1. Reference problem#
1.1. Geometry#
The configuration studied consists of two coaxial cylindrical shells \(4m\) in height.
The inner shell has an average radius \({R}_{1}\) of \(\mathrm{0,98}m\) and a thickness \({e}_{1}\) of \(4\mathrm{cm}\).
The outer shell has an average radius \({R}_{2}\) of \(\mathrm{1,105}m\) and a thickness \({e}_{2}\) of \(1\mathrm{cm}\).
Note:
The thickness and the average radius of the annular space between the two shells are given |
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by |
\(H\mathrm{=}{R}_{\text{ext}}\mathrm{-}{R}_{\text{int}}\mathrm{=}\mathrm{0,1}m\) |
\(R\mathrm{=}\frac{{R}_{\text{int}}+{R}_{\text{ext}}}{2}\mathrm{=}\mathrm{1,05}m\) |
with |
\({R}_{\text{int}}\mathrm{=}R1+\frac{{e}_{1}}{2}\mathrm{=}1m\) |
\({R}_{\text{ext}}\mathrm{=}{R}_{2}–\frac{{e}_{2}}{2}\mathrm{=}\mathrm{1,1}m\) |
1.2. Material properties#
The material that makes up the two shells is steel. Its physical characteristics are
\(\rho \mathrm{=}7800\mathit{kg}\mathrm{/}{m}^{3}\) |
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1.3. Boundary conditions and loads#
The outer shell is supposed to be rigid: all the knots are embedded.
Regarding the internal shell, the support conditions are as follows: embedded end in the lower part (\(z\mathrm{=}0\)) and free in the upper part (\(z\mathrm{=}\mathrm{4m}\)).