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Week - 1 - Consistency of Units

OBJECTIVE: To convert the given SI Unit measurements into other system of units mentioned below. SI Unit measurements: 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 to which the measurements are to be converted:…

LS-DYNA

Mohammad Labeeb Ihsan
updated on 17 Nov 2021

OBJECTIVE:

To convert the given SI Unit measurements into other system of units mentioned below.

SI Unit measurements:

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 to which the measurements are to be converted:

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

Calculation for conversion of measurements from SI units to gm/mm/ms unit system:

Mass:

1 Kg = 1000 gm

Conversion Factor: $10^{3}$ $10^3$

Length:

1m = 1000 mm

Conversion Factor: $10^{3}$ $10^3$

Time:

1 s = 1000 ms

Conversion Factor: $10^{3}$ $10^3$

Force:

1 N = 1 Kg * 1 m/ $s^{2}$ $s^2$

= (1000 gm * 1000 mm)/ ${(1000 m s)}^{2}$ $(1000 ms)^2$

= 1 (gm*mm)/ $m s^{2}$ $ms^2$

Conversion Factor: 1

Stress:

1 Pa = 1 N/ $m^{2}$ $m^2$

= 1 (Kg * m/ $s^{2}$ $s^2$ )/ $m^{2}$ $m^2$

= 1 Kg/(m* $s^{2}$ $s^2$ )

= 1000 gm/(1000 mm * (1000 ms * 1000 ms))

= $10^{- 6}$ $10^-6$ gm/(mm* $m s^{2}$ $ms^2$ )

Conversion Factor: $10^{- 6}$ $10^-6$

Energy:

1 Nm = 1 (Kg * m/ $s^{2}$ $s^2$ )*m

= (1000 gm * (1000 mm *1000 mm))/(1000 ms * 1000 ms)

= $10^{3}$ $10^3$ (gm* $m m^{2}$ $mm^2$ )/ $m s^{2}$ $ms^2$

Conversion Factor: $10^{3}$ $10^3$

Density:

1 Kg/ $m^{3}$ $m^3$ = 1000 gm/(1000 mm * 1000 mm * 1000 mm)

= $10^{- 6}$ $10^-6$ gm/ $m m^{3}$ $mm^3$

Conversion Factor: $10^{- 6}$ $10^-6$

Young’s Modulus:

210GPa = 210* $10^{9}$ $10^9$ Pa

= 210* $10^{9}$ $10^9$ N/ $m^{2}$ $m^2$

= 210* $10^{9}$ $10^9$ (Kg * m/ $s^{2}$ $s^2$ )/ $m^{2}$ $m^2$

= 210* $10^{9}$ $10^9$ [1000 gm/(1000 mm * (1000 ms * 1000 ms))]

= 210* $10^{9}$ $10^9$ [ $10^{- 6}$ $10^-6$ gm/(mm* $m s^{2}$ $ms^2$ )]

= 210* $10^{3}$ $10^3$ gm/(mm* $m s^{2}$ $ms^2$ )

Conversion Factor: $10^{3}$ $10^3$

Velocity:

1 KMPH = $10^{6}$ $10^6$ mm/(3600 * 1000) ms …………….{1 Km = $10^{6}$ $10^6$ mm}; {1 hr = 3600*1000 ms}

= 10/36 mm/ms

= 0.2777 mm/ms

Therefore, 56.33 KMPH = 56 * 0.2777 mm/ms

= 15.64 mm/ms

Conversion Factor: 0.2777

Gravity:

9.8 m/ $s^{2}$ $s^2$ = 9.8 (1000 mm/(1000 ms *1000 ms))

= 9.8* $10^{- 3}$ $10^-3$ mm/ $m s^{2}$ $ms^2$

Conversion Factor: $10^{- 3}$ $10^-3$

Conversion from SI Units to other system of units mentioned:

