Consistency of Units
Aim:
To convert given measurements into different system of units and finding their corresponding conversion factors.
Measurements given:
MASS – 1KG
LENGTH – 1M
TIME – 1S
FORCE – 1N
STRESS – 1Pa
ENERGY – 1NM
DENSITY – 1KG/M3
YOUNGS MODULUS – 210GPa
VELOCITY – 56.33KMPH
GRAVITY – 9.8M/S2
Systems 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
Purpose:
The main purpose of the challenge is that LS DYNA does not have a default system of units. The user needs to input material properties and physical dimensions according to a consistent system of units as per their choice. Hence, the values needs to be converted from one system to the other.
Conversions: (From SI unit to gm/mm/ms unit system)
Mass: 1kg = 1000gm Conversion Factor:103
Length: 1m =1000mm Conversion Factor:103
Time: 1s = 1000ms Conversion Factor:103
Force: 1N = 1kg*1m/s2
= (1000g*1000mm) / (1000ms) 2
= 106*10-6 (g*mm)/ms2
= 1 (g*mm)/ms2
Conversion Factor: 1
Stress: 1Pa = 1N/m2 = (1kg*(1m/s2))/m2 = 1kg/(m*s2)
= 1000g/(1000mm*(1000ms)2)
= 10-6 g/ (mm*ms2)
Conversion Factor: 10-6
Energy: 1J = 1Nm = (1kg*1m/s2)*m = 1(kg*m2/s2)
= (1000g *(1000mm)2) / (1000ms)2
= (109 g*mm2) / (106ms2)
= 103 (g*mm2/ms2)
Conversion Factor: 103
Density: 1kg/m3 = 1000g/(1000mm)3
= 10-6 g/mm3
Conversion Factor: 10-6
Youngs Modulus: 210GPa = 210e+9kg/(m*s2) = 210e9*10-6g/(mm*ms2)
= 210*103g/(mm*ms2)
Conversion Factor: 103
Velocity: 56.33Kmph = 56.33*(106mm/(3600*1000ms))
= 15.647 mm/ms
Conversion Factor: 5/18
Gravity: 9.8m/s2 = 9.8*1000mm/(1000ms)2
= 9.8*10-3mm/ms2
Conversion Factor: 10-3
Conversion Table:
|
Unit System |
Mass |
Length |
Time |
Force |
Stress |
Energy |
Density |
Youngs Modulus |
Velocity |
Gravity |
|
Kg m s |
1kg |
1m |
1s |
1N=1kg*m/s2 |
1Pa=1kg/(m*s2) |
1J=1kg*m2/s2 |
1kg/m3 |
210GPa=210e+9kg/(m*s2) |
56.33Kmph=5/18m/s |
9.8m/s2 |
|
Kg cm ms |
1kg |
102cm |
103ms |
10-4kg*cm/ms2 |
10-8kg/(cm*ms2) |
10-2kg*cm2/ms2 |
10-6kg/cm3 |
210*10kg/(cm*ms2) |
1.5647cm/ms |
9.8*10-4cm/ms2 |
|
Kg cm s |
1kg |
102cm |
1s |
102kg*cm/ms2 |
10-2kg/cm*s2) |
104kg*cm2/s2 |
10-6kg/cm3 |
210*107kg/(cm*s2) |
1564.7cm/s |
9.8*102cm/s2 |
|
G mm ms |
103g |
103mm |
103ms |
1g*mm/ms2 |
10-6g/(mm*ms2) |
103g*mm2/ms2 |
10-6 g/mm3 |
210*103g/(mm*ms2) |
5/18 mm/ms |
9.8*10-3mm/ms2 |
|
G cm s |
103g |
102cm |
1s |
105g*cm/s2 |
10g/(cm*s2) |
107g*cm2/s2 |
10-3g/cm3 |
210*1010g/(cm*s2) |
1564.7cm/s |
9.8*102cm/s2 |
|
G cm µs |
103g |
102cm |
106ms |
10-7g*cm/µs2 |
10-5g/cm*µs2) |
10-5g*cm2/µs2 |
10-3g/cm3 |
210*10-2g/(cm*µs2) |
0.00156cm/µs |
9.8*10-10cm/µs2 |
|
G mm s |
103g |
103mm |
1s |
106g*mm/s2 |
1g/(mm*s2) |
109g*mm2/s2 |
10-6g/mm3 |
210*109g/(mm*s2) |
15647mm/s |
9.8*103mm/s2 |
|
Ton mm s |
10-3tonn |
103mm |
1s |
1ton*mm/s2 |
10-6ton/(mm*s2) |
103ton*mm2/s2 |
10-12ton/mm3 |
210*103ton/(mm*s2) |
15647mm/s |
9.8*103mm/s2 |
|
Slug ft s |
0.068slug |
3.28ft |
1s |
0.2246slug*ft/s2 |
0.0208slug/(ft*s2) |
0.7366slug*ft2/s2 |
35.2875slug/ft3 |
4.368*109slug/(ft*s2) |
51.3229ft/s |
32.144ft/s2 |
|
Kg mm s |
1kg |
103mm |
1s |
103kg*mm/s2 |
10-3kg*mm/s2 |
106kg*mm2/s2 |
10-9kg/mm3 |
210*106kg/(mm*s2) |
15647mm/s |
9.8*103mm/s2 |
|
G cm ms |
103 |
102cm |
103ms |
10-1g*cm/ms2 |
10-5g*cm/ms2 |
10g*cm2/ms2 |
10-3g/cm3 |
210*104g/(cm*ms2) |
1564.7cm/s |
9.8*10-4cm/ms2 |
|
Kg mm ms |
1kg |
103mm |
103ms |
10-3kg*mm/ms2 |
10-9kg/(mm*ms2) |
1kg*mm2/ms2 |
10-9kg/mm3 |
210kg/(mm*ms2) |
5/18 mm/ms |
9.8*10-3mm/ms2 |
Conclusion:
Hence, by performing this project we conclude that we have created the conversion table for the conversion of unit systems in inputting the values in LS-DYNA.