Week - 1 - Consistency of units

There is no default system of units in LS dyna and also, LS dyna doesn't understand what units the model uses so units must be compatible. The users has to be conversant with converting quantities from one system of units to another. This allow us to use LS dyna in different scenarios.

Different industries use different system of units as per their convenience. The units for the basic measurement quantities, mass distance and time - dictate how the other derived quantities will be expressed. For example, 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.

OBJECTIVE: -

I. We need to write the given measurements in the below different system of units.

GIVEN MEASUREMENTS -

MASS 1kg
LENGTH 1m
TIME 1s
FORCE 1N
STRESS 1Pa
ENERGY 1Nm
DENSITY 1Kg/m^3
YOUNG'S MODULUS 210GPa
VELOCITY 56.33kmph
GRAVITY 9.8m/s^2

GIVEN 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

II. A detailed calculation for conversion from SI unit to gm mm ms unit system.

INVOLVED CALCULATIONS: -

Conversion from SI unit to gm mm ms

• Mass= 1 kg

Conversion to gm mm ms= 1000g

Conversion factor= 10³

• Length= 1 m

Conversion to gm mm ms= 1000mm

Conversion factor= 10³

• Time= 1 s

Conversion to gm mm ms= 1000ms

Conversion factor= 10³

• Force= 1 N = kg m/s²

Conversion to gm mm ms= (1000g x 1000mm/1000²ms²)= 1 g mm/ms²

Conversion factor= 1

• Stress= 1 Pa = 1 N/m²

Conversion to gm mm ms= (1/1000² g/ mm ms²)

Conversion factor= 10^-6

• Energy= 1 J = 1 Nm

Conversion to gm mm ms= (1 g mm/ms² x 1000mm) = 10³ g mm²/ms²

Conversion factor= 10³

• Density= 1 kg/m³

Conversion to gm mm ms= (1000g/ 1000³ mm³) =10^-6 g/mm³

Conversion factor= 10^-6

• Young’s modulus= 210 GPa = 210x10⁹ N/m²

Conversion to gm mm ms= (210x 10⁹ x 10^-6 g/mm ms²) = 210x 10³ g/mm ms²

Conversion factor= 10^-6

• Velocity = 56.33 kmph = 56.33x 1000/60x 60 = 15.647 m/s

Conversion to gm mm ms = (15.647x 1000mm/1000ms) = 15.647 mm/ms

Conversion factor = 1

• Gravity = 9.8 m/s²

Conversion to gm mm ms= (9.8 x 1000mm/1000² ms²) = 9.8 x10^-3 mm/ms²

Conversion factor= 10^-3

Below table contains calculation of conversion measured quantities to different unit systems:

Unit System	Mass	Length	Time	Force	Stress	Energy	Density	Young’s Modulus	Velocity	Gravity
Kg cm ms	1 kg	100cm	103 ms	10-4 kg cm/ms2	10-8 kg /cm ms2	10-2 kg cm2/ms2	10-6 kg/cm3	210x10 kg/cm ms2	15.647x10-1 cm/ms	9.8x10-4 cm/ms2
Kg cm s	1 kg	100cm	1s	102 kg/ cm s2	10-2 kg/ cm s2	104 kg cm2/s2	10-6 kg/cm3	210x107 kg/cm s2	15.647x102cm/s	9.8x102 cm/s2
Kg m s	1 kg	1 m	1s	1 kg m/s2	1 kg/ ms2	1 kg m2/s2	1 kg/m3	210x109 kg/m s2	15.647 m/s	9.8 m/s2
g cm s	1000g	100cm	1s	105g/cm s2	10 g/ cm s2	107 g cm2/s2	10-3 g/cm3	210x1010 g/cm s2	15.647x 102cm/s	9.8x102 cm/s2
g cm us	1000g	100cm	106us	10-7g/ cm us2	10-11 g/cm us2	10-5 g cm2/us2	10-3 g/cm3	210x10-2 g/cm us2	15.647x 10-4 cm/us	9.8x10-10 cm/us2
g mm s	1000g	103 mm	1s	106g mm/s2	1 g/mm s2	109 g mm2/s2	10-6 g/mm3	210x109 g/mm s2	15.647x103 mm/s	9.8x103 mm/s2
ton mm s	10-3 ton	103 mm	1s	1 ton mm/s2	10-6 ton mm/s2	103 ton mm2/s2	10-12 ton /mm3	210x103 ton/mm s2	15.647x103 mm/s	9.8x103 mm/s2
slug ft s	0.068 slug	3.28 ft	1s	0.2246 slug ft/s2	0.0208 slug/ft s2	0.7366 slug ft2/s2	1.93x 10-3 slug/ft3	4.368x109 slug/ft s2	51.322 ft/s	32.144 ft/s2
Kg mm s	1 kg	103 mm	1s	103 kg mm/s2	10-3 kg /mm s2	106 kg mm2/s2	10-9 kg/mm3	210x106 kg/mm s2	15.647x103 mm/s	9.8x103 mm/s2
g cm ms	1000kg	100cm	103 s	0.1gcm/ms2	10-5g /cm ms2	10g cm2 /ms2	10-3 g/cm3	210x104g/ cm ms2	1.5647 cm/ms	9.8x10-4 cm/ms2
Kg mm ms	1 kg	103 mm	103 ms	10-3 kg mm/ms2	10-9 kg/ mm ms2	1kgmm2/ms2	10-9kg/mm3	210 kg/ mm ms2	15.647 mm/ms	9.8x10-3 mm/ms2

LEARNING OUTCOME: -

1. This challange provides understanding about the unit system in LS DYNA.