Solution de référence ===================== Méthode de calcul utilisée pour la solution de référence -------------------------------------------------------- Modélisation A ~~~~~~~~~~~~~~ Les équations régissant le comportement sont des équations différentielles non linéaires. Pour valider la réponse obtenue avec *Code_Aster* en statique non linéaire les valeurs obtenues sont comparées aux valeurs analytiques. .. _RefNumPara__3869_1409840568: Résultats de référence ---------------------- La comparaison est réalisée sur lesmoments ('MZ') obtenus en fonction des rotations 'DRZ' imposées pour les différents éléments et les chargements appliqués, avec un pas de temps de calcul de :math:`1.0s` . Les instants sont en :math:`s` et les moments en :math:`N.m` . Les courbes ci-dessous permettent de vérifier que les passages des seuils et changements de pente sont bien détectés et pris en compte même avec un pas de temps de calcul très grossier. .. image:: images/10000201000005F7000003E6629FC035A4B46810.png :width: 6.3374in :height: 4.1417in .. _RefImage_10000201000005F7000003E6629FC035A4B46810.png: **Figure** 2.2-a **: Courbe** **Moment-rotation,** **élément 1.** La réponse donnée par *Code_Aster* est testée pour les valeurs suivantes: **Tableau** 2.2-a **:** **rotationset** **moments,** **élément 1.** .. csv-table:: "**Instant**", "*rotation* :math:`{\theta}_{z}`", "*Moment* :math:`{M}_{z}`" "1.0000000000E+00", "1.0000000000E+03", "1.0000000000E-03" "3.0000000000E+00", "-1.0000000000E+03", "-1.0000000000E-03" "5.0000000000E+00", "1.4000156777E+03", "3.0000000000E-03" "7.0000000000E+00", "-1.6500032505E+03", "-3.0000000000E-03" "9.0000000000E+00", "1.8000256320E+03", "5.0000000000E-03" "1.1000000000E+01", "-1.8500108811E+03", "-5.0000000000E-03" "1.3000000000E+01", "2.2000192257E+03", "1.1000000000E-02" "1.5000000000E+01", "-2.4833453804E+03", "-1.1000000000E-02" "1.7000000000E+01", "2.3601391920E+03", "1.5000000000E-02" "1.9000000000E+01", "-2.6166696872E+03", "-1.5000000000E-02" "2.1000000000E+01", "2.5600393177E+03", "2.0000000000E-02" "2.3000000000E+01", "-2.7833327927E+03", "-2.0000000000E-02" .. image:: images/10000201000005F7000003E61295576838939B58.png :width: 6.3374in :height: 4.1417in .. _RefImage_10000201000005F7000003E61295576838939B58.png: **Figure** 2.2-b **: Courbe** **Moment-rotation,** **élément 2.** La réponse donnée par *Code_Aster* est testée pour les valeurs suivantes: **Tableau** 2.2-b **:** **rotationset** **moments,** **élément 2.** .. csv-table:: "**Instant**", "*rotation* :math:`{\theta}_{z}`", "*Moment* :math:`{M}_{z}`" "1.0000000000E+00", "-1.0000000000E+03", "-1.0000000000E-03" "3.0000000000E+00", "1.0000000000E+03", "1.0000000000E-03" "5.0000000000E+00", "-1.6500000701E+03", "-3.0000000000E-03" "7.0000000000E+00", "1.4000143913E+03", "3.0000000000E-03" "9.0000000000E+00", "-1.8500245881E+03", "-5.0000000000E-03" "1.1000000000E+01", "1.8000013063E+03", "5.0000000000E-03" "1.3000000000E+01", "-2.4500169230E+03", "-1.1000000000E-02" "1.5000000000E+01", "2.2000156060E+03", "1.1000000000E-02" "1.7000000000E+01", "-2.6166668190E+03", "-1.5000000000E-02" "1.9000000000E+01", "2.3601185361E+03", "1.5000000000E-02" "2.1000000000E+01", "-2.7833347518E+03", "-2.0000000000E-02" "2.3000000000E+01", "2.5600383030E+03", "2.0000000000E-02" .. image:: images/10000201000005F7000003E6E477314F4FEE71E9.png :width: 6.3374in :height: 4.1417in .. _RefImage_10000201000005F7000003E6E477314F4FEE71E9.png: **Figure** 2.2-c **: Courbe** **Moment-rotation,** **éléments5 et 6.** **Tableau** 2.2-c **:** **rotationset** **moments,** **éléments5 et 6.