2. Reference solution

2.1. Calculation method used for the reference solution

The field of movement along the \(y\) axis at the end of the plate (segment \(\mathit{BC}\)) is given in the hypothesis of beam theory by:

\({u}_{y}^{\mathit{BC}}=\frac{{\mathit{PL}}^{3}}{{\mathrm{3EI}}_{z}}(1+0.98\frac{{l}^{2}}{{L}^{2}})\) (solution taking into account the shear force in a Timoshenko beam)

Hence \({u}_{y}^{\mathit{BC}}=0.00121m\)

The normal stress field \({\sigma }_{\mathit{xx}}\) due to bending is given by:

\({\sigma }_{\mathit{xx}}=\frac{\mathit{Pl}}{{\mathrm{2I}}_{z}}(L-x)\) on the \(\mathit{AB}\) ridge

Be \({\sigma }_{\mathit{xx}}=37.8\times {10}^{6}(L-x)\)

2.2. Benchmark results

• \({u}_{y}\) movements of nodes \(B\) and \(C\)

• \({\sigma }_{\mathit{xx}}\) constraints of nodes \(A\), \(B\), \(E\)

2.3. Uncertainty about the solution

• Analytical solution.

2.4. Bibliographical references

S. Tymoshenko.*Material resistance, part 1. Librairie Polytechnique Ch. Béranger, Paris, 1947, pp 163-168.