Modélisation A ============== Caractéristiques de la modélisation ----------------------------------- Une analyse modale est réalisée en prenant en compte les masses, rigidité. Par la suite, la réponse dynamique est obtenu par l’opérateur «COMB_SISM_MODAL». Pour cette étude, la combinaison choisie est la combinaison avec règle des 10% soit COMB_MODE/TYPE = ‘DPC’. Pour rappel, pour ce type de combinaison les modes voisins (dont les fréquences différentes de moins de 10%) sont d’abord combinés par sommation des valeurs absolues. Les valeurs résultant de cette première combinaison sont ensuite combinées quadratiquement. La combinaison retenue suivant les directions est la combinaison quadratique (COMB_DIRECTION/TYPE=’QUAD’). Caractéristiques du maillage ---------------------------- La longueur des éléments est d’environ 303mm. Le tableau suivant résume les éléments présents dans le maillage: Tableau 6: Caractéristiques générales du maillage .. csv-table:: "**PARAMÈTRE**", "**TYPE**", "**NOMBRE**" "Éléments", "Poutre (SEG2) Ressorts (SEG2) Masse ponctuelle", "204 8 22" "", "Total d’éléments Total de nœuds", "**234** **21** 3" Grandeurs testées et résultats ------------------------------ Les valeurs testés sont: * les fréquences propres * les déplacements et rotations à différents nœuds * efforts (‘EFGE_ELNO’) à différents nœuds .. csv-table:: "**Mode**", "**NUREG – Fréquence (Hz)**", "**Code_Aster – Fréquence (Hz)**", "Écart **(%)**" "1", "6.39", "6.35", "0.61" "2", "9.99", "9.91", "0.83" "3", "13.27", "13.25", "0.18" "4", "14.49", "14.47", "0.169" "5", "15.33", "15.32", "0.056" "6", "17.50", "17.42", "0.459" "7", "19.09", "19.08", "0.073" "8", "19.62", "19.58", "0.24" "9", "21.44", "21.25", "0.89" "10", "28.71", "28.64", "0.229" "11", "29.86", "29.69", "0.57" "12", "31.48", "31.30", "0.59" "13", "32.01", "31.82", "0.59" "14", "36.37", "35.95", "1.2" "15", "40.98", "40.82", "0.389" "16", "41.37", "41.45", "0.21" "17", "47.39", "47.10", "0.61" "18", "49.77", "49.53", "0.5" "19", "50.13", "50.01", "0.25" "20", "52.93", "52.17", "1.5" "21", "56.90", "56.53", "0.66" "22", "58.51", "58.01", "0.85" "23", "67.47", "67.34", "0.2" "24", "70.46", "70.41", "0.073" "25", "75.41", "75.12", "0.389" "26", "79.18", "78.46", "0.91" "27", "80.74", "80.39", "0.44" "28", "86.11", "85.06", "1.3" "29", "88.28", "86.52", "2.0" "30", "92.74", "92.45", "0.32" "31", "99.36", "97.43", "2.0" Tableau 7: **Comparaison des résultats de l’analyse modale** +-----------+----------------+-----------+----------------+---------------+ | **Noeud** | **Composante** | **NUREG** | **Code_Aster** | **Écart (%)** | +-----------+----------------+-----------+----------------+---------------+ | PT_3 | DX (mm) | 0.089 | 0.120 | 3.52921E+01 | | +----------------+-----------+----------------+---------------+ | | DY (mm) | 0.064 | 0.069 | 9.39667E+00 | | +----------------+-----------+----------------+---------------+ | | DZ (mm) | 0.081 | 0.093 | 1.49315E+01 | | +----------------+-----------+----------------+---------------+ | | DRX (mrad) | 0.073 | 0.083 | 1.38046E+01 | | +----------------+-----------+----------------+---------------+ | | DRY (mrad) | 0.062 | 0.084 | 3.41959E+01 | | +----------------+-----------+----------------+---------------+ | | DRZ (mrad) | 0.061 | 0.081 | 3.28204E+01 | +-----------+----------------+-----------+----------------+---------------+ | PT_6 | DX (mm) | 0.297 | 0.393 | 3.2097E+01 | | +----------------+-----------+----------------+---------------+ | | DY (mm) | 0.066 | 0.073 | 1.06215E+01 | | +----------------+-----------+----------------+---------------+ | | DZ (mm) | 0.310 | 0.354 | 1.41841E+01 | | +----------------+-----------+----------------+---------------+ | | DRX (mrad) | 0.011 | 0.013 | 2.02646E+01 | | +----------------+-----------+----------------+---------------+ | | DRY (mrad) | 0.057 | 0.075 | 3.02786E+01 | | +----------------+-----------+----------------+---------------+ | | DRZ (mrad) | 0.006 | 0.007 | 1.72135E+01 | +-----------+----------------+-----------+----------------+---------------+ | PT_9 | DX (mm) | 0.119 | 0.165 | 3.79149E+01 | | +----------------+-----------+----------------+---------------+ | | DY (mm) | 0.069 | 0.075 | 9.53364E+00 | | +----------------+-----------+----------------+---------------+ | | DZ (mm) | 0.117 | 0.139 | 1.88680E+01 | | +----------------+-----------+----------------+---------------+ | | DRX (mrad) | 0.068 | 0.074 | 