Week - 1 - Consistency of Units

Aim: Converting the given values into different system units

Introduction:

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. 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. This ensures accurate and consistent results across various industries and regions. To convert quantities, users should identify the given and desired unit systems, determine conversion factors, apply these factors to all relevant quantities (material properties, loads, boundary conditions, and output parameters), and check for consistency and accuracy. Finally, input the converted quantities into the simulation software to conduct the analysis using the desired unit system, ensuring that simulations accurately represent real-world problems and prevent errors or inconsistencies that may lead to incorrect results.

MASS (kg) LENGTH (m) TIME (s) FORCE (N) STRESS (Pa) ENERGY (Nm) DENSITY (kg/m3) YOUNG'S Modulus (GPa) Velocity (KMPH) GRAVITY (m/s2) SI 1 1 1 1 1 1 1 210 56.33 9.8 Kg cm ms 1 100 1000 0.0001 0.00000001 0.01 0.000001 2.10E+03 1.5647222 0.00098 Kg cm s 1 100 1 100 0.01 10000 0.000001 2.10E+09 1564.7222 980 gm mm ms 1000 1000 1000 1 0.000001 1000 0.000001 2.10E+05 15.647222 0.0098 kg m s 1 1 1 1 1 1 1 2.10E+11 15.647222 9.8 g cm s 1000 100 1 100000 10 10000000 0.001 2.10E+12 1564.7222 980 g cm us 1000 100 1000000 0.0000001 1E-11 0.00001 0.001 2.10E+00 0.001564722 9.8E-10 g mm s 1000 1000 1 1000000 1 1000000000 0.000001 2.10E+11 15647.222 9800 ton mm s 0.001 1000 1 1 0.000001 1000 1E-12 2.10E+05 15647.222 9800 slug ft s 0.0685 3.28 1 0.22468 0.020884146 0.7369504 0.001941194 4.39E+09 51.32288816 32.144 kg mm s 1 1000 1 1000 0.001 1000000 0.000000001 2.10E+08 15647.222 9800 g cm ms 1000 100 1000 0.1 0.00001 10 0.001 2.10E+06 1.5647222 0.00098 kg mm ms 1 1000 1000 0.001 0.000000001 1 0.000000001 2.10E+02 15.647222 0.0098

For the gm/mm/ms unit system, here are the detailed conversion calculations:

1. MASS: 1 kg = 1000 g ; Conversion factor = 1000

2. LENGTH: 1 m = 1000 mm ; Conversion factor = 1000

3. TIME: 1 s = 1000 ms ; Conversion factor = 1000

4. FORCE: (1 kg * 1000 mm) / (1 ms)^2 = 1000 N ; Conversion factor = 1000

5. STRESS: (1 kg * 1000 mm) / (1 ms)^2 * (1 m^2) = 1 N / 1e6 mm^2 = 0.000001 Pa ; Conversion factor = 1 / 1e6 = 1e-6

6. ENERGY: (1 kg * 1000 mm * 1000 mm) / (1 ms)^2 = 1e6 Nm ; Conversion factor = 1e6

7. DENSITY: (1 kg) / (1000 mm * 1000 mm * 1000 mm) = 0.000001 kg/m^3 ; Conversion factor = 1 / 1e6 = 1e-6

8. YOUNG'S Modulus: 210 GPa = 210e+9 Pa (210e+9 Pa) * (1 m / 1000 mm)^2 = 210e+5 GPa ; Conversion factor = 1 / 1e4 = 1e-4

9. Velocity: 56.33 km/h = 56.33 * 1000 m/h * (1 h / 3600 s) = 15.647222 m/s ; Conversion factor = 1

10. GRAVITY: 9.8 m/s^2 ; Conversion factor = 1