1. Reference problem#

1.1. Geometry#

_images/10000000000003C0000002D09AB0F97673C6F9DF.png

Coordinates of the points (\(m\)):

\(A:(0.,6.\cdot {10}^{-3})\)

\(B:(48.\cdot {10}^{-\mathrm{3,}}6.\cdot {10}^{-3})\)

\(C:(48.\cdot {10}^{-\mathrm{3,}}-6.\cdot {10}^{-3})\)

\(D:(0.,-6.\cdot {10}^{-3})\)

Plate geometry (\(m\)):

Thickness: \(h=\mathrm{0,001}\)

Width: \(L=0.048\)

Height: \(H=0.012\)

Mesh group: \(\text{BORD\_CH}\) right surface (\(\mathrm{BC}\))

Mesh group: \(\mathrm{ENCAST}\) left surface (\(\mathrm{AD}\))

Mesh group: \(\mathrm{SURF}\) inner surface

1.2. Material properties#

  • \(E=3.\cdot {10}^{10}\mathrm{Pa}\)

  • \(\nu =0.25\)

1.3. Boundary conditions and loads#

  • Imposed travel:

    • \(\mathrm{ENCAST}\): \(\mathrm{DX}=\mathrm{DY}=0.\)

  • Charging:

    • Parabolic distribution over height, constant over thickness.

\(Y(m)\)

-0.006

-0.003

-0.003

0

0.003

0.006

2D Shear Stress (\(\mathrm{Pa.m}\))

0

3.75E6

3.75E6

3.75E6

0

The integration of this constraint on the height \(H\) leads to a constraint resulting from \(80.{10}^{3}\mathrm{Pa.m}\) which is noted \(P\) in the following.