Solutions de référence ====================== Méthode de calcul utilisée pour les solutions de référence ---------------------------------------------------------- Modélisation A ~~~~~~~~~~~~~~ Pour la direction axiale, l’équation du comportement non-linéaire est connue ainsi que le chargement en déplacement, la solution est calculée de façon analytique. La réponse en effort de la loi de comportement est : .. csv-table:: "**INST**", "DX [mm]", "Force [N]" "1.000E-01", "1.1755705046E+00", "3.6359182479E+02" "1.500E-01", "1.6180339887E+00", "3.9812608291E+02" "2.000E-01", "1.9021130326E+00", "4.1019465908E+02" "2.500E-01", "2.0000000000E+00", "4.1334696516E+02" "3.000E-01", "1.9021130326E+00", "3.7419217820E+02" "3.500E-01", "1.6180339887E+00", "2.6056056066E+02" "4.000E-01", "1.1755705046E+00", "8.3575166995E+01" "4.500E-01", "6.1803398875E-01", "-1.3943943934E+02" "5.500E-01", "-6.1803398875E-01", "-4.2538927701E+02" "6.000E-01", "-1.1755705046E+00", "-4.3218671109E+02" "6.500E-01", "-1.6180339887E+00", "-4.3565267662E+02" "7.000E-01", "-1.9021130326E+00", "-4.3733359687E+02" "7.500E-01", "-2.0000000000E+00", "-4.3783890390E+02" "8.000E-01", "-1.9021130326E+00", "-3.9868411694E+02" "8.500E-01", "-1.6180339887E+00", "-2.8505249940E+02" "9.000E-01", "-1.1755705046E+00", "-1.0806710573E+02" "9.500E-01", "-6.1803398875E-01", "1.1494750060E+02" "1.050E+00", "6.1803398875E-01", "4.3970639868E+02" "1.100E+00", "1.1755705046E+00", "4.4151193260E+02" "1.150E+00", "1.6180339887E+00", "4.4260216756E+02" "1.200E+00", "1.9021130326E+00", "4.4318572288E+02" "1.250E+00", "2.0000000000E+00", "4.4336937364E+02" "1.300E+00", "1.9021130326E+00", "4.0421458667E+02" "1.350E+00", "1.6180339887E+00", "2.9058296914E+02" "1.400E+00", "1.1755705046E+00", "1.1359757547E+02" "1.450E+00", "6.1803398875E-01", "-1.0941703086E+02" Les variables internes de la loi de comportement sont également calculées et seront testées. .. csv-table:: "", "Nom de la variable", "" "V1", "FORCEX", "Force axiale dans le repère local" "V4", "DEPLX", "Déplacement axial dans le repère local" "V7", "DISSTHER", "Dissipation" "V8", "PCUM", "Déplacement anélastique cumulé" "V9", "DEPLPX", "Déplacement anélastique" Les variables internes de la loi de comportement: .. csv-table:: "**INST**", "**V1**", "**V4**", "**V7**", "**V9**", "**V8**" "1.000E-01", "3.63592E+02", "1.17557E+00", "8.68431E+01", "2.66591E-01", "2.66591E-01" "1.500E-01", "3.98126E+02", "1.61803E+00", "2.23467E+02", "6.22719E-01", "6.22719E-01" "2.000E-01", "4.10195E+02", "1.90211E+00", "3.26206E+02", "8.76626E-01", "8.76626E-01" "2.500E-01", "4.13347E+02", "2.00000E+00", "3.63271E+02", "9.66633E-01", "9.66633E-01" "3.000E-01", "3.74192E+02", "1.90211E+00", "3.63271E+02", "9.66633E-01", "9.66633E-01" "3.500E-01", "2.60561E+02", "1.61803E+00", "3.63271E+02", "9.66633E-01", "9.66633E-01" "4.000E-01", "8.35752E+01", "1.17557E+00", "3.63271E+02", "9.66633E-01", "9.66633E-01" "4.500E-01", "-1.39439E+02", "6.18034E-01", "3.63271E+02", "9.66633E-01", "9.66633E-01" "5.500E-01", "-4.25389E+02", "-6.18034E-01", "5.82185E+02", "4.45439E-01", "1.48783E+00" "6.000E-01", "-4.32187E+02", "-1.17557E+00", "8.14129E+02", "-9.51037E-02", "2.02837E+00" "6.500E-01", "-4.35653E+02", "-1.61803E+00", "1.00241E+03", "-5.28902E-01", "2.46217E+00" "7.000E-01", "-4.37334