Consider a solid disc of radius $R$ and height $h$ which we glue onto an infinite plane surface. If we now change the temperatur and the assume that
- the (linear) thermal expansion coefficient of the substrate vanishes, $\alpha_{substrate} = 0 \mu m /(K m)$,
- the (linear) thermal expansion coefficient of the disc is given by $\alpha>0$, and
- that the glue hold the disc and the substrate perfectly in place,
does anybody know a formula to describe the (free) surface of the disc? I'm not looking for finite element simulations, but a descriptive formula, which gives me some intuition about the shape. I expect, that the shape depends on all kind of properties, like e.g. Young's module $E$, and the height $h$. However, this problem seems to be fundamental for all kind of engineering work.