Consistency of Units

AIM:

Convert the given measurements into different system of units & finding their corresponding conversion factors.

Value of the following measurements are given as follows:

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

Description:

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.

Procedure:

MASS:

Mass is a property of a physical body and a measure of its resistance to acceleration when a net force is applied. An object's mass also determines the strength of its gravitational attraction to other bodies. The SI unit of mass is kilogram.

LENGTH:

Length is a measure of distance and quantities, length is a quantity with dimension distance. The SI unit of length is metre.

TIME:

The measured or measurable period during which an action, process, or condition exists or continous. A nonspatial continuum that is measured in terms of events which succeed one another from past through present to future. The Si unit of time is second.

FORCE:

A force is a push or pull upon an object resulting from the object's interaction with another object. Whenever there is an interaction between two objects, there is a force upon each of the objects. Forces only exist as a result of an interaction. The SI unit of force is N

STRESS:

Stress is the ratio of applied force to a cross section area & its defined as force per unit area. It expresses the internal forces that neighbouring particles of a continuous material exert on each other. The SI unit of stress is Pascal.

ENERGY:

Energy is the quantitative property that must be transferred to a body or physical system to perform work on the body or to heat it. Energy is a conserved quantity, the law of conservation of energy states that energy can be converted in form, but not created or neither can be destroyed. The SI unit of energy is Joule.

DENSITY:

The density, of a substance is its mass per unit volume. The symbol for density is ρ. In mathematically, density is defined as mass divided by volume: {displaystyle rho ={frac {m}{V}}} where ρ is the density, m is the mass, and V is the volume. The SI unit of density is kilogram per cubic metre.

YOUNGS MODULUS:

The mechanical property of a material to withstand the compression or the elongation with respect to its length. The SI unit of Youngs Modulus is Pascal.

VELOCITY:

Velocity is quickness of motion, speed or action. Generally velocity refers to the measurement of the rate and direction of change in position of an object. The SI unit of velovity is m/s.

GRAVITY:

The universal force of attraction acting between all matter on earth all bodies have a weight or downward force of gravity, proportional to their mass, which earth's mass exerts on them. Gravity is measured by the acceleration that it gives to freely falling objects. The SI unit of gravity is m/s^-2.The standard acceleration of gravity denotes 9.8 m/s^-2

Conversions: (SI units to gm/mm/ms unit system)

`Mass 1kg = 1000gm Conversion factor - 10^3`

`Length 1m = 1000mm Conversion factor - 10^3`

`Time 1s = 1000ms Conversion factor - 10^3`

`Force 1N = 1kg*1m/s^2 Conversion factor - 1`

`=(1000g*1000mm)/(1000ms^2)``=10^6*10^-6(g*mm)/ms^2`

`=1(g*mm)/ms^2`

`Stress 1Pa = 1N/m^2 = {1kg*(1m/s^2)}/m^2 Conversion factor - 10^-6`

`=1kg/(m*s2)`

`=1000g/{1000mm*(1000ms)^2}`

`=10^-6g/(mm*ms^2)`

`Energy 1J = 1Nm = (1kg*1m/s^2)*m Conversion factor - 10^3`

`=1(kg*m^2/s^2)`

`={1000g*(1000mm)^2}/(1000ms)^2`

`=(10^9g*mm^2)/(10^6ms^2)`

`=10^3(g*mm^2/ms^2)`

`Density 1kg/m^3 = 1000g/(1000mm)^3 Conversion factor - 10^-6`

`=10^-6 g/mm^3`

`Youngs Modulus 210 GPa = 210e+9 kg/(m*s^2) Conversion factor - 10^3`

`=210e+9*10^-6 g/(mm*ms^2)`

`=210e+3 g/(mm*ms^2)`

`=210*10^3 g/(mm*ms^2)`

`Velocity 56.33 Kmph = 56.33*{10^6mm/(3600*1000ms)} Conversion factor - 10^-3`

`=15.647 mm/ms`

`Gravity 9.8m/s^2 = 9.8*1000mm/(1000ms)^2 Conversion factor - 10^-3`

`=9.8*10^-3 mm/ms^2`

RESULT:

Thus the give measurements are converted into respective unit systems & used in LS-DYNA calculations.