Example 5.12: The laminate in Example 5.1 is subjected to a thermal gradient of . Calculate the thermal residual stress at the top of the laminate.

Solution: The  matrix for this material is calculated as

Now,  matrix for  and  is calculated as

The coefficients of thermal expansion in global directions for  and  layers are

and

And the A, B and D matrices are calculated as

The thermal forces are

Now we calculate the thermal moments as

We can write for the thermal forces and moments as

which becomes,

Solving for the mid-plane strains and curvatures

The total strains at the top of the laminate, that is, at  in  lamina is

We calculate the mechanical strains by subtracting the thermal strains from total strains.

Now the thermal strain in top lamina is

Thus, the mechanical strains become

And the stresses at the top of the laminate are given as