1. Reference problem#

1.1. Geometry#

The structure is composed of a slender oriented beam carried in space by the direction vector axis \((\mathrm{1,}\mathrm{1,}1)\).

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Regarding the section of the beam, two cases are considered:

  • Constant square section, with area \(4.0{10}^{-4}{m}^{2}\) (A, B, C and D models),

  • Circular section with homothetic variation, with initial radius \(2.0{10}^{-2}m\) and final radius \(4.0{10}^{-2}m\) (modeling E).

In all of the above cases, the length of the beam is \(0.5m\).

1.2. Material properties#

\(E=2.{10}^{11}\mathrm{Pa}\)

\(\nu =0\)

\(\rho =7800\mathrm{kg}/{m}^{3}\)

1.3. Boundary conditions and loads#

Embedded beam free to rotate around an axis perpendicular to its largest dimension and passing through the center of the embedded face.

Rotation vector coordinates: \((\mathrm{1,}\mathrm{0,}–1)\).

Rotation speed: \(\omega =3000\mathrm{rd}/s\).

There is nothing physical about the important value of the speed of rotation.