2. Benchmark solution#

2.1. Calculation method used for the reference solution#

The value of the displacement field \(v\), at the free end of the plate (edge \(\mathit{BC}\)) is given by:

\({v}_{L}\mathrm{=}\frac{{\mathit{PL}}^{3}}{{\mathrm{3EI}}_{y}}\) (neglected shear)

Hence \({v}_{L}\mathrm{=}0.129m\)

The flexural stress field \({\sigma }_{\mathit{xx}}\) is given by:

\({\sigma }_{\mathit{xx}}\mathrm{=}\frac{\mathit{Ph}}{{\mathrm{2l}}_{y}}(L\mathrm{-}x)\) on the \(\mathit{AB}\) ridge

Be \({\sigma }_{\mathit{xx}}\mathrm{=}2.04\mathrm{\times }{10}^{8}(L\mathrm{-}x)(\mathit{Pa})\)

2.2. Benchmark results#

  • Move \({v}_{L}\) of nodes \(B\) and \(C\)

  • \({\sigma }_{\mathit{xx}}\) constraints at nodes \(A\) and \(B\) and \(E\)

2.3. Uncertainty about the solution#

Analytical solution.

2.4. Bibliographical references#

    1. TIMOSHENKO, Material Strength, Part 1. Librairie Polytechnique Ch.Béranger, Paris, 1947. p. 169 to 168