Unit System	Mass	Length	Time	Force	Stress	Energy	Density	Young's Modulus	Velocity	Gravity
Kg cm ms	1 Kg	$10^{2}$ $10^2$ cm	$10^{3}$ $10^3$ ms	$10^{- 4}$ $10^-4$ kg*cm/ $m s^{2}$ $ms^2$	$10^{- 8}$ $10^-8$ kg/(cm* $m s^{2}$ $ms^2$ )	$10^{- 2}$ $10^-2$ kg* $c m^{2}$ $cm^2$ / $m s^{2}$ $ms^2$	$10^{- 6}$ $10^-6$ kg/ $c m^{3}$ $cm^3$	2100 kg/(cm* $m s^{2}$ $ms^2$ )	1.5647 cm/ms	9.8* $10^{- 4}$ $10^-4$ cm/ $m s^{2}$ $ms^2$
Kg cm s	1 Kg	$10^{2}$ $10^2$ cm	1 s	$10^{2}$ $10^2$ kg*cm/ $s^{2}$ $s^2$	$10^{- 2}$ $10^-2$ kg/(cm* $s^{2}$ $s^2$ )	$10^{4}$ $10^4$ kg* $c m^{2}$ $cm^2$ / $s^{2}$ $s^2$	$10^{- 6}$ $10^-6$ kg/ $c m^{3}$ $cm^3$	210e+7 kg/(cm* $s^{2}$ $s^2$ )	1564.7 cm/s	9.8* $10^{2}$ $10^2$ cm/ $s^{2}$ $s^2$
kg m s	1 Kg	1 m	1 s	1 kg*m/ $s^{2}$ $s^2$	1 kg/(m* $s^{2}$ $s^2$ )	1 kg* $m^{2}$ $m^2$ / $s^{2}$ $s^2$	1 kg/ $m^{3}$ $m^3$	210e+9 kg/(m* $s^{2}$ $s^2$ )	15.647 m/s	9.8 m/ $s^{2}$ $s^2$
g cm s	$10^{3}$ $10^3$ g	$10^{2}$ $10^2$ cm	1 s	$10^{5}$ $10^5$ g*cm/ $s^{2}$ $s^2$	10 g/(cm* $s^{2}$ $s^2$ )	$10^{7}$ $10^7$ g* $c m^{2}$ $cm^2$ / $s^{2}$ $s^2$	$10^{- 3}$ $10^-3$ g/ $c m^{3}$ $cm^3$	210e+10 g/(cm* $s^{2}$ $s^2$ )	1564.7 cm/s	9.8* $10^{2}$ $10^2$ cm/ $s^{2}$ $s^2$
g cm $μ$ $mu$ s	$10^{3}$ $10^3$ g	$10^{2}$ $10^2$ cm	$10^{6}$ $10^6$ $μ$ $mu$ s	$10^{- 7}$ $10^-7$ g*cm/ $μ s^{2}$ $mus^2$	$10^{- 11}$ $10^-11$ g/(cm* $μ s^{2}$ $mus^2$ )	$10^{- 5}$ $10^-5$ g* $c m^{2}$ $cm^2$ / $μ s^{2}$ $mus^2$	$10^{- 3}$ $10^-3$ g/ $c m^{3}$ $cm^3$	2.10 g/(cm* $μ s^{2}$ $mus^2$ )	15.647* $10^{- 4}$ $10^-4$ cm/ $μ$ $mu$ s	9.8* $10^{- 10}$ $10^-10$ cm/ $μ s^{2}$ $mus^2$
g mm s	$10^{3}$ $10^3$ g	$10^{3}$ $10^3$ mm	1 s	$10^{6}$ $10^6$ g*mm/ $s^{2}$ $s^2$	1 g/(mm* $s^{2}$ $s^2$ )	$10^{9}$ $10^9$ g* $m m^{2}$ $mm^2$ / $s^{2}$ $s^2$	$10^{- 6}$ $10^-6$ g/ $m m^{3}$ $mm^3$	2.10e+11 g/(mm* $s^{2}$ $s^2$ )	15647 mm/s	9.8* $10^{3}$ $10^3$ mm/ $s^{2}$ $s^2$
ton mm s	$10^{- 3}$ $10^-3$ ton	$10^{3}$ $10^3$ mm	1 s	1 ton*mm/ $s^{2}$ $s^2$	$10^{- 6}$ $10^-6$ ton/(mm* $s^{2}$ $s^2$ )	$10^{3}$ $10^3$ ton* $m m^{2}$ $mm^2$ / $s^{2}$ $s^2$	$10^{- 12}$ $10^-12$ ton/ $m m^{3}$ $mm^3$	210e+3 ton/(mm* $s^{2}$ $s^2$ )	15647 mm/s	9.8* $10^{3}$ $10^3$ mm/ $s^{2}$ $s^2$
slug ft s	0.068 slug	3.28 ft	1 s	0.2246 slug*ft/ $s^{2}$ $s^2$	0.0208 slug/(ft* $s^{2}$ $s^2$ )	0.7366 slug* $f t^{2}$ $ft^2$ / $s^{2}$ $s^2$	1.93* $10^{- 3}$ $10^-3$ slug/ $f t^{3}$ $ft^3$	4.368e+9 slug/(ft* $s^{2}$ $s^2$ )	51.322 ft/s	32.144 ft/ $s^{2}$ $s^2$
kg mm s	1 Kg	$10^{3}$ $10^3$ mm	1 s	$10^{3}$ $10^3$ kg*mm/ $s^{2}$ $s^2$	$10^{- 3}$ $10^-3$ kg/(mm* $s^{2}$ $s^2$ )	$10^{6}$ $10^6$ kg* $m m^{2}$ $mm^2$ / $s^{2}$ $s^2$	$10^{- 9}$ $10^-9$ kg/`mm^3	210e+6 kg/(mm* $s^{2}$ $s^2$ )	15647 mm/s	9.8* $10^{3}$ $10^3$ mm/ $s^{2}$ $s^2$
g cm ms	$10^{3}$ $10^3$ g	$10^{2}$ $10^2$ cm	$10^{3}$ $10^3$ ms	$10^{- 1}$ $10^-1$ g*cm/ $m s^{2}$ $ms^2$	$10^{- 5}$ $10^-5$ g/(cm* $m s^{2}$ $ms^2$ )	10 g* $c m^{2}$ $cm^2$ / $m s^{2}$ $ms^2$	$10^{- 3}$ $10^-3$ g/ $c m^{3}$ $cm^3$	210e+4 g/(cm* $m s^{2}$ $ms^2$ )	1.5647 cm/ms	9.8* $10^{- 4}$ $10^-4$ cm/ $m s^{2}$ $ms^2$
kg mm ms	1 Kg	$10^{3}$ $10^3$ mm	$10^{3}$ $10^3$ ms	$10^{- 3}$ $10^-3$ kg*mm/ $m s^{2}$ $ms^2$	$10^{- 9}$ $10^-9$ kg/(mm* $m s^{2}$ $ms^2$ )	1 kg* $m m^{2}$ $mm^2$ / $m s^{2}$ $ms^2$	$10^{- 9}$ $10^-9$ kg/`mm^3	210 kg/(mm* $m s^{2}$ $ms^2$ )	15.647 mm/ms	9.8* $10^{- 3}$ $10^-3$ mm/ $m s^{2}$ $ms^2$

CONCLUSION:

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