Week - 1 - Consistency of Units

AIM :

• The objective of this challenge is to create a consisten system of units for the given input.. LS DYNA doesn't have a default system of units.
• User need to input material properties and physical dimension according to a consistent system of units as per their units as per their choice.This warrants that to use LS-DYNA in different circumstances, user has to be converting quantities from one system of units to another.

PROCEDURE :

• Each and every measurement given in the input parameters are converted into respective system of units.The input measurement values are displayed below,

MASS	1kg
LENGTH	1m
TIME	1s
FORCE	1N
STRESS	1Pa
ENERGY	1Nm
DENSITY	1Kg/m3
YOUNG'S MODULUS	210Gpa
VELOCITY	56.33 KMPH
GRAVITY	9.8 m/s2

• The above mentioned system of units are converted into the below displayed units.They are

1	Kg cm ms
2	kg cm s
3	gm mm ms
4	kg m s
5	g cm s
6	g cm us
7	g mm s
8	ton mm s
9	slug ft s
10	kg mm s
11	g cm ms
12	kg mm ms

• In calculation part the conversion of values with respect to the units are very important . So that only one results will come as accurate . Each and every problem contains three important factors they are , mass (kg),time(s) and length (m). This the actual representation of the system of units in deriviation problems.they are converted into the above mentioned system of units

CONVERSION:

• 1 Kg = 1000 g = 0.001 tonne = 0.06852 slug
• 1m = 100 cm = 1000 mm = 3.28084 ft
• 1s = 1000 ms = 1000000 us

• FORCE UNIT CONVERSION

• Force (N) = Mass (m) * Acceleration (a)

  F = m * a

  F = `kg.m/s^2` or F = `g . (mm//ms^2)`

• STRESS UNIT CONVERSION

Stress = Force / Area

Stress = `kg.(m//s^2)//m^2` or Stress = `g//mm.ms^2`

• ENERGY UNIT CONVERSION

The energy common it expressed as in terms of Joule , so the equations for the energy is

Energy = Length * Force

J = `(m) . (kg.m/s^2)` or J = `g.mm^2//ms^2`

• DENSITY UNIT CONVERSION

Density = Mass / Volume

Density = `kg // m^3` or Density = `g//mm^3`

• YOUNG'S MODULUS UNIT CONVERSION

In given problem the Young's modulus (E) is given as 210 Gpa . This the Young's modulus value for mild steel. So the expression for the young's modulus written as

Young's Modulus ( E ) = Stress / Strain

E = `210000 (g//mm.ms^2)`

• VELOCITY UNIT CONVERSION

In our problem, the velocity value is given as 56.33 kmph and this value is converted into m/s and then to mm/ms. The expression for velocity is written as,

Velocity = Displacement / Time

For converting km/h to m/s, multiply by 5/18

Velocity = 56.33 * (5/18)

Velocity = `m/s` or Velocity = `0.277778 mm//ms`

• ACCELERATION DUE TO GRAVITY UNIT CONVERSION

g = 9.81 . `m/s^2` or g = 9.81 `mm//ms^2`

S.NO	INPUT	MASS	LENGTH	TIME	FORCE	STRESS	ENERGY	DENSITY	YOUNG'S MODULUS	VELOCITY	GRAVITY
1	Kg cm ms	1	100	1000	0.0001	0.00001	0.01	0.000001	2100	0.0277778	0.00098
2	kg cm s	1	100	1	100	0.01	10000	0.000001	2.10E+12	27.778	980
3	gm mm ms	1000	1000	1000	1	1E-06	1000	0.000001	210000	0.277778	0.0098
4	kg m s	1	1	1	1	1	1	1	2.10E+11	0.277778	9.8
5	g cm s	1000	100	1	100000	10	10000000	0.001	2.10E+12	27.778	980
6	g cm us	1000	100	1000000	1E-07	1.00E-11	0.00001	0.001	2.1	2.7778E-05	9.80E-10
7	g mm s	1000	1000	1	1000000	1	1000000000	0.000001	2.10E+11	277.778	9800
8	ton mm s	0.001	1000	1	1	1E-06	1000	1.00E-12	210000	277.778	9800
9	slug ft s	0.068	3.28	1	0.224	0.0208	0.7372	0.00194	4386951220	0.91111184	32.144
10	kg mm s	1	1000	1	0.001	0.001	1000000	1.00E-09	210000000	277.778	9800
11	g cm ms	1000	100	1000	0.1	0.00001	10	0.001	2100000	0.0277778	0.00098
12	kg mm ms	1	1000	1000	0.001	1.00E-09	1	1.00E-09	210	0.277778	0.0098

CONCLUSION :

Thus the given input measurements are converted into respective unit systems and this is used in LS - DYNA calculations.