Week - 1 - Consistency of Units

Objective:-

To understand the importance of unit consistancy while dealing with LS Dyna as it does not have default units system. Secondly to convert all the given SI units to the units given with proper calulation explaination.

Procedure:-

Unit consistency is an important part of dyna as the software does not have it as default. Different industries uses different units such as automotive industries use kg,mm,ms as their standard unit system. Construction industries are likely to use tonne,m,s as their unit system. Similarly, PCB simulation in electronic industry uses gm, micrometer,ms as their system of units.

So, fo this consistency of units is important. So starting with the detail sample conversion calculation for each of the units.

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

The above parameters need to be converted to the gm/mm/ms unit system:-

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

So, all the default values before conversion are in SI units:-

For mass:-

1kg=1000g=0.001 tonne=0.06852 slugs. (1tonne=68.522slugs).

For length:-

1m=100cm=1000mm=3.28ft.

For Time:-

1s=1000ms=1000000us

For force(N):-

Force=mass * acceleration

N=kg * meter/sec^2

So,after converting we get,

Force= g*(mm/ms^2)

Conversion factor=1

For Stress:-

Stress(sigma)=F/A=N/m^2

So, Stress=g(mm/ms^2)/mm^2

stress=g/(mm.ms^2)

Conversion factor=10^-6

For Energy:-

Energy (J)=length*force

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

Conversion factor=10^3

For density:-

Rho=m/v=kg/m^3

Rho=g/mm^3

Conversion factor=10^-6

For Young's modlus:-

general formula is E=stress/strain, since the strain does not have any unit so stress units are considered.

E=N/m^2

E=210*10^9 (kg*m/s^2)/(m^2)

=g*(mm/ms^2)/mm^2

E=210000(g/mm*ms^2)

Conversion factor=10-6

For Velocity:-

Velocity=displacement/time

but the given value is 56.33kmph so we have to convert km/hr value to m/s by multiply by 5/18 .

So,1kmph=0.277m/s

ultimately which means 0.277mm/ms.

Conversion factor=1

For gravity:-

gravity=9.81 m/s^2

=9.81*(1000mm/1000^2 ms)

Gravity=0.0098 mm/ms^2

Conversion factor=10^-3

	MASS	LENGTH	TIME	FORCE	STRESS	ENEGRY	DENSITY	YOUNG'S MODULUS	VELOCITY	GRAVITY
Kg cm ms	1	100	1000	0.0001	0.00000001	0.01	0.000001	2100	0.0277	0.00098
Kg cm s	1	100	1	100	0.01	10000	0.000001	2100000000	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	210e+11	0.277778	9.8
g cm s	1000	100	1	1000000	10	10000000	0.001	210e+12	27.7778	980
g cm us	1000	100	1000000	0.0000001	1e-11	0.00001	0.001	2.1	0.0000277778	9.80e-10
g mm s	1000	1000	1	1000000	1	1000000000	0.000001	210000000000	277.778	9800
ton mm s	0.001	1000	1	1	0.000001	1000	1e-12	210000	277.778	9800
slug ft s	0.068	3.28	1	0.2230	0.0207	0.7315712	0.00194119	4.385670732	0.91111184	32.144
kg mm s	1	1000	1	1000	0.001	1000000	0.000000001	210000000	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	0.000000001	1	0.000000001	210	0.277778	0.0098