1. Reference problem#

1.1. Geometry#

3-point flexure

_images/Shape1.gif

Characteristics of plates \((m)\):

Length: \(L=10\)

Width: \(l=1\)

Thickness 1: \({e}_{1}=0.1\)

Thickness 2: \({e}_{2}=0.08\)

Eccentricity: \(e=0.01\)

Coordinates of points \((m)\):

\(A:(\mathrm{0,0})\) \(E:(\mathrm{5,1})\)

\(B:(\mathrm{5,0})\) \(F:(\mathrm{0,1})\)

\(C:(\mathrm{10,0})\) \(G:(2.5\mathrm{,0})\)

\(D:(\mathrm{10,1})\) \(H:(2.5\mathrm{,1})\)

1.2. Material properties#

Elastic

  • \(E=2.1\times {10}^{11}\mathrm{Pa}\) Young’s module

  • \(\nu =0.3\) Poisson’s ratio

1.3. Boundary conditions and loads#

Imposed displacement \((m)\):

  • segment \(\mathrm{AF},\mathrm{CD}\): \(\mathrm{DZ}=0\)

  • segment \(\mathrm{FA}\): \(\mathrm{DX}=0\)

  • point \(A\): \(\mathrm{DX}=\mathrm{DY}=\mathrm{DRZ}=0\)

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  • Pressure on \(\mathrm{BE}\): \(p=2.\times {10}^{5}N/m\) \(P=\mathrm{pl}\)