1. Reference problem#
1.1. Geometry#
It is a hollow cylinder, similar to the one treated in SSNA106.
\({R}_{0}\) |
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\({R}_{1}\) |
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1.2. Material properties#
1.2.1. Umat data#
For the Umat behavior present as an example in the Code_Aster sources, elasticity is expressed by:
\(\mathrm{C1}=\lambda =\frac{E\nu }{(1+\nu )(1-2\nu )}\)
\(\mathrm{C2}=\mu =\frac{E}{2(1+\nu )}\)
\(\mathrm{C3}=\mathrm{C4}=\mathrm{C5}=0\)
1.2.2. Aster data#
Young’s module: \(E=1\mathrm{MPa}\)
Poisson’s ratio: \(\nu =0.3\)
Expansion coefficient: \(\alpha =0.7\)
1.3. Boundary conditions and loads#
Boundary conditions:
The cylinder is locked at \(\mathrm{DY}\) on the \([\mathrm{AB}]\) and \([\mathrm{CD}]\) sides.
Charging:
The cylinder is subjected to a temperature field \(T(r,t)=t{r}^{2}\)