Consistency of units in LS Dyna
Objective:
To convert the Given measurement values to different Unit Systems
FUNDAMENTAL QUANTITY:
The Fundamental Quantity is an independent Physical Quantity that is not possible to express in other Physical Quantity, eg Time(s), Mass (kg), Length (m).
DERIVED QUANTITY:
Derived quantities are those that may be expressed in terms of base or derived quantities by means of the mathematical symbols of multiplication and division only (no addition or subtraction or any other sign), eg: Acceleration-(m/s^2), velocity-(m/s), Density-(kg/m^3).
The fundamental quantities are converted into different measurements.
1. Mass
1kg => 1000g
1kg => 0.001 tonne
1kg => 0.0685218
2.Length
1m => 1000mm
1m => 100cm
1m => 3.2808 feet
3.Time
1s= 1000ms
1s= 1e6+6 microseconds (us)
1. Conversion in Kg cm ms
Force:-
Force is calculated By Newton.
Force =1N
1N=1 (kg)(m/s²)
=1*1*(100/1000²)
=10⁻⁴ kg*cm/ms²
Conversion factor= 10⁻⁴
Stress:-
Unit of stress is pascal
1pa=1N/m²
1N=1 (kg)(m/s²)
=1 (kg)(m/s²) / m²
=1*1*(100/1000²) / (100*100)
=10⁻⁸ Kg/(cm*ms²)
Conversion factor= 10⁻⁸
Energy:-
Energy is represented by Joule.
1J= 1Nm
= 1 (kg)(m/s²) / m
=1*1*(100/1000²) / 100
=10⁻²kg*cm²/ms²
Conversion factor= 10⁻²
Density:-
Unit of Density=kg/m³
=1/(100³)
=10⁻⁶ kg/cm³
Conversion factor= 10⁻⁶
Young's modulus:-
Unit of young's modulus is in Gpa
=1Gpa=10⁹pa
=210Gpa= 210*10⁹ pa
=1pa=1N/m²
=210*10⁹ N/m²
=210*10⁹ (kg)(m/s²) /m²
=210*10⁹*1*(100/1000²) / (100²)
=2100kg/(cm*ms²)
Conversion factor= 10
Velocity:-
unit of velocity=m/s
56.33 kmph
1.5647 cm/ms
Conversion factor= 1
Gravity:-
unit of gravity=9.81m/s²
=9.8*10⁻⁴ cm/ms²
Conversion factor= 10⁻⁴
2. Conversion in Kg m s:
Force 1N
1 Kg*1 m/s²
Conversion factor=1
Stress 1pa
Unit of stress is pascal
1pa=1N/m²
1N=1 (kg)(m/s²)
=1 (kg)(m/s²) / m²
=kg/m*s²
Conversion factor=1
Energy 1Nm
Energy is represented by Joule.
1J= 1Nm
= 1 (kg)(m/s²) / m
=kg m² / s²
Conversion factor=1
Density
Unit of Density=kg/m³
Conversion factor=1
Young's Modulus 210Gpa
=1Gpa=10⁹pa
=210Gpa= 210*10⁹ pa
=1pa=1N/m²
=210*10⁹ N/m²
=210*e⁹ kg/ ms²
Conversion factor=10⁹
Velocity 56.33 kmph
=15.647 m/s
Conversion factor=1
Gravity:
unit of gravity=9.81m/s²
No change needed:
Conversion factor=1
3. conversion in g mm s:
Force 1N
1 Kg*1 m/s²
10⁶g*mm/s²
Conversion factor=10⁶
Stress 1pa
Unit of stress is pascal
1pa=1N/m²
1N=1 (kg)(m/s²)
=1g/ mm*s²
Conversion factor=1
Energy 1Nm
Energy is represented by Joule.
1J= 1Nm
= 1 (kg)(m/s²) / m
=10⁹ g*mm² /s²
Conversion factor=10⁹
Density
Unit of Density=kg/m³
=10⁻⁶ g/mm³
Conversion factor=10⁻⁶
Young's Modulus 210Gpa
=1Gpa=10⁹pa
=210Gpa= 210*10⁹ pa
=1pa=1N/m²
=210*10⁹ N/m²
=210*e⁹ kg/ ms²
=210e⁹ g/(mm*s²)
Conversion factor=10⁹
Velocity 56.33 kmph
=15647mm/s
Conversion factor=1
Gravity:
unit of gravity=9.81m/s²
=9.8*10³ mm/s²
Conversion factor=10³
4.Conversion in g cm s:
Force 1N
1 Kg*1 m/s²
10⁵g*cm/s²
Conversion factor=10⁵
Stress 1pa
Unit of stress is pascal
1pa=1N/m²
1N=1 (kg)(m/s²)
=10g/(cm*s²)
Conversion factor=10
Energy 1Nm
Energy is represented by Joule.
