Thermal Effects:
Thermal strains in principal material coordinates are proportional to the temperature change . These are given using coefficient of thermal expansion as
 |
(4.46) |
where  .
Transformation of the thermal strains  to the strains  in global coordinates gives
 |
(4.47) |
Let  . Thus, Equation (4.47) becomes
 |
(4.48) |
or
 |
(4.49) |
Thermo-Elastic Constitutive Equation:
The total strain due to mechanical and thermal loading in principal material directions is given as
 |
(4.50) |
We can write for the mechanical strains as
 |
(4.51) |
Thus, Equation (4.50) becomes
 |
(4.52) |
Re-arranging the above equation, we can write for the stresses as
 |
(4.53) |
The above equation can be written in global coordinate system as
|
