!EXPANSION_COEFF¶
Definition of the coefficient of linear thermal expansion
The coefficient of linear thermal expansion entered here is not the value of the coefficient of linear thermal expansion \(\alpha\) itself at each temperature, but the interval average from the reference temperature \(T_\mathrm{ref}\) to each temperature \(T\), as shown in the following equation.
\[\begin{equation} \hat{\alpha}_T = \frac{1}{T-T_\mathrm{ref}} \int_{T_\mathrm{ref}}^{T^\prime} \alpha(T^\prime) dT^\prime \end{equation}\]
In the figure, the slope of the blue dotted line is the coefficient of linear thermal expansion \(\alpha(T)\) at temperature \(T\), and the slope of the green solid line is the interval average \(\hat{\alpha}_T\) from the reference temperature \(T_\mathrm{ref}\) to temperature \(T\).
Parameters¶
TYPE = material type
ISOTROPIC (isotropic: Default) / ORTHOTROPIC (orthotropic)
DEPENDENCIES = 0 (Default value) / 1
** Second and subsequent lines **
For TYPE=ISOTROPIC¶
For TYPE=ORTHOTROPIC¶
| Variable | Type | Description |
|---|---|---|
| expansion | R | Coefficient of linear thermal expansion |
| α11, α22, α33 | R | Coefficient of linear thermal expansion |
| Temperature | R | Temperature (required when DEPENDENCIES=1) |