II.1.13 Units

All the quantities introduced in this Chapter have been given without dimensions. Since version 3.0.1, units can be attributed to all the CLA quantities defined in FeResPost, except of course the dimensionless quantities. This allows the user to express all the CLA quantities in a units system compatible, for example, with the unit system used for finite element modeling.

An engineer should be able to figure out the units of the different quantities introduced in this Chapter from the definitions given for the quantities or from the expressions used for their calculations. However, we think it might be useful to remind the units of the different quantities to avoid ambiguities.

In the rest of the section, one assumes a consistent set of units compatible with MKS system is used. This is what we recommend for FeResPost, as well as finite element models. The default “base” units are:

• Lengths are expressed in meters [m].
• Masses are expressed in kilograms [kg].
• Time is expressed in seconds [s].
• Force is expressed in Newtons [N].
• Energy is expressed in joules [J].
• Temperatures are expressed in Celsius degrees [$\text{o}$C].
• Moisture contents are expressed in percentage of weight [%w]. (Weight of water divided by the weight of dry material in %.)

One notes that units have been defined for force and energy, despite the fact that they can be derived from mass, length and time units. Practically, the definition of additional base units for the force and energy are of interest for mechanical engineers.

All the other units of FeResPost are obtained by combining these base units. The most important ones are summarized in Tables II.1.4, II.1.5 and II.1.6.

If one of the base units above is modified, the user is responsible for modifying the derived units coherently. For example, we expressed the moisture content in [%w]. This influences the units of moisture content $H$ as well as the units of coefficients of moisture expansion $\beta$.

Other units systems can be used with the CLA classes. Each CLA object has an attribute corresponding to the units system in which all its characteristics are defined.

• Length: “micron”, “mm”, “cm”, “m”, “mil” (milli-inch), “in”, “ft”.
• Mass: “g”, “kg”, “t” (tons), “dat” (deca-tons), “lbm”, “kbm” (kilo-pounds).
• Time: “s”, “min”, “hour”.
• Force: “N”, “daN”, “kN”, “kgf” (kilogram-force), “lbf” (pound-force), “kips” (kilo-pound-force).
• Energy: “J”, “cal”, “BTU”, “ft.lbf”, “in.lbf”, “kgf.m”.
• Temperature: “$\text{o}$C”, “$\text{o}$F”, “K”.
• Moisture content: “%w”.

The units of CLA object can be obtained with “getUnits” method that returns a Hash containing pairs of Strings. The first String describes the kind of dimension: “L” for length, “M” for mass, “t” for time, “T” for temperature, “E” for energy, “W” for moisture and “F” for force. The second String corresponds to one of the unit listed above for the selected quantity.

The units of a CLA object can also be modified by calling “setUnits” or “changeUnits” methods:

• The “setUnits” method changes the units attributed to an object without modifying the values of the different quantities defining the object. (No unit conversion is done.)
• The “changeUnits” method performs the units conversion.

Both “setUnits” and “changeUnits” methods have an Hash argument corresponding to the object returned by “getUnits” method.

When laminate calculations are done, the properties of material used in laminate layup definition are converted in laminate system of units if necessary. The same is true for loading units for the calculation of laminate load response. The ply results (shell forces, shell moments, stresses, temperatures...) are expressed in laminate system of units. When a failure criterion is calculated, calculations are done in laminate system of units. This means that ply allowables are first convered to the laminate system of units. Of course, the use of a consistent system of units for all the composite calculations is recommended, as it reduces the risk of errors and the calculation time.