm/ cm3	210*1010 gm/cm*s2	1564.7 cm/s	9.8* 102 cm/s2
g cm µs	103gm	102cm	106µs	10-7 gm*cm/µs2	10-11 gm/cm*µs2	10-5gm*cm2/µs2	10-3gm/cm3	2.10gm/cm*µs2	15.647*10-4cm/µs	9.8* 10-10 cm/µs2
g mm s	103gm	103mm	1s	106gm*mm/s2	1gm/mm*s2	109gm*mm2/s2	10-6gm/mm3	2.10*1011gm/mm*s2	15647mm/s	9.8*103mm/s2
Ton mm s	10-3 ton	103mm	1s	1ton*mm/s2	10-6 ton/mm*s2	103 ton*mm2/s2	10-12 ton/mm3	210*103ton/mm*s2	15647mm/s	9.8*103 mm/s2
slug ft s	0.068 slug	3.28ft	1s	.2246slug*ft/s2	.0208slug/ft*s2	.7366slug*ft2/s	1.93* 10-3 slug/ft3	4.368*109 slug/ft*s2	51.322ft/s	32.144ft/s2
Kg mm s	1kg	103mm	1s	103kg*mm/s2	10-3 kg/mm*s2	106kg*mm/s2	10-9 kg/mm3	210*106kg/mm*s2	15647mm/s	9.8*103 mm/s2
gmcm ms	103gm	102cm	103s	10-1 gm*cm/ms2	10-5 gm/cm*ms2	10gm*cm/ms2	10-3 gm/cm3	210*104gm/cm*ms2	1.5647cm/ms	9.8*10-4 cm/ms2
Kg mm ms	1kg	103mm	103s	10-3 kg*mm/ms2	10-9 kg/mm*ms2	1kg*mm/ms2	10-9 kg/mm3	210kg/mm*ms2	15.647mm/ms	9.8*10-3 mm/ms2

Conclusion

Performed conversion of units as LS-DYNA doesn’t have default system of units. User needs to be conversant with converting quantities from one system of units to another so that error won’t occur while performing simulations.