Week - 1 - Consistency of Units

AIM:- To convert given measurement values into the different unit systems and mention their conversation factor

OBJECTIVES:-

• The assignment should show the detailed calculations for conversion from SI unit to gm/mm/ms unit system.
• For others, only the answers in the form of a table are sufficient with the unit systems as rows and measured quantities as columns.

Given Measurements

• 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

Given Unit systems

• 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

PROCEDURE:-

As we know that the conversions of different units are as follows

(I) LENGTH

• 1 m = 100 cm = 1000 mm = 3.281 ft

(II) MASS

• 1 kg = 1000 gm = 0.0685218 slug

(III) TIME

• 1 sec = 1000 ms

Now we can convert the given measurements from Kg mm ms to gm mm ms as discussed in the below steps

(I) FORCE 1 N

• Force = mass X acceleration
• 1 N = kg.`frac(m)(s^2)`
• Now we have to change the 1 N to gm mm ms
• it will become

F = (1000 gm).`frac(1000 mm)((1000 ms)^2)`

F = 1 gm.`frac(mm)(mm^2)`

conversion factor = 1

(II) STRESS 1 Pa

• Stress = force/area
• 1 Pa = `frac(N)(m^2)`
• Now we have to change the 1 Pa to gm mm ms
• It will become

Stress = (1 `gm*frac(mm)(ms^2`)/(`(1000mm)^2`

Stress = `10^-6 frac(gm)(mm*ms^2`

Conversion factor = `10^-6`

(III) Energy 1 Nm

• energy = force. Displacement
• 1 Nm = (1 N).(1 m)
• Now we have to change the 1 Pa to gm mm ms
• It will become

Energy = `1 frac(gm*mm)(ms^2) *(1000 mm)`

Energy = `1000 frac(gm*mm^2)(ms^2)`

Conversion factor = 1000

(IV) DENSITY 1 `frac(kg)(m^3)`

• Density = `frac(mass)(volume`
• Density = `frac(1 kg)(1 mm^3)`
• Now we have to change the 1 `frac( 1kg)(1 mm^3)` to gm mm ms
• It will become

Density = `frac(1000 gm)((1000 mm)^3`

Density = `10^-6 frac(gm)(mm^3`

Conversion factor = `10^-6`

(V) YOUNGS MODULUS 210 GPa

• Young's modulus has the same unit as the stress so the conversion is the same as like stress
• Young's modulus =`210*10^9 Pa`

Young's modulus = `210*10^9 frac(gm)(mm*ms^2)`

Conversion factor = `10^3`

(VI) Velocity 56.33KMPH

• Velocity = `frac(distance)(time`
• Velocity = `1 frac(m)(s`
• Now we have to change KMPH to gm mm ms
• It will become

Velocity = `56.33 frac(10^6 mm)(1000 ms)`

Velocity = `56.33*10^3frac(mm)(ms`

Conversion factor = 1000

(VII) GRAVITY 9.8m/s2

• Acceleration = `frac(velocity)(time)`
• Acceleration = `frac(1 m)((1 s)^2`
• Now we have to change `frac(m)(s^2)` to gm mm ms
• It will become

Gravity = `9.8 frac(1000 mm)((1000 ms)^2`

`Gravity = 9.8*10^-3 frac(mm)(ms^2`

Conversion factor = `10^-3`

• Now the conversions of all the systems are as shown below

Input	mass	length	time	force	stress	Energy	Density	Youngs modulus	Velocity	acceleration
Kg cm ms	1	100	1000	0.0001	1.00E-07	0.01	0.000001	2100	0.0277778	0.00098
Kg cm s	1	100	1	100	0.01	10000	0.000001	21E+8	27.7778	980
gm mm ms	1000	1000	1000	1	0.000001	1000	0.000001	210000	0.277778	0.0098
kg m s	1	1	1	1	1	1	1	2.1E+11	0.277778	9.8
g cm s	1000	100	1	100000	10	10E+06	0.001	21E+12	27.7778	980
g cm us	1000	100	1000000	0.0000001	1.00E-11	0.00001	0.001	2.1	27.7778E-6	9.80E-10
g mm s	1000	1000	1	1000000	1	1.00E+9	0.000001	2.1E+11	277.778	9800
ton mm s	0.1	1000	1	1	0.000001	1000	1.00E-12	210000	277.778	9800
slug ft s	0.068	3.28	1	0.2230	0.0207	0.73157	0.001927	43536585	0.91111184	32.144
kg mm s	1	1000	1	1000	0.001	10E+5	1.00E-8	21E+7	277.778	9800
g cm ms	1000	100	1000	0.1	0.00001	10	0.001	2100000	0.0277778	0.00098
kg mm ms	1	1000	1000	0.001	1.00E-08	1	1.00E-8	210	0.277778	0.0098

CONCLUSION:-

• All the given measurements are converted into the given unit system and the conversion factor for the SI system to gm mm ms unit system

LEARING OUTCOMES:-

• In this assignment, we become aware of the different unit systems and the conversion of one unit system to the other unit system
• 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.