Thermal bending of a free thick plate

[Yang]

Hello elmer develop group,
I'm now using Elmer to simulate the thermal stress in a free thick plate.
In my simulation, temperature only varies along the thickness direction. According to the elasticity theory, the normal stress in the top and bottom surface should be zero. But in my simulation result, the norm stress in top and bottom surface was very large. It seems that there is something wrong with my simulation. Could anybody help me correct this? Many thanks.

Following is the boundary condition part in my case.sif file. I also attached my .grd and .sif files.
--------------------------------------------------
Boundary Condition 1
Target Boundaries(1) = 5
Name = "bottom"
Temperature = 100
Normal Force =0
End

Boundary Condition 2
Target Boundaries(1) = 6
Name = "top"
Temperature = 500
Normal Force =0
End
------------------------------------------------------------