Example 18: Thermally induced stresses in plate.

A plate (of size $1$ by $1$) is initially stress free and in thermal equilibrium with its environment (all initial temperatures are $0$). Then the left edge of the plate is prescribed a temperature $1$ which will heat the plate. The plate starts convecting energy at its other edges; the coefficient for heat convection is $10^3$, the convection environmental temperature is $0$ and the conductivity of the plate is $50$. The first plot shows the stationary temperature distribution. A mesh with 16 by 16 linear finite elements is used for the numerical analysis.

Due to the temperatures, thermal stresses will be induced in the plate. The plate cannot deform at its left edge, but is otherwise free to deform. The Young's modulus is $206 \; 10^9$, the Poisson ratio is $0.3$, and a plane stress situation is assumed ($\sigma_{zz}$ is $0$). The thermal expansion coefficient is $8.4 \; 10^{-4}$. The second plot shows the size of the deviatoric stresses (the von Mises stress) which indicates if plasticity is to be expected.