Week - 1 - Consistency of Units
Aim: Convert given system into different system of units and finding their corresponding factor.
Measurements Given:
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
Conversions:
Mass 1 kg = 1000gm Conversion factor: 103
Length 1 m = 1000mm Conversion factor: 103
Time 1s = 1000ms Conversion factor: 103
Force: 1N = 1kg*1 m/s2
= (1000g*1000mm)/(1000ms)2
= 106*10-6 (g*mm)/ms2
= 1(g*mm)/ms2
Stress: 1 Pa = 1N/m2 = 1kg*(1m/s2)/m2 = 1kg/m*s2
= 1000g/ {1000mm (1000ms)2
= 10-6 (g*mm2/ms2)
Energy: 1J = 1Nm = 1kg*m/s2*m = 1(kg*m2/s2)
= (1000g*1000mm2) /(1000ms)2
= (109 g*mm2) / (106 ms2)
= 103 (g*mm2/ms2)
Density: 1kg/m3 = 1000g/(1000mm)3
=10-6g/mm3
Young’s Modulus: 210GPa = 210e +9kg (m*s2)
= 210e +9*10-6g/(mm*ms2)
= 210e +3g(mm*ms2)
= 210*103 g/(mm*ms2)
Velocity: 56.33 kmph = 56.33 {106mm/(3600*1000ms)}
= 15.647 mm/ms2
Gravity: 9.8m/s2 = 9.8* 1000mm/(1000ms)2
= 9.8 * 103mm/ms2
Table of units as Rows and Measurements as columns:
|
SI Units |
Mass |
Length |
Time |
Force |
Stress |
Energy |
|
Kg m s |
1kg |
1m |
1s |
1N = 1kg m/s2 |
1Pa = 1 kg (m*s2) |
1J =1 Nm = 1kg* m2/s2 |
|
kg cm ms |
1kg |
102 cm |
103 ms |
10 -4kg*cm/ms2 |
10 -8kg/(cm*ms2) |
10-2kg*cm2/ms2 |
|
kg cm s |
1kg |
102cm |
1s |
102kg*cm/s2 |
10-2 kg/(cm*s2) |
104 Kg*cm2/s2 |
|
g mm ms |
103g |
103mm |
103ms |
1g*mm/ms2 |
10-6 g/mm*ms2) |
103g*mm2/ms2 |
|
g cm s |
103g |
102cm |
1s |
105g*cm/s2 |
10g/cm*s2 |
107g*cm2/s2 |
|
g cm µs |
103g |
102cm |
106 µs |
10-7g*cm/ µs2 |
10-11g/ (cm* µs2) |
10-5 g*cm2/ µs2 |
|
g mm s |
103g |
103mm |
1s |
106g*mm/s2 |
1g/(mm*s2) |
109g*mm2/s2 |
|
Ton mm s |
10-3ton |
103mm |
1s |
1 ton*mm/s2 |
10-6 Ton/(mm*s2) |
103ton*mm2/s2 |
|
slug ft s |
0.068slug |
3.28ft |
1s |
0.2246 Slug*ft/s2 |
0.0208slug/ (ft*s2) |
0.7366slug*ft2/s2 |
|
kg mm s |
1kg |
103mm |
1s |
103kg*mm/s2 |
10-3 Kg/(mm*s2) |
106 kg*mm2/s2 |
|
g cm ms |
103g |
102cm |
103ms |
10-1 g*cm/ms2 |
10-5g/(cm*ms2) |
10g*cm2/ms2 |
|
kg mm ms |
1kg |
103mm |
103ms |
10-3kg*mm/ ms2 |
10-9 kg/(mm*ms2) |
1kg*mm2/ms2 |
Conclusion: Since LS DYNA does not have any default system of units , the user needs to imply the units required as per the material properties and physical dimensions required to analyse the system.