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II.1.13 Units

All the quantities introduced in this Chapter have been given without dimensions. Since version 3.0.1, units can be assigned 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 unit system compatible, for example, with the one 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, a consistent set of units compatible with the MKS system is assumed. This is what we recommend for FeResPost, as well as for finite element models. The default “base” units are:

Note 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 force and energy is of interest to 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 β.


Table II.1.4: Units of the different quantities related to loading, stresses or load responses.
Quantities Symbols Units
Strains ϵ, γ or Γ [L/L] or [-]
Stresses σ or τ [F/L2]
Curvatures κ [1/L]
Forces {N} or {Q} [F/L]
Moments {M} [FL/L] or [F]
Temperatures T [T]
Moistures H [W] (always [%w])
Failure indices F I []
Reserve factors RF []


Table II.1.5: Units of the different quantities related to material properties.
Quantities Symbols Units
Materials stiffnesses or moduli Cijkl, [C], E or G [F/L2]
Materials compliance matrices cijkl, [c], [g] [L2/F]
Poisson coefficients νij [-]
Thermal conductivity λijT [E/(LT)]
Coefficients of thermal expansion α [L/(LT)] or [1/T]
Moisture conductivity λij H [1/(Lt)]
Coefficients of moisture expansion β [L/(LW)] or [1/W]
Density ρ [M/L3]
Specific heat capacity Cp [E/(MT)]
Coefficients of quadratic failure criteria F i [L2/F]
Coefficients of quadratic failure criteria F ij [L4/F2]


Table II.1.6: Units of the different quantities related to laminate properties.
Quantities Symbols Units
Thicknesses t [L]
Membrane stiffness matrix [A] [F/L]
Membrane-bending coupling stiffness matrix [B] [F]
Bending stiffness matrix [D] [FL]
Out-of-plane shear stiffness matrix [G] [F/L]
Membrane compliance matrix [a] [L/F]
Membrane-bending coupling compliance matrix[b] [1/F]
Bending compliance matrix [d] [1/(FL)]
Out-of-plane shear compliance matrix [g] [L/F]
In-plane thermal conductivity matrix [ΛT ] [E/(tT)]
Out-of-plane thermal resistance R33 T [L2Tt/E]
Areal heat capacity (ρCp h ) lam [E/L2/T]
In-plane moisture conductivity matrix [ΛH ] [1/t]
Out-of-plane moisture resistance R33 H [L2t]

Other unit 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.

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:

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

When laminate calculations are done, the properties of the material used in the laminate layup definition are converted to the laminate system of units if necessary. The same applies to loading units for the calculation of laminate load response. The ply results (shell forces, shell moments, stresses, temperatures...) are expressed in the laminate system of units. When a failure criterion is calculated, calculations are performed in the laminate system of units. This means that ply allowables are first converted 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.