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Commit 4d762393 authored by Dmitri Naumov's avatar Dmitri Naumov
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[web] TM; Add citation; fix formula for rendering.

use pandoc, not md, because of formula rendering.
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## Problem description
We solve a thermo-mechanical homogeneous model in cube domain. The dimensions of this cube model are 1\,m in all directions. The boundary conditions and temperature loadings, as well as the material can refer Chapter 14 in Kolditz et al. for detailed problem description.
We solve a thermo-mechanical homogeneous model in cube domain. The dimensions of
this cube model are 1 m in all directions. The boundary conditions and
temperature loadings, as well as the material can refer Chapter 14 in Kolditz et
al. \cite Kolditz2012 for detailed problem description.
## Results and evaluation
Result showing temperature and stresses development with time in the centre node of the model:
Result showing temperature and stresses development with time in the centre node
of the model:
{{< img src="../temperature.png" >}}
{{< img src="../stress.png" >}}
The analytical solution of stresses after heating is:
$$
\begin{equation}
\sigma_{xx} = \sigma_{yy} = \sigma_{zz} = - \frac{\alpha \Delta T E}{1 - 2 \nu} = - 3.260869\, \mathrm{MPa}
\end{equation}
$$
$$\begin{equation}
\sigma_{xx} = \sigma_{yy} = \sigma_{zz} = - \frac{\alpha \Delta T E}{1 - 2 \nu}
= - 3.260869\, \textrm{MPa}
\end{equation}$$
The relative error between the numerical simulation and the analytical solution is $9.2 \cdot 10^{-13}$.
The relative error between the numerical simulation and the analytical solution
is 9.2<span class="math inline">⋅10<sup>-13</sup></span>.
## References
......
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