1J= 1Nm
= 1 (kg)(m/s²) / m
=10⁷ g*cm² /s²
Conversion factor=10⁷
Density
Unit of Density=kg/m³
=10⁻³g/cm³
Conversion factor=10⁻³
Young's Modulus 210Gpa
=1Gpa=10⁹pa
=210Gpa= 210*10⁹ pa
=1pa=1N/m²
=210*e⁹ N/m²
=210*e⁹ kg/ ms²
=210*e¹⁰ g/(cm*s²)
Conversion factor=10¹⁰
Velocity 56.33 kmph
=1564.7m/s
Conversion factor=1
Gravity:
unit of gravity=9.81m/s²
=9.8*10² cm/s²
Conversion factor=10²
5. conversion in kg cm s:
Force 1N
1 Kg*1 m/s²
10²kg*cm/s²
Conversion factor=10²
Stress 1pa
Unit of stress is pascal
1pa=1N/m²
1N=1 (kg)(m/s²)
=10⁻²kg/(cm*s²)
Conversion factor=10⁻²
Energy 1Nm
Energy is represented by Joule.
1J= 1Nm
= 1 (kg)(m/s²) / m
=10⁴ kg*cm² /s²
Conversion factor=10⁴
Density
Unit of Density=kg/m³
=10⁻⁶ kg/cm³
Conversion factor=10⁻⁶
Young's Modulus 210Gpa
=1Gpa=10⁹pa
=210Gpa= 210*10⁹ pa
=1pa=1N/m²
=210*e⁹ N/m²
=210*e⁹ kg/ ms²
=210*e⁷ kg/(cm*s²)
Conversion factor=10⁷
Velocity 56.33 kmph
=1564.7cm/s
Conversion factor=1
Gravity:
unit of gravity=9.81m/s²
=9.8*10² cm/s²
Conversion factor=10²
6. conversion in gm mm ms:
Force 1N
1 Kg*1 m/s²
1 g*mm/ms²
Conversion factor=10²
Stress 1pa
Unit of stress is pascal
1pa=1N/m²
1N=1 (kg)(m/s²)
=e⁻⁶ g/mm*ms²
Conversion factor=10⁻⁶
Energy 1Nm
Energy is represented by Joule.
1J= 1Nm
= 1 (kg)(m/s²) / m
=10³ g*mm²/ms²
Conversion factor=10³
Density
Unit of Density=kg/m³
=10⁻⁶g/mm³
Conversion factor=10⁻⁶
Young's Modulus 210Gpa
=1Gpa=10⁹pa
=210Gpa= 210*10⁹ pa
=1pa=1N/m²
=210*e⁹ N/m²
=210*e⁹ kg/ ms²
=210*e³ g/(mm*ms²)
Conversion factor=10³
Velocity 56.33 kmph
=15.647mm/ms
Conversion factor=1
Gravity:
unit of gravity=9.81m/s²
=9.8*10⁻³ mm/ms²
Conversion factor=10⁻³
7. conversion in g cm us:
(us: Microsecond)
Force 1N
1 Kg*1 m/s²
10⁻⁷g*cm/us²
Conversion factor=10⁻⁷
Stress 1pa
Unit of stress is pascal
1pa=1N/m²
1N=1 (kg)(m/s²)
=10⁻¹¹ g/(cm*us²)
Conversion factor=10⁻¹¹
Energy 1Nm
Energy is represented by Joule.
1J= 1Nm
= 1 (kg)(m/s²) / m
=10⁻⁵ g*cm²/us²
Conversion factor=10⁻⁵
Density
Unit of Density=kg/m³
=10⁻³g/cm³
Conversion factor=10⁻³
Young's Modulus 210Gpa
=1Gpa=10⁹pa
=210Gpa= 210*10⁹ pa
=1pa=1N/m²
=210*e⁹ N/m²
=210*e⁹ kg/ ms²
=2.10g/cm*us²
Conversion factor=10⁻²
Velocity 56.33 kmph
=15.647*10⁻⁴ cm/us
Conversion factor=10⁻⁴
Gravity:
unit of gravity=9.81m/s²
=9.8*10⁻¹⁰ cm/us²
Conversion factor=10⁻¹⁰
8. conversion in ton mm s:
Force 1N
1 Kg*1 m/s²
=1 ton*mm/s²
Conversion factor=1
Stress 1pa
Unit of stress is pascal
1pa=1N/m²
1N=1 (kg)(m/s²)
=10⁻⁶ ton/(mm*s²)
Conversion factor=10⁻⁶
Energy 1Nm
Energy is represented by Joule.
1J= 1Nm
= 1 (kg)(m/s²) / m
=10³ ton*mm²/s²
Conversion factor=10³
Density
Unit of Density=kg/m³
=10⁻¹² ton/mm³
Conversion factor=10⁻¹²
Young's Modulus 210Gpa
=1Gpa=10⁹pa
=210Gpa= 210*10⁹ pa
=1pa=1N/m²
=210*e⁹ N/m²
=210*e⁹ kg/ ms²
=210 e³ ton/(mm*s²)
Conversion factor=10³
Velocity 56.33 kmph
=15647 mm/s
Conversion factor=1
Gravity:
unit of gravity=9.81m/s²
=9.8*10³ mm/s²
Conversion factor=10³
9. conversion in slug ft s:
Force 1N
1 Kg*1 m/s²
=0.2246 slug*ft/s²
Conversion factor=1
Stress 1pa
Unit of stress is pascal
1pa=1N/m²
1N=1 (kg)(m/s²)
=0.0208 slug/(ft*s²)
Conversion factor=1
Energy 1Nm
Energy is represented by Joule.
