I study "Thermoelastic damping", and in calculation of strain energy, when ignore the thermal strain and consider the total stress(mechanical+thermal) , the governing equation is different from what is reported in the literature. When I consider the thermal strain, elastic strain, thermal stress and mechanical stress, the governing equation is similar to what has been reported. But I could not find a reference that shows that the thermal strain in the strain energy is effective
In any problem, If thermal strain occurs and body can be easily expanded, stresses do not exist. So strain energy density does not ocur. If termal strain is equal to zero due to temperature change, stress ocur. For example, in free bar subjected to temperature change, stress does not ocur. But two ends fixed bar has thermal stresses and no thermal strain.
In any problem, If thermal strain occurs and body can be easily expanded, stresses do not exist. So strain energy density does not ocur. If termal strain is equal to zero due to temperature change, stress ocur. For example, in free bar subjected to temperature change, stress does not ocur. But two ends fixed bar has thermal stresses and no thermal strain.
Dear Mr. Bostani,
your question is not really clear in the absense of the underlying equations. You asked for a reference. I suggest to read the book
Boley, B. A. and Weiner, J. H. (1997). Theory of thermal stresses. Dover Publications, Mineola,USA
which contains a large number of sub-problems in thermo-elasticity. May be it will help.
S.H.
Thanks to Professor Karakuzu and Professor Hartmann. I think you've pretty much answered my question.
To clarify my question, I send an attachment.
Dear Mr Bostani,
I think your problem is in equation (6) : the 1/2 comes from the integration of a linear function, so it only works in elasticity. The work is \int \sigma d\epsilon. The thermal strain being independent from the stress, the work associated to it is \sigma \alpha \theta, without 1/2.
NB
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