1. Reference problem#
1.1. Geometry#
Lengths are expressed in meters.
The cylindrical panel is embedded along its 4 sides and subjected to surface force.
given in the global frame of reference for modeling A:
\(\mathrm{f}\mathrm{=}\mathrm{-}{f}_{z}{e}_{z};{f}_{z}>0\)
given in the local coordinate system for modeling B:
\(\mathrm{f}\mathrm{=}\mathrm{-}{f}_{z}n;{f}_{z}>0\)
which leads to membrane compression of the panel, accompanied by localized flexions. In the case of B modeling, \(n\) is normal to the updated geometry of the panel.
Because of the geometric and physical symmetry of the problem, only quarter \({P}_{1}{P}_{2}{P}_{3}{P}_{4}\) of the panel is modeled, taking into account symmetry conditions.
1.2. Material properties#
Elastic behavior:
\(E\mathrm{=}450000\mathit{MPa};\nu \mathrm{=}0.3\)
1.3. Boundary conditions and loads#
Boundary conditions |
\(\mathrm{P2P3}\): \(\mathrm{DX}=0.\) |
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\(\mathrm{P3P4}\): \(\mathrm{DX}=0.\) |
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Symmetry: |
\(\mathrm{P1P2}\): |
\(\mathrm{DY}=0.\) |
\(\mathrm{DRX}=0.\) |
\(\mathrm{DRZ}=0.\) |
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\(\mathrm{P4P1}\): \(\mathrm{DX}=0.\) |
\(\mathrm{DRY}=0.\) |
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We look for the successive states of equilibrium under the load consisting of the surface force given in the global coordinate system:
\({f}_{z}(t)\mathrm{=}t\)
\(t\) being the nickname.
We are interested in the only vertical component of displacement in \({P}_{1}\).