Modélisation A ============== Caractéristiques de la modélisation ----------------------------------- Le modèle est composé de 10 éléments poutre droite d’Euler. **Section S1:** section circulaire variable .. csv-table:: "à l’encastrement,", ":math:`\mathrm{R1}=0.1m` (section pleine)" "à l’extrémité libre,", ":math:`\mathit{R2}=0.05m` (section pleine)" **Section S2:** section rectangulaire variable .. csv-table:: "à l’encastrement,", ":math:`{H}_{\mathit{y1}}=0.05m`", ":math:`{H}_{\mathit{z1}}=0.10m`" "à l’extrémité libre,", ":math:`{H}_{\mathit{y2}}=0.05m`", ":math:`{H}_{\mathit{z2}}=0.05m`" **Section S3 :** section générale variable .. csv-table:: "à l’encastrement,", ":math:`{A}_{1}={10}^{2}{m}^{4}`", ":math:`{I}_{\mathit{y1}}=8.3333{10}^{6}{m}^{4}`" "à l’extrémité libre,", ":math:`{A}_{2}=2.5{10}^{3}{m}^{2}`", ":math:`{I}_{\mathit{y2}}=5.20833{10}^{7}{m}^{4}`" Caractéristiques du maillage ---------------------------- 3 sections :math:`\times` 10 éléments POU_D_E Grandeurs testées et résultats ------------------------------ .. csv-table:: "**Cas de charge**", "**Section**", "**Identification**", "**Référence**", "**Tolérance %**" "1", ":math:`\mathit{S1}`", ":math:`u(l)`", "3.1831E–08", "1.00E-05" "", "", ":math:`n(0)`", "1.0000E+02", "1.00E-05" "", "", ":math:`n(l)`", "1.0000E+02", "1.00E-05" "", "", ":math:`{\sigma}_{xx}(0)`", "3.1831E+03", "1.00E-05" "", "", ":math:`{\sigma}_{xx}(l)`", "1.2732E+04", "1.00E-05" "2", ":math:`\mathit{S1}`", ":math:`v(l)`", "4.2441E–06", "1.00E-05" "", "", ":math:`{\theta}_{z}(l)`", "8.4882E–06", "1.00E-05" "", "", ":math:`{v}_{y}(0)`", "1.0000E+02", "1.00E-05" "", "", ":math:`{v}_{y}(l)`", "1.0000E+02", "1.00E-05" "", "", ":math:`{\mathit{mf}}_{z}(0)`", "1.0000E+02", "1.00E-05" "", "", ":math:`{\mathit{mf}}_{z}(l)`", "0.0000E+00", "1.00E-05" "", "", ":math:`{\sigma}_{xx}(0)`", "1.2732E+05", "1.00E-05" "", "", ":math:`{\sigma}_{xx}(l)`", "0.0000E+00", "1.00E-05" "3", ":math:`\mathit{S1}`", ":math:`{\theta}_{x}(l)`", "3.8621E–05", "1.00E-05" "", "", ":math:`{m}_{x}(0)`", "1.0000E+02", "1.00E-05" "", "", ":math:`{m}_{x}(l)`", "1.0000E+02", "1.00E-05" "4", ":math:`\mathit{S1}`", ":math:`w(l)`", "–8.4882E–06", "1.00E-05" "", "", ":math:`{\theta}_{y}(l)`", "2.9708E–05", "1.00E-05" "", "", ":math:`{v}_{z}(0)`", "0.0000E+00", "1.00E-05" "", "", ":math:`{v}_{z}(l)`", "0.0000E+00", "1.00E-05" "", "", ":math:`{\mathit{mf}}_{y}(0)`", "1.0000E+02", "1.00E-05" "", "", ":math:`{\mathit{mf}}_{y}(l)`", "1.0000E+02", "1.00E-05" "", "", ":math:`{\sigma}_{xx}(0)`", "1.2732E+05", "1.00E-05" "", "", ":math:`{\sigma}_{xx}(l)`", "1.0185E+06", "1.00E-05" "5", ":math:`\mathit{S1}`", ":math:`u(l)`", "1.2296E–08", "1.00E-02" "", "", ":math:`n(0)`", "1.0000E+02", "1.00E-05" "", "", ":math:`n(l)`", "0.0000E+00", "1.00E-03 (absolu)" "", "", ":math:`{\sigma}_{xx}(0)`", "3.1831E+03", "1.00E-05" "", "", ":math:`{\sigma}_{xx}(l)`", "0.0000E+00", "1.00E-03 (absolu)" "6", ":math:`\mathit{S1}`", ":math:`v(l)`", "1.3486E–06", "1.00E-02" "", "", ":math:`{\theta}_{z}(l)`", "2.1220E–06", "1.00E-02 (absolu)" "", "", ":math:`{v}_{y}(0)`", "1.0000E+02", "1.00E-05" "", "", ":math:`{v}_{y}(l)`", "0.0000E+00", "1.00E-03 (absolu)" "", "", ":math:`{\mathit{mf}}_{z}(0)`", "5.0000E+01", "1.00E-02" "", "", ":math:`{\mathit{mf}}_{z}(l)`", "0.0000E+00", "1.00E-03 (absolu)" "", "", ":math:`{\sigma}_{xx}(0)`", "6.3662E+04", "1.00E-05" "", "", ":math:`{\sigma}_{xy}(0)`", "3.1831E+03", "1.00E-05" .. csv-table:: "**Cas de charge**", "**Section**", "**Identification**", "**Référence**", "**Ecart %**" "1", ":math:`\mathit{S2}`", ":math:`u(l)`", "1.3862E–07", "1.00E-05" "", "", ":math:`n(0)`", "1.0000E+02", "1.00E-05" "", "", ":math:`n(l)`", "1.0000E+02", "1.00E-05" "", "", ":math:`{\sigma}_{xx}(0)`", "2.0000E+04", "1.00E-05" "", "", ":math:`{\sigma}_{xx}(l)`", "4.0000E+04", "1.00E-05" "2", ":math:`\mathit{S2}`", ":math:`v(l)`", "1.8969E–04", "2.30E-02" "", "", ":math:`{\theta}_{z}(l)`", "3.0238E–04", "2.70E-02" "", "", ":math:`{v}_{y}(0)`", "1.0000E+02", "1.00E-05" "", "", ":math:`{v}_{y}(l)`", "1.0000E+02", "1.00E-05" "", "", ":math:`{\mathit{mf}}_{z}(0)`", "1.0000E+02", "1.00E-05" "", "", ":math:`{\mathit{mf}}_{z}(l)`", "0.0000E+00", "1.00E-03 (absolu)" "", "", ":math:`{\sigma}_{xx}(0)`", "2.4000E+06", "1.00E-05" "", "", ":math:`{\sigma}_{xx}(l)`", "0.0000E+00", "1.00E-03 (absolu)" "", "", ":math:`{\sigma}_{xy}(0)`", "2.0000E+04", "1.00E-05" "", "", ":math:`{\sigma}_{xy}(l)`", "4.0000E+04", "1.00E-05" "3", ":math:`\mathit{S2}`", ":math:`{\theta}_{x}(l)`", "8.3506E–04", "5.70E-02" "", "", ":math:`{m}_{x}(0)`", "1.0000E+02", "1.00E-05" "", "", ":math:`{m}_{x}(l)`", "1.0000E+02", "1.00E-05" "", "", ":math:`{\sigma}_{xy}(0)`", "1.5600E+06", "1.00E-05" "", "", ":math:`{\sigma}_{xy}(l)`", "4.0371E+06", "5.00E-02" "", "", ":math:`{\sigma}_{xz}(0)`", "1.5600E+06", "1.00E-05" "", "", ":math:`{\sigma}_{xz}(l)`", "4.0371E+06", "5.00E-02" "4", ":math:`\mathrm{S2}`", ":math:`w(l)`", "–1.2000E–04", "3.00E-03" "", "", ":math:`{\theta}_{y}(l)`", "3.600E–04", "4.00E-03" "", "", ":math:`{v}_{z}(0)`", "0.0000E+00", "1.00E-03 (absolu)" "", "", ":math:`{v}_{z}(l)`", "0.0000E+00", "1.00E-03 (absolu)" "", "", ":math:`{\mathit{mf}}_{y}(0)`", "1.0000E+02", "1.00E-05" "", "", ":math:`{\mathit{mf}}_{y}(l)`", "1.0000E+02", "1.00E-05" "", "", ":math:`{\sigma}_{xx}(0)`", "1.2000E+06", "1.00E-05" "", "", ":math:`{\sigma}_{xx}(l)`", "4.8000E+06", "1.00E-05" "5", ":math:`\mathit{S2}`", ":math:`u(l)`", "6.1370E–08", "1.00E-05" "", "", ":math:`n(0)`", "1.0000E+02", "1.00E-05" "", "", ":math:`n(l)`", "0.0000E+00", "1.00E-03 (absolu)" "", "", ":math:`{\sigma}_{xx}(0)`", "2.0000E+04", "1.00E-05" "", "", ":math:`{\sigma}_{xx}(l/2)`", "1.3333E+04", "1.00E-05" "", "", ":math:`{\sigma}_{xx}(l)`", "0.0000E+00", "1.00E-03 (absolu)" "6", ":math:`\mathrm{S2}`", ":math:`v(l)`", "6.8626E–05", "2.00E-02" "", "", ":math:`{\theta}_{z}(l)`", "9.4847E–05", "2.40E-02" "", "", ":math:`{v}_{y}(0)`", "1.0000E+02", "1.00E-05" "", "", ":math:`{v}_{y}(l)`", "0.0000E+00", "1.00E-03 (absolu)" "", "", ":math:`{\mathrm{mf}}_{z}(0)`", "5.0000E+01", "1.00E-02" "", "", ":math:`{\mathrm{mf}}_{z}(l)`", "0.0000E+00", "1.00E-03 (absolu)" "", "", ":math:`{\sigma}_{xx}(0)`", "1.2000E+06", "1.00E-05" "", "", ":math:`{\sigma}_{xx}(l)`", "0.0000E+00", "1.00E-03 (absolu)" "7", ":math:`\mathrm{S3}`", ":math:`w(l)`", "–3.8259E–05", "1.00E-02" "", "", ":math:`{\theta}_{y}(l)`", "5.7388E–05", "1.00E-02" "", "", ":math:`{v}_{z}(0)`", "–4.4633E+02", "1.00E-03" "", "", ":math:`{\mathrm{mf}}_{y}(0)`", "1.7535E+02", "1.00E-02" Remarques --------- La modélisation étant faite en poutres d’Euler, les coefficients de cisaillement sont :math:`\mathit{ky}=\mathit{kz}=1` .