1. Reference problem#
1.1. Geometry#
A
B
Inner radius: |
\({R}_{1}=\mathrm{0,1}m\) |
External radius: |
\({R}_{2}=\mathrm{0,6}m\) |
Thickness: |
\(t=\mathrm{0,2}m\) |
Semi major axis: |
\(a=\mathrm{0,05}m\) |
Half minor axis: |
\(b=\mathrm{0,0125}m\) |
1.2. Material properties#
Young’s module |
\(E\mathrm{=}2{10}^{5}\mathit{MPa}\) |
Poisson’s Ratio |
\(\nu \mathrm{=}0.3\) |
Density |
\(\rho \mathrm{=}7800\mathit{kg}\mathrm{/}{m}^{3}\) |
1.3. Boundary conditions and loading#
The model will be limited to the part of the thick disk located in half-space \(Y\ge 0\), the plane of the vertical crack being a plane of symmetry.
In the absence of knots on the axis of revolution, a rigid mode will be blocked by a linear relationship between degrees of freedom.
Let’s say the points: |
\(A({R}_{1}\mathrm{,0},t)\) |
|
Blocking translation in \(X\): \(\mathit{UX}(A)+\mathit{UX}(B)\mathrm{=}0\)
Blocking the translation in \(Y\): \(\mathrm{UY}=0\) in plane \(\mathrm{XOZ}\), except for the lips of the crack.
Blocking translation in \(Z\): \(\mathrm{UZ}(A)=0\)
Blocking the rotation around \(\mathrm{OX}\): ensured by the condition at the symmetry limits in the \(\mathrm{XOZ}\) plane
Blocking rotation around \(\mathrm{OY}\): \(\mathrm{UZ}(B)=0\)
Blocking the rotation around \(\mathrm{OZ}\): ensured by the condition at the symmetry limits in the \(\mathrm{XOZ}\) plane
Loading: stationary angular speed \(\omega =500\mathrm{rad}/s\)