Week - 1 - Consistency of Units

Aim: Convert given measurements into different units and find their corresponding conversion factors.

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

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

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 have to be conversant with converting quantities from one system of units to another.

Conversions: (From SI unit to gm/mm/ms unit system)
MASS : 1kg = 1000gm Conversion factor : 1000
LENGTH : 1m = 1000mm Conversion factor : 1000
TIME : 1s = 1000ms Conversion factor : 1000

FORCE : 1N = 1kg*1 m/s
= (1000g*1000mm)/(1000ms)
= 10 *10 (g*mm)/ms
= 1 (g*mm)/ms
Conversion factor : 1

STRESS : 1Pa = 1N/m2 = {1kg*(1 m2/s )}/m2 = 1 kg/ (m2* s )
= 1000g/{1000mm*(1000ms) }
= 1e-6 g/ (mm*ms )
Conversion factor : 1e-6

ENERGY : 1J = 1Nm = (1kg*1 m/s ) * m 1 (kg*m /s )
= {1000g * (1000mm) }/(1000ms)
= (10 g*mm ) / (10 ms )
= 10 (g*mm / ms )
Conversion factor : 1e3

DENSITY : 1Kg/m3 = 1000g/(1000mm)
= 10 g/mm
Conversion factor : 1e-6

YOUNGS MODULUS : 210GPa = 210e+9 kg/(m*s^2 ) = 210e+9 * 10 g/ (mm*m s^2 )
= 210e+3 g/ (mm*m s^2 ) = 210*10 g/ (mm*m s^2 )
Conversion factor : 210000gm/mm*ms^2


VELOCITY : 56.33 Kmph = 56.33 * {10 mm/(3600*1000ms)}
= 15.647 mm/ms
Conversion factor : 5/18

GRAVITY : 9.8m/s2 = 9.8 * 1000mm/(1000ms)
= 9.8* 10 mm/ms
Conversion factor : 10^-3

Table unit systems as rows and measured quantities as columns :
Unit system Mass Length Time Force Stress

Conclusion:
The unit conversion was done for different systems of units.