## Analytical solution for thermal stresses in a rectangular plate

Hello everybody,

I am solving a 2D problem of thermal stresses in a rectangular plate in which temperature is changing only y direction. Plate has fixed displacement conditions. Could anyone help me to find out analytical solution of thermal stresses for my problem? Does anyone suggest me where I can find analytical solution?

Best regards,
Sargam

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 What are "fixed displacement conditions"? Solutions could be something like a parabola or a cosine in the transverse direction, multiplied by a tanh in the expansion direction. Try a few ones.
 Hi, Thanks for the reply. I have mistakenly mention fixed displacement boundary condition but actually all surfaces of rectangle are traction free (free surfaces). Temperature change is parabolic on y-axis. Could you please let me know where I can get analytical solution for this problem?

## Analytical solution for thermal stresses in a rectangular plate

If temperature is uniform along the X axis and all edges are free to move, stress is zero everywhere, whatever the profile is along the Y axis.

In the more general case, try a product of cos(x) and cos(y) with different harmonic periods - but a particular polynomial solution can look good.

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