1J= 1Nm
= 1 (kg)(m/s²) / m
=0.7366slug*ft²/s²
Conversion factor=1
Density
Unit of Density=kg/m³
=1.93*10⁻³ slug/ft³
Conversion factor=10⁻³
Young's Modulus 210Gpa
=1Gpa=10⁹pa
=210Gpa= 210*10⁹ pa
=1pa=1N/m²
=210*e⁹ N/m²
=210*e⁹ kg/ ms²
=4.368 e⁹ slug/(ft*s²)
Conversion factor=10⁹
Velocity 56.33 kmph
=51.322 ft/s
Conversion factor=1
Gravity:
unit of gravity=9.81m/s²
=32.144ft/s²
Conversion factor=1
The converted values of the rest of the unit System are Plotted as a table below:
|
Unit system (SI unit) |
Mass | Length | Time |
Force 1N |
Stress | Energy | Density |
Young's Modulus (210gpa) |
Velocity 56.33kmph |
Gravity |
|
kg, m, s |
1kg | 1m | 1s | 1 Kg m/s² | kg/m*s² | kg m² / s² | kg/m³ | 210*e⁹ kg/ ms² | 15.647 m/s | 9.81m/s² |
|
kg, cm, ms |
1kg | 10²cm | 10³ms | 10⁻⁴ kg*cm/ms² | 10⁻⁸ Kg/(cm*ms²) | 10⁻²kg*cm²/ms² | 10⁻⁶ kg/cm³ | 2100kg/(cm*ms³) | 1.5647 cm/ms | 9.8*10⁻⁴ cm/ms² |
| kg, cm, s | 1kg | 10²cm | 1s | 10²kg*cm/s² | 10⁻²kg/(cm*s²) | 10⁴ kg*cm² /s² | 10⁻⁶ kg/cm³ | 210*e⁷ kg/(cm*s²) | 1564.7cm/s | 9.8*10² cm/s² |
| g, mm, ms | 10³g | 10³mm | 10³ms | 1 g*mm/ms² | 10⁻⁶g/(mm*ms²) | 10³ g*mm²/ms² | 10⁻⁶ g/mm³ | 210e³ g/(mm*ms²) | 15.647 mm/ms | 9.8*10⁻³ mm/ms² |
| g, cm, s | 10³g | 10²cm | 1s | 10⁵g*cm/s² | 10g/(cm*s²) | 10⁷ g*cm² /s² | 10⁻³g/cm³ | 210*e¹⁰ g/(cm*s²) | 1564.7m/s | 9.8*10² cm/s² |
| g, cm, us | 10³g | 10²cm | 10⁶us | 10⁻⁷g*cm/us² | 10⁻¹¹ g/(cm*us²) | 10⁻⁵ g*cm²/us² | 10⁻³g/cm³ | 2.10g/cm*us² | 15.647*10⁻⁴ cm/us | 9.8*10⁻¹⁰ cm/us² |
| g, mm,s | 10³g | 10³mm | 1s | 10⁶g*mm/s² | 1g/(mm*s²) | 10⁹g*mm²/s² | 10⁻⁶g/mm³ | 2.10e¹¹g/mm*s² | 15647mm/s | 9.8*10³mm/s² |
| Ton, mm,s | 10⁻³ton | 10³mm | 1s | 1 ton*mm/s² | 10⁻⁶ ton/(mm*s²) | 10³ ton*mm²/s² | 10⁻¹² ton/mm³ | 210 e³ ton/(mm*s²) | 15647 mm/s | 9.8*10³ mm/s² |
| Slug, ft, s | 0.068 slug | 3.28ft | 1s | 0.2246 slug*ft/s² | 0.0208 slug/(ft*s²) | 0.7366slug*ft²/s² | 1.93*10⁻³ slug/ft³ | 4.368 e⁹ slug/(ft*s²) | 51.322 ft/s | 32.144ft/s² |
| Kg, mm,s | 1Kg | 10³mm | 1s | 10³kg*mm/s² | 10⁻³kg/mm*s² | 10⁶kg*mm²/s² | 10⁻⁹kg/mm³ | 210e⁶kg/mm*s² | 15647mm/s | 9.8*10³mm/s² |
| g, cm, ms | 10³g | 10²cm | 10³ms | 10⁻¹g*cm/ms² | 10⁻⁵g/cm*ms² | 10g*cm²/ms² | 10⁻³g/cm³ | 210e⁴g/cm*ms² | 1.5647cm/ms | 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) | 15.647 mm/ms | 9.8*10⁻³mm/ms² |
Conclusion:
The Values are Converted into the Specific Unit System.
Since Ls Dyna doesn't have a specific unit system the above assignment will be useful in deploying the Units while performing Simulation