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How to simulation thermal expansion with a T dependent CTE

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I would like to simulate the thermal expansion of an combined object from cryo temperature to room temperature.

My current conditions are:
COMSOL version 3.5a,
simulation model is smsld,
the CTE (alpha) is defined as a function of T (Temp_smsld),
reference temperature is defined as Tinit (1K),
strain temperature is defined as Tfinal (which is controlled by the simulation from 1K-300K).

Simulations I tried are parametric and time dependent.
The simulation results I obtained were the program used the alpha at Tfinal to calculate the expansion of object from Tinit to Tfinal, e.g. alpha(Tfinal)*(Tfinal-Tinit), which is not correct.
The expected calculation should be the Integration from Tinit to Tfinal of alpha(T).

Do you have any suggestion on doing such a simulation?

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