Week - 1 - Consistency of Units

Aim: Convert the given values in the required conversation factor units with detailed calculations.

Procedure:

• LS-DYNA does not have any default system of units.user need to input material properties and physical Dimensions according to the consistant system of units as per their choice.from this we can known that LS-DYNA simulate according to the given values.

Value of the following measurments are as given below:

Given data:

MASS : 1kg

LENGTH: 1m

TIME : 1s

FORCE : 1N

STRESS : 1pa

ENERGY : 1Nm

DENSITY : 1kg/m^3

YOUNG'S Modulus : 210 Gpa

Velocity : 56.33KMPH

GRAVITY : 9.8m/s^2

Now,here are few system of units to convert:

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

• conversion from SI unit to gm/mm/ms unit system:

MASS :1kg=1000gm =10^3gm

LENGTH :1m=100cm=1000mm=10^3mm

TIME :1s=1000ms=10^3ms

FORCE :1N

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

=10^6gm*mm/10^6ms^2

• FORCE =1N= 1gm*mm/ms^2

STRESS :1pa

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

= 10^-6gm/mm*ms^2

DENSITY :1kg/m^3

1*10^3gm/10^9mm^3=10^-6gm/mm^3

Young's modulus :210Gpa

=210*10^9*n/m^2=210*10^9*10^-6gm/mm*ms^2=210*10^3gm/mm*ms^2

Velocity : 56.33KMPH=56.33KM/hr

=56.33*10^6mm/3600*10^3ms=15.647mm/ms

GRAVITY : 9.8m/s^2

9.8*10^3mm/10^6ms^2=9.8*10^-3mm/ms^2

• As per the requirement the detail view of gm/mm/ms is shown the remaining will be tabulated.

Units MASS(1KG) LENGTH(1M) TIME (1S) FORCE(1N) STRESS(1pa) ENERGY(1NM) DENSITY(1kg/M^3) Young's modulus (210Gpa) velocity(56.33KM/hr) GRAVITY(9.8m/s^2)

Kg cm ms 1kg 100cm 10^3ms 10^-4kg*cm/ms^2 10^-8kg/cm*ms^2 10^-2kg*cm^2/ms^2 10^-6kg/cm^3 2100kg/cm*ms^2 1.56472cm/ms 9.8*10^-4cm/ms^2

Kg cm s 1kg 100cm 1s 10^2kg*cm/s^2 10^-2kg/cm*s^2 10^4kg*cm^2/s^2 10^-6kg/cm^3 210*10^7kg/cm*s^2 1564.72cm/s 9.8*10^-2cm/s^2

gm mm ms 10^3gm 10^3mm 10^3ms 1gm*mm/ms^2 10^-6gm/mm*ms^2 10^3gm*mm^2/ms^2 10^-6gm/mm^3 210*10^3gm/mm*ms^2 15.6472mm/ms 9.8*10^-3mm/ms^2

Kg m s 1kg 1m 1s 1kg*m/s^2 1kg/m*s^2 1kg*m^2/s^2 1kg/m^3 210*10^9n/m^2 15.6472m/s 9.8m/s^2

g cm s 10^3gm 100cm 1s 10^5gm*cm/s^2 10gm/cm*ms^2 10^7gm*cm^2/s^2 10^-3gm/cm^3 210*10^10gm/cm*s^2 1564.72cm/s 9.8*10^2cm/s^2

g cm mus 10^3gm 100cm 10^6mus 10^-7gm*cm/mus 10^-11gm/cm*mus^2 10^-5gm*cm^2/mus^2 10^-3gm/cm^3 2.1gm/cm*mus^2 15.64*10^-4cm/mus 9.8*10^-10cm/mus^2

g mm s 10^3gm 10^3mm 1s 10^6gm*mm/s^2 1gm/mm*s^2 10^9gm*mm^2/s^2 10^-6gm/mm^3 210*10^11gm/mm*s^2 156472mm/s 9.8*10^3mm/s^2

ton mm s 10^3gm 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*s^2 156472mm/s 9.8*10^3mm/s^2

slug ft s 0.068slug 3.28ft 1s 0.224slug*ft/s^2 0.0208slug/mm*s^2 0.7366slug*ft^2/s^2 1.93*10^-3slug/ft^3 4.368slug/ft*s^2 51.322ft/s 32.144ft/s^2

Kg mm s 1kg 10^3mm 1s 10^3kg*mm/s^2 10^-3kg/mm*s^2 10^6kg*mm^2/s^2 10^-9kg/mm^3 210*10^6kg/mm*s^2 156472mm/s 9.8*10^3mm/s^2

g cm ms 10^3gm 100cm 10^3ms 10^-1gm* cm/ms^2 10^-5gm/cm*ms^2 10gm*cm^2/ms^2 10^-3gm/cm^3 210*10^4gm/cm*ms^2 1.56472cm/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 15.6472mm/ms 9.8*10^-3mm/s^2

• As LS-DYNA has no unit system,we have converted each unit as per the requirements.
• These units can be used to calculate the approximate equations.

Result:

converting the given values into the required conversation factor is done.