Week - 1 - Consistency of Units

AIM; 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.

OBJECTIVE;

• The assignment should show detailed calculation for conversion from SI unit to gm/mm/ms unit system.
• And also Write the given measurements in the below given different system of units. Also, mention the conversion factors.

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

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

show detailed calculation for conversion from SI unit to gm/mm/ms unit system.

MASS=1kg=1000gm; convesation factor=10^3.

LENGTH=1m=1000mm; conservation factor=10^3.

TIME 1s=1000ms; conservation factor=10^3.

FORCE 1N=kgm/s^2

(1000gm*1000mm)/(1000ms)^2=10^6/10^6=1

1(gm*mm)/s^2.

conversation factor=1.

STRESS 1Pa=1N/m^2 ; {(1Kg.m/s2)/m^2)}

{(1000gm*1000mm)/(1000ms)^2/(1000mm)^2}

{(10^3*10^3)/(10^6)/10^6)}=(10^6/10^6)*(1/10^6) =10-6

10-6gm*mm/ms^2.

Conservation factor=10-6.

ENERGY 1Nm={(1kg.m/s^2)*m)}

(1000gm*1000mm)/(1000ms)^2*1000mm

1gm*mm/ms^2*10^3mm

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

Conservation factor=10^3.

DENSITY 1Kg/m3

1000gm/1000mm^3

10^3/(10^3)^3= 10^3*10^-9= 10-6gm/mm^3.

conservation factor=10-6.

YOUNG'S Modulus 210GPa=210*10^9N/m2

210*10^9(kg.m)/s2/m2

210*10^9{(1000gm*1000mm)/(1000ms)^2/(1000mm)^2}

210*10^9(gm*mm/ms^2)/10^6mm2

210*10^3gm*mm/ms^2.

Conservation factor=10^3.

Velocity 56.33KMPH=(56.33*1000m)/H.

1H=3600sec

55.33*10^6mm/3600*1000ms

55.33*10^6/36*10^5

15.36mm/ms.

and for considereing 1kmph

1000m/3600sec=(10^3*10^3)mm/(3600*10^3)ms

5/18

Conversation factor=5/18

GRAVITY 9.8m/s2

9.8*(1000mm)/(1000ms^2)

9.8*(10^3mm)/(10^6ms^2)

9.8*10-3mm/ms^2.

Conversation factor=10-3.

Units	Mass	Length	Time	Force	Stress	Energy	Density	Youngs Modulus	Velocity	Gravity
Kg Cm Ms	1kg	100 or 10^2cm	1000 or10^3ms	10^-4kg*cm/ms^2	10^-8kg*cm/ms^2	10^-2kg*cm^2/ms^2	10^-6kg/cm^3	2100kg/cm*ms^2	1.564cm/ms	9.81*10^-4cm/ms^2
Kg Cm S	1kg	10^2cm	1s	10^2kg*cm/sec^2	10^-2kg/cm*sec^2	10^4kg*cm^2/sec^2	10^-6kg/cm^3	210*10^7kg/cm*sec^2	1564.72cm/s	9.81*10^2cm/s^2
gm mm ms	10^3gm	10^3mm	10^3ms	1(gm*mm)/s^2	10-6gm*mm/ms^2	10^3gm*mm^2/ms^2	10^-6gm/mm^3	210*10^3gm*mm/ms^2	15.36mm/ms.	9.8*10-3mm/ms^2.
kg m s	1kg	1m	1s	1kg*m/s^2	1kg/m*s^2	1k*m2/s^2	1kg/m^3	210*10^9kg/m^-2s-^2	15.64m/s	9.81m/s^2
g cm s	10^3g	10^2cm	1s	10^5gm*cm/s2	10g/cm*s^2	10^7gm*cm^2/s^2	10-3g/cm^3*s	210*10^10g/cm*s^2	1564.72cm/s	9.8*10^2cm/s^2
g cm us	10^3g	10^2cm	10^6us	10^-7g*cm/us	10^-11g/cm*us^2	10^-5g*cm^2/us^2	10-3g/cm^3	2.1gm/cm*us^2	1.56*10^-3cm/us	9.8*10^-10cm/us^2
g mm s	10^3g	10^3mm	1s	10^6g*mm/s^2	1gm/mm*s^2	10^9gm*mm^2/S^2	10^-6g/mm^3	210*10^9g/mm*s^2	15647.2mm/s	9.8*10^3mm/s^2
ton mm s	10^-3ton	10^3mm	1s	1Ton*mm/s^2	10^-6Ton/mm*s^2	10^3Ton*mm^2/s^2	10^-12ton/mm^3	210*10^3ton/mm*ms^2	15647.2mm/s	9.8*10^3mm/s^2
slug ft s	0.068slug	3.28ft	1s	0.22slug*ft/s^2	0.020slug/ft*s^2	0.78slug*ft^2/s^2	1.92*10^-3slug/ft^3	435slug/ft*s2	51.33ft/s	32.17ft/s^2
kg mm s	1kg	10^3mm	1s	10^3kg*mm/sec^2	10^3kg/mm*sec^2	10^6kg*mm^2/sec^2	10^-9kg/mm^3	210*10^6kg/mm*s^2	15647.2mm/s	9.8*10^3mm/s^2
g cm ms	10^3g	10^2cm	10^3ms	10^-1gm*cm/ms2	10^-5g/cm*ms^2	10^-1gm*cm^2/ms^2	10-3g/cm^3	210*10^4g/cm*ms^2	1.56cm/ms	9.8*10^-4cm/ms^2
kg mm ms	1kg	10^3mm	10^3ms	10^-3kg*mm/ms^2	10^-9kg/mm*ms^2	1kg*mm^2/ms^2	10^-9kg/mm^3	210kg/mm*ms^2	15.64mm/ms	9.8*10^-3mm/ms^2