** .. csv-table:: "**Instant**", "*rotation* :math:`{\theta}_{z}`", "*Moment* :math:`{M}_{z}`" "3.0000000000E+00", "1.8000004556E+03", "5.0000000000E-03" "6.0000000000E+00", "2.1600162134E+03", "1.0000000000E-02" "9.0000000000E+00", "2.3600225066E+03", "1.5000000000E-02" "1.2000000000E+01", "2.5599993245E+03", "2.0000000000E-02" "1.5000000000E+01", "1.1054534813E+03", "1.5000000000E-02" "1.8000000000E+01", "-1.2000046711E+03", "1.0000000000E-02" "2.1000000000E+01", "-1.9499993974E+03", "5.0000000000E-03" **Tableau** 2.2-d **:** **rotationset** **moments,** **élément 3.** .. csv-table:: "**Instant**", "*rotation* :math:`{\theta}_{z}`", "*Moment* :math:`{M}_{z}`" "1.0000000000E+00", "1.1904121201E+03", "1.1545287124E-03" "3.0000000000E+00", "-1.3331111483E+03", "-1.1545081204E-03" "5.0000000000E+00", "1.7237265601E+03", "3.4638528074E-03" "7.0000000000E+00", "-1.9588403006E+03", "-3.4638188809E-03" "9.0000000000E+00", "2.2570514348E+03", "5.7731769015E-03" "1.1000000000E+01", "-2.2255575302E+03", "-5.7731814447E-03" "1.3000000000E+01", "2.6190094112E+03", "1.2701327870E-02" "1.5000000000E+01", "-2.9330146633E+03", "-1.2701282573E-02" "1.7000000000E+01", "2.8324211293E+03", "1.7320099228E-02" "1.9000000000E+01", "-3.1107779579E+03", "-1.7320059070E-02" "2.1000000000E+01", "3.0989885500E+03", "2.3093563448E-02" "2.3000000000E+01", "-3.3330038571E+03", "-2.3093529688E-02" **Tableau** 2.2-e **:** **rotationset** **moments,** **élément 4.** .. csv-table:: "**Instant**", "*rotation* :math:`{\theta}_{z}`", "*Moment* :math:`{M}_{z}`" "1.0000000000E+00", "-1.3331111481E+03", "-1.1545081204E-03" "3.0000000000E+00", "1.1904121201E+03", "1.1545287124E-03" "5.0000000000E+00", "-1.9588485809E+03", "-3.4638188656E-03" "7.0000000000E+00", "1.7237108264E+03", "3.4638528189E-03" "9.0000000000E+00", "-2.2255289211E+03", "-5.7731814457E-03" "1.1000000000E+01", "2.2570794615E+03", "5.7731768999E-03" "1.3000000000E+01", "-2.9330774561E+03", "-1.2701282533E-02" "1.5000000000E+01", "2.6190179987E+03", "1.2701327871E-02" "1.7000000000E+01", "-3.1108083764E+03", "-1.7320059051E-02" "1.9000000000E+01", "2.8325478530E+03", "1.7320099228E-02" "2.1000000000E+01", "-3.3330092804E+03", "-2.3093529684E-02" "2.3000000000E+01", "3.0989396258E+03", "2.3093563476E-02" **Tableau** 2.2-f **:** **rotationset** **moments,** **élément 7.** .. csv-table:: "**Instant**", "*rotation* :math:`{\theta}_{z}`", "*Moment* :math:`{M}_{z}`" "3.0000000000E+00", "2.2570241105E+03", "5.7731769185E-03" "6.0000000000E+00", "2.5656146751E+03", "1.1546635072E-02" "9.0000000000E+00", "2.8326866571E+03", "1.7320099213E-02" "1.2000000000E+01", "3.0989736939E+03", "2.3093563449E-02" "1.5000000000E+01", "1.1994330950E+03", "1.7320334952E-02" "1.8000000000E+01", "-1.8045529425E+03", "1.1547265855E-02" "2.1000000000E+01", "-2.2218840472E+03", "5.7738233936E-03" **Tableau** 2.2-g **:** **rotationset** **moments,** **élément 8.** .. csv-table:: "**Instant**", "*rotation* :math:`{\theta}_{z}`", "*Moment* :math:`{M}_{z}`" "3.0000000000E+00", "4.6662898355E+06", "3.0801270189E-03" "6.0000000000E+00", "9.3318646247E+06", "6.1602540378E-03" "9.0000000000E+00", "1.3997034885E+07", "9.2403810568E-03" "1.2000000000E+01", "1.8662205044E+07", "1.2320508076E-02" "1.5000000000E+01", "1.3996314269E+07", "9.2403810568E-03" "1.8000000000E+01", "9.3304234944E+06", "6.1602540378E-03" "2.1000000000E+01", "4.6637232079E+06", "3.0801270189E-03" Incertitude sur la solution --------------------------- Modélisation A ~~~~~~~~~~~~~~ La solution de référence est obtenue par intégration numérique d’un système différentiel non linéaire.