Consistency of Units

AIM

LS-DYNA doesn't have a default system of units. We have to input material properties and physical dimensions according to a consistent system of units as per our 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.

And also write a detailed report on unit conversion with calculations and with there units.

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

Now, here are a few system of 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

DIFFERENT TYPES SYSTEMS

1. CGS SYSTEM
2. FPS SYSTEM
3. MKS SYSTEM

PROCEDURE

As per the requirement I'd explained below with detail calculation for conversion from SI unit to gm/mm/ms. I'd also plotted table below.

SI unit for gm mm ms

Mass 1 Kg = 1000gm

Length 1 m = 1000mm

Time 1 s = 1000 ms

Force 1 N = (1Kg*m)/s^2

(1000gm*1000mm)/(1000ms*1000ms)

( 1 gm * mm)/ms^2

Stress 1pa = N/m^2 = [(1gm *mm/ms^2]/(1000ms*1000ms)

= 10^-6gm/,,*ms^2.

Energy 1 Nm = [(1kg*m/s^2]*(1000mm)

= 10^3gm*mm^2/ms^2

DENSITY 1Kg/m3 = 1000gm/(10^3 ms)^3

= 10^3 gm/10^9 ms^3

= 10^-6 gm/ms^3

Youngs's Modulus 210Gpa { 1Gpa = 10^9 × (N/m^2)}

210 Gpa = 210 × [10^9 ×(N/m^2)]

= 210[10^9 × (10^-6gm/mm*ms^2)]

= 210 × 10^3 gm/mm*ms^2

= 210000 gm/mm*ms^2.

Velocity [1Km = 10^6mm]

1KMPH = 10^6mm/(3600*1000ms) [1HR = 3600*1000ms]

10/36 = 0.277mm/ms

56.33 KMPH = 56.33×0.277

= 15.64 mm/ms

GRAVITY 9.8m/s2

1m/s2 = 1000mm/ (1000ms × 1000ms )

= 10-3 mm/ms^2

9.8 m/s2 = 9.8 × 10^-3 mm/ms^2.

UNITS	MASS	LENGTH	TIME	FORCE	STRESS	ENERGY	DENSITY	YOUNG’S MODULUS	VELOCITY	GRAVITY
Kg cm ms	1 kg	100m	1000ms	10^-4 Kg*cm/ms^2	10^ -8Kgcm/ms^2	10^-2 Kg*cm^2/ms^2	10^-6 Kg/cm^3	210 Kg/cm*ms^2	156.4*10^-2cm/ms	9.8*10^-4 cm/ms^2
Kg cm s	1kg	100cm	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	210*10^7 Kg/cm*s^2	15647.22 cm/s`	980 cm/ s^2
Gm mm ms	1000 gm	1000 mm	1000 ms	1 gm *mm/ms^2	10^-6 gm/mm * ms^2	10^3 gm*mm^2/ ms^2	10^-6 Gm/mm^3	210000 Gm/mm*ms^2	15.64 Mm/ms	9.8* 10^-3 mm/ms^2
Kg m s	1 Kg	1 m	1 s	1 Kg *m/s^2	1 Kg *m/s^2	Kg *m^2/s^2	Kg/m^3	210* 10 ^ 9 Kg/m*s^2	15.64 m/s	9.8 m/ s^2
g cm s	1000gm	100 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	210*10^10 g/cm*s^2	1564.7 cm/s	980 cm/s^2
g cm us	1000gm	100cm	1000000 us	10^-7 gm*cm/us^2	10^-11 gm/cm*us^2	10^-5gm*cm^2/us^2	10gm/cm	210*10^-2 gm/cm*us^2	1564.710^-6 cm/us	9.8*10^-10 cm/us^2
g mm s	1000 gm	1000 mm	1 s	10^6 gm*mm/s^2	1 gm/mm*s^2	10^9 gm*mm^2/s^2	10^-6 gm/mm^3	210*10^9 gm/mm*s^2	15647.2 mm/s	9.8*10^3 m/s^2
Ton mm s	0.001 ton	1000 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	210*10^3 ton/mm*s^2	15647 mm/ms	9.8*10^3mm/s^2
Slug ft s	0.068 slug	3.28 ft	1 s	0.223 slug*ft/s^2	0.020 slug/ft*s^2	0.731 slug/ft*s^2	1.92*10^-3 slug/ft^3	4.2*10^9 slug/ft*s^2	51.33ft/s	32.144ft/s^2
Kg mm s	1 kg	1000 mm	1 s	1000kg*mm/s^2	10^-3 Kg/mm*s^2	10^6 Kg/mm^3	10^-9 Kg/mm^3	210 * 10^6Kg/mm*s^2	15647.22mm/s	9.8*10^3m/s^2
G cm ms	1000 gm	100 cm	1000 ms	0.1g*cm/ms^2	10^-5 gm/cm*ms^2	10 g*cm^2/ms^2	10^-6 gm/cm^3	210*10^4 gm/cm*ms^2	1564*10^-3 cm/s^2	9.8*10^-4 cm/s^2
Kg mm ms	1 kg	1000 mm	1000 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	15647*10^-3 mm/ms	9.8*10^-3 mm/ms^2