E+02", "-1.90211E+00", "1.12458E+03", "-8.08779E-01", "2.74204E+00" "7.500E-01", "-4.37839E+02", "-2.00000E+00", "1.16686E+03", "-9.05403E-01", "2.83867E+00" "8.000E-01", "-3.98684E+02", "-1.90211E+00", "1.16686E+03", "-9.05403E-01", "2.83867E+00" "8.500E-01", "-2.85052E+02", "-1.61803E+00", "1.16686E+03", "-9.05403E-01", "2.83867E+00" "9.000E-01", "-1.08067E+02", "-1.17557E+00", "1.16686E+03", "-9.05403E-01", "2.83867E+00" "9.500E-01", "1.14948E+02", "-6.18034E-01", "1.16686E+03", "-9.05403E-01", "2.83867E+00" "1.050E+00", "4.39706E+02", "6.18034E-01", "1.35299E+03", "-4.81232E-01", "3.26284E+00" "1.100E+00", "4.41512E+02", "1.17557E+00", "1.59669E+03", "7.17907E-02", "3.81586E+00" "1.150E+00", "4.42602E+02", "1.61803E+00", "1.79109E+03", "5.11529E-01", "4.25560E+00" "1.200E+00", "4.43186E+02", "1.90211E+00", "1.91626E+03", "7.94149E-01", "4.53822E+00" "1.250E+00", "4.43369E+02", "2.00000E+00", "1.95945E+03", "8.91577E-01", "4.63565E+00" "1.300E+00", "4.04215E+02", "1.90211E+00", "1.95945E+03", "8.91577E-01", "4.63565E+00" "1.350E+00", "2.90583E+02", "1.61803E+00", "1.95945E+03", "8.91577E-01", "4.63565E+00" "1.400E+00", "1.13598E+02", "1.17557E+00", "1.95945E+03", "8.91577E-01", "4.63565E+00" "1.450E+00", "-1.09417E+02", "6.18034E-01", "1.95945E+03", "8.91577E-01", "4.63565E+00" Modélisations B et C ~~~~~~~~~~~~~~~~~~~~~~ Cas tests de non-régression Modélisation D ~~~~~~~~~~~~~~~~~~ La modélisation D combine A et B avec la présence de FX et FTAN dans DEFI_MATERIAU en même temps. Modélisation E ~~~~~~~~~~~~~~ Dans le plan tangentiel, l’équation du comportement non-linéaire est connu ainsi que le chargement en déplacement, la solution est calculée de façon analytique. La réponse en effort de la loi de comportement est: .. csv-table:: "**INST**", "DTAN [mm]", "Force_TAN [N]" "1.000E-01", "1.1755705046E+00", "3.6359182479E+02" "1.500E-01", "1.6180339887E+00", "3.9812608291E+02" "2.000E-01", "1.9021130326E+00", "4.1019465908E+02" "2.500E-01", "2.0000000000E+00", "4.1334696516E+02" "3.000E-01", "1.9021130326E+00", "3.7419217820E+02" "3.500E-01", "1.6180339887E+00", "2.6056056066E+02" "4.000E-01", "1.1755705046E+00", "8.3575166995E+01" "4.500E-01", "6.1803398875E-01", "1.3943943934E+02" "5.500E-01", "6.1803398875E-01", "4.2538927701E+02" "6.000E-01", "1.1755705046E+00", "4.3218671109E+02" "6.500E-01", "1.6180339887E+00", "4.3565267662E+02" "7.000E-01", "1.9021130326E+00", "4.3733359687E+02" "7.500E-01", "2.0000000000E+00", "4.3783890390E+02" "8.000E-01", "1.9021130326E+00", "3.9868411694E+02" "8.500E-01", "1.6180339887E+00", "2.8505249940E+02" "9.000E-01", "1.1755705046E+00", "1.0806710573E+02" "9.500E-01", "6.1803398875E-01", "1.1494750060E+02" "1.050E+00", "6.1803398875E-01", "4.3970639868E+02" "1.100E+00", "1.1755705046E+00", "4.4151193260E+02" "1.150E+00", "1.6180339887E+00", "4.4260216756E+02" "1.200E+00", "1.9021130326E+00", "4.4318572288E+02" "1.250E+00", "2.0000000000E+00", "4.4336937364E+02" "1.300E+00", "1.9021130326E+00", "4.0421458667E+02" "1.350E+00", "1.6180339887E+00", "2.9058296914E+02" "1.400E+00", "1.1755705046E+00", "1.1359757547E+02" "1.450E+00", "6.1803398875E-01", "1.0941703086E+02" Les variables internes de la loi de comportement sont également calculées et seront testées. .. csv-table:: "", "Nom de la variable", "" "V2", "FORCEY", "Force