!EXPANSION_COEFF

Definition of coefficient of linear expansion

The coefficient to be input here is not the coefficient of linear expansion \(\alpha\) at each temperature, but its averaged value between the reference temperature \(T_\mathrm{ref}\) and each temperature \(T\) as follows:

\[\begin{equation} \hat{\alpha}_T = \frac{1}{T-T_\mathrm{ref}} \int_{T_\mathrm{ref}}^{T^\prime} \alpha(T^\prime) dT^\prime \end{equation}\]

In the figure, the slope of the blue dotted line is the coefficient of linear expansion \(\alpha(T)\) at temperature \(T\), and the slope of the green solid line is the averaged value \(\hat{\alpha}_T\) from the reference temperature \(T_\mathrm{ref}\) to temperature \(T\).

Parameter

TYPE = ISOTROPIC(Default) / ORTHOTROPIC
DEPENDENCIES = 0(Default) / 1

** 2nd Line or later **

In case of TYPE=ISOTROPIC

(2nd line) expansion, Temperature

In case of TYPE=ORTHOTROPIC

(2nd line) $\alpha$11, $\alpha$22, $\alpha$33, Temperature

Parameter Name	Attributions	Contents
expansion	R	Coefficient of thermo expansion
\(\alpha\)11, \(\alpha\)22, \(\alpha\)33	R	Coefficient of thermo expansion
Temperature	R	Temperature (required when DEPENDENCIES = 1)