1. Reference problem#

1.1. Geometry#

_images/Shape1.gif

Dimension in \((m)\)

  • Average radius of curvature \(R=\mathrm{0.1m}\)

  • Thickness: \(h=0.005m\)

  • Width: \(b=0.010m\) (perpendicular plane)

  • Area: \(A=5\times {10}^{-5}{m}^{2}\)

  • Moment of inertia: \({I}_{z}=1.042\times {10}^{-10}{m}^{4}\) \({I}_{y}=4.167\times {10}^{-10}{m}^{4}\)

  • Torsional moment: \(J=2.859\times {10}^{-10}{m}^{4}\)

1.2. Material properties#

      • Elastic

        • \(E=7.2\times {10}^{10}\mathrm{Pa}\) Young’s module

        • \(\nu =0.3\) Poisson’s ratio

        • \(\rho =2700\mathrm{kg}/{m}^{3}\) Density

1.3. Boundary conditions and loads#

  • Moves: all points in the ring are free

  • Charging: none