selon Y dans le repère local" "V3", "FORCEZ", "Force selon Z dans le repère local" "V5", "DEPLY", "Déplacement selon Y dans le repère local" "V6", "DEPLZ", "Déplacement selon Z dans le repère local" "V10", "DEPLPY", "Déplacement anélastique selon Y dans le repère local" "V11", "DEPLPZ", "Déplacement anélastique selon Z dans le repère local" "V18", "DISSTANG", "Dissipation dans le plan tangentiel" "V19", "PCUM", "Déplacement anélastique cumulé dans le plan tangentiel" , "F_TAN", ":math:`(V2^2+V3^2)^{1/2}`, Force tangentielle dans le plan YOZ" , "D_TAN", ":math:`(V5^2+V6^2)^{1/2}`, Déplacement tangentiel dans le plan YOZ" , "DP_TAN",":math:`(V10^2+V11^2)^{1/2}`, Déplacement anélasitque tangentiel" Les variables internes de la loi de comportement: .. csv-table:: "**INST**", "**F_TAN**", "**D_TAN**", "**V18**", "**DP_TAN**", "**V19**" "1.000E-01", "3.63592E+02", "1.17557E+00", "8.68431E+01", "2.66591E-01", "2.66591E-01" "1.500E-01", "3.98126E+02", "1.61803E+00", "2.23467E+02", "6.22719E-01", "6.22719E-01" "2.000E-01", "4.10195E+02", "1.90211E+00", "3.26206E+02", "8.76626E-01", "8.76626E-01" "2.500E-01", "4.13347E+02", "2.00000E+00", "3.63271E+02", "9.66633E-01", "9.66633E-01" "3.000E-01", "3.74192E+02", "1.90211E+00", "3.63271E+02", "9.66633E-01", "9.66633E-01" "3.500E-01", "2.60561E+02", "1.61803E+00", "3.63271E+02", "9.66633E-01", "9.66633E-01" "4.000E-01", "8.35752E+01", "1.17557E+00", "3.63271E+02", "9.66633E-01", "9.66633E-01" "4.500E-01", "1.39439E+02", "6.18034E-01", "3.63271E+02", "9.66633E-01", "9.66633E-01" "5.500E-01", "4.25389E+02", "6.18034E-01", "5.82185E+02", "4.45439E-01", "1.48783E+00" "6.000E-01", "4.32187E+02", "1.17557E+00", "8.14129E+02", "9.51037E-02", "2.02837E+00" "6.500E-01", "4.35653E+02", "1.61803E+00", "1.00241E+03", "5.28902E-01", "2.46217E+00" "7.000E-01", "4.37334E+02", "1.90211E+00", "1.12458E+03", "8.08779E-01", "2.74204E+00" "7.500E-01", "4.37839E+02", "2.00000E+00", "1.16686E+03", "9.05403E-01", "2.83867E+00" "8.000E-01", "3.98684E+02", "1.90211E+00", "1.16686E+03", "9.05403E-01", "2.83867E+00" "8.500E-01", "2.85052E+02", "1.61803E+00", "1.16686E+03", "9.05403E-01", "2.83867E+00" "9.000E-01", "1.08067E+02", "1.17557E+00", "1.16686E+03", "9.05403E-01", "2.83867E+00" "9.500E-01", "1.14948E+02", "6.18034E-01", "1.16686E+03", "9.05403E-01", "2.83867E+00" "1.050E+00", "4.39706E+02", "6.18034E-01", "1.35299E+03", "4.81232E-01", "3.26284E+00" "1.100E+00", "4.41512E+02", "1.17557E+00", "1.59669E+03", "7.17907E-02", "3.81586E+00" "1.150E+00", "4.42602E+02", "1.61803E+00", "1.79109E+03", "5.11529E-01", "4.25560E+00" "1.200E+00", "4.43186E+02", "1.90211E+00", "1.91626E+03", "7.94149E-01", "4.53822E+00" "1.250E+00", "4.43369E+02", "2.00000E+00", "1.95945E+03", "8.91577E-01", "4.63565E+00" "1.300E+00", "4.04215E+02", "1.90211E+00", "1.95945E+03", "8.91577E-01", "4.63565E+00" "1.350E+00", "2.90583E+02", "1.61803E+00", "1.95945E+03", "8.91577E-01", "4.63565E+00" "1.400E+00", "1.13598E+02", "1.17557E+00", "1.95945E+03", "8.91577E-01", "4.63565E+00" "1.450E+00", "1.09417E+02", "6.18034E-01", "1.95945E+03", "8.91577E-01", "4.63565E+00" Incertitude sur la solution --------------------------- Modélisation A, E ~~~~~~~~~~~~~~~~~~~ Aucune, la solution de référence est exacte. Modélisations B, C, D ~~~~~~~~~~~~~~~~~~~~~~~ Sans objet