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!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

** 2nd line and later **

For TYPE=ISOTROPIC

(2nd line) expansion, Temperature

For TYPE=ORTHOTROPIC

(2nd line) α11, α22, α33, Temperature

Parameter Name	Attribute	Description
expansion	R	Coefficient of linear thermal expansion
α11, α22, α33	R	Coefficient of linear thermal expansion
Tempearture	R	Temperature (required when DEPENDENCIES=1)