expandable Laminate eXplorer - eLamX

h1. Theory

h2. Units

Input data, for example layer stiffness, strength or loads, are required to use eLamX². But as many other software eLamX² basically works independently of unit systems. The user must ensure that the data entered come from a common, consistent system of units, such as the SI or the imperial system of units. The following table shows some common consistent systems of units.

|                 |\5.    System of Units (see /UNITS-Kommando)                                     |

|_. Quantity      |_. SI      |_. CGS      |_. MPA         |_. BFT        |_. BIN                   |

| Mass            | [kg]      |  [g]       | [tonne]       | [slug]       | ([lbf][sec]²)/[in]      |

| Length          | [m]       | [cm]       | [mm]          | [ft]         | [in]                    |

| Time            | [s]       | [s]        | [s]           | [sec]        | [sec]                   |

| Temperatur      | [K]       | [K]        | [K]           | [°R]         | [°R]                    |

| Speed           | [m]/[s]   | [cm]/[s]   | [mm]/[s]      | [ft]/[sec]   | [in]/[sec]              |

| Acceleration    | [m]/[s]²  | [cm]/[s]²  | [mm]/[s]²     | [ft]/[sec]²  | [in]/[sec]²             |

| Force           | [N]       | [dyn]      | [N]           | [lbf]        | [lbf]                   |

| Moment          | [N] [m]   | [dyn] [cm] | [N] [mm]      | [ft] [lbf]   | [in] [lbf]              |

| Pressure        | [Pa]      | [Ba]       | [MPa]         | [lbf]/[ft]²  | [psi]                   |

| Density         | [kg]/[m]³ | [g]/[cm]³  | [tonne]/[mm]³ | [slug]/[ft]³ | ([lbf][sec]²/[in])/[in]³|

| Energy          | [J]       | [erg]      | [mJ]          | [ft]/[lbf]   | [in]/[lbf]              |

The units given in the tooltips correspond to the MPA system. Results of calculations are given in the derived units of the system of units used.

h2. Coordinate systems

The direction-dependent properties of fiber composites claim the definition of coordinate systems. Two coordinate systems are used within eLamX². The properties of the individual unidirectional layer are represented by the indices ∥ and ⟂ and form the local coordinate system. The symbols reflect the properties along and perpenticular to the fibre direction of the individual layer. All sizes that relate to the overall laminate are given the direction indices _x_ and _y_. _x_ stands for the 0° and _y_ the 90° direction of the global coordinate system of the laminate.

h2. Pointer contraction numbers

In which order (German or Anglo-Saxon) is the Poisson's ratio indicated?

The first index of the transverse contraction number indicates the direction of the load, the second index shows in which direction the transverse contraction acts. Thus $ \ nu _ {\ parallel \ perp} $ is the larger of the two Poisson's contraction numbers and the following applies:

$$ E _ {\ parallel} \ nu _ {\ perp \ parallel} = E _ {\ perp} \ nu _ {\ parallel \ perp} $$