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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.

\begin{figure}\centerline{\epsfig{file=ps/ex18tem.ps,width=5cm}}\end{figure}

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.

\begin{figure}\centerline{\epsfig{file=ps/ex18seq.ps,width=5cm}}\end{figure}


next up previous contents
Next: Example 19: Nonlocal plasticity Up: Examples Previous: Example 17: Hertz contact   Contents
tochnog 2001-09-02