8.0747E+00 | | +----------------+-----------+----------------+---------------+ | | DRY (mrad) | 0.062 | 0.075 | 1.97586E+01 | | +----------------+-----------+----------------+---------------+ | | DRZ (mrad) | 0.065 | 0.081 | 2.52836E+01 | +-----------+----------------+-----------+----------------+---------------+ | PT_12 | DX (mm) | 0.140 | 0.184 | 3.19612E+01 | | +----------------+-----------+----------------+---------------+ | | DY (mm) | 0.099 | 0.105 | 6.08625E+00 | | +----------------+-----------+----------------+---------------+ | | DZ (mm) | 0.132 | 0.158 | 1.99237E+01 | | +----------------+-----------+----------------+---------------+ | | DRX (mrad) | 0.050 | 0.054 | 7.91922E+00 | | +----------------+-----------+----------------+---------------+ | | DRY (mrad) | 0.058 | 0.070 | 2.10168E+01 | | +----------------+-----------+----------------+---------------+ | | DRZ (mrad) | 0.070 | 0.085 | 2.17501E+01 | +-----------+----------------+-----------+----------------+---------------+ | PT_18 | DX (mm) | 0.165 | 0.222 | 3.46224E+01 | | +----------------+-----------+----------------+---------------+ | | DY (mm) | 0.173 | 0.221 | 2.78519E+01 | | +----------------+-----------+----------------+---------------+ | | DZ (mm) | 0.218 | 0.264 | 2.10765E+01 | | +----------------+-----------+----------------+---------------+ | | DRX (mrad) | 0.062 | 0.074 | 1.88360E+01 | | +----------------+-----------+----------------+---------------+ | | DRY (mrad) | 0.043 | 0.054 | 2.50748E+01 | | +----------------+-----------+----------------+---------------+ | | DRZ (mrad) | 0.026 | 0.031 | 1.71645E+01 | +-----------+----------------+-----------+----------------+---------------+ | PT_24 | DX (mm) | 0.163 | 0.194 | 1.91709E+01 | | +----------------+-----------+----------------+---------------+ | | DY (mm) | 0.102 | 0.111 | 8.93288E+00 | | +----------------+-----------+----------------+---------------+ | | DZ (mm) | 0.112 | 0.140 | 2.56284E+01 | | +----------------+-----------+----------------+---------------+ | | DRX (mrad) | 0.021 | 0.024 | 1.41253E+01 | | +----------------+-----------+----------------+---------------+ | | DRY (mrad) | 0.032 | 0.035 | 8.70203E+00 | | +----------------+-----------+----------------+---------------+ | | DRZ (mrad) | 0.029 | 0.030 | 3.43153E+00 | +-----------+----------------+-----------+----------------+---------------+ | PT_30 | DX (mm) | 0.566 | 0.595 | 5.05972E+00 | | +----------------+-----------+----------------+---------------+ | | DY (mm) | 0.051 | 0.051 | 9.17199E-01 | | +----------------+-----------+----------------+---------------+ | | DZ (mm) | 0.107 | 0.131 | 2.31266E+01 | | +----------------+-----------+----------------+---------------+ | | DRX (mrad) | 0.132 | 0.130 | 1.57814E+00 | | +----------------+-----------+----------------+---------------+ | | DRY (mrad) | 0.043 | 0.046 | 6.51731E+00 | | +----------------+-----------+----------------+---------------+ | | DRZ (mrad) | 0.066 | 0.065 | 1.04947E+00% | +-----------+----------------+-----------+----------------+---------------+ | PT_36 | DX (mm) | 0.206 | 0.203 | 1.09275E+00 | | +----------------+-----------+----------------+---------------+ | | DY (mm) | 1.750 | 1.738 | 7.05878E-01 | | +----------------+-----------+----------------+---------------+ | | DZ (mm) | 0.384 | 0.397 | 3.52455E+00 | | +----------------+-----------+----------------+---------------+ | | DRX (mrad) | 0.241 | 0.241 | 6.32093E-03 | | +----------------+-----------+----------------+---------------+ | | DRY (mrad) | 0.053 | 0.057 | 4.97626E+00 | | +----------------+-----------+----------------+---------------+ | | DRZ (mrad) | 0.278 | 0.273 | 1.96532E+00 | +-----------+----------------+-----------+----------------+---------------+ | PT_39 | DX (mm) | 0.145 | 0.136 | 6.34394E+00 | | +----------------+-----------+----------------+---------------+ | | DY (mm) | 0.277 | 0.281 | 1.50518E+00 | | +----------------+-----------+----------------+---------------+ | | DZ (mm) | 0.135 | 0.134 | 2.18570E-01 | | +----------------+-----------+----------------+---------------+ | | DRX (mrad) | 0.188 | 0.191 | 1.55268E+00 | | +----------------+-----------+----------------+---------------+ | | DRY (mrad) | 0.080 | 0.084 | 5.03604E+00 | | +----------------+-----------+----------------+---------------+ | | DRZ (mrad) | 0.305 | 0.300 | 1.50026E+00 | +-----------+----------------+-----------+----------------+---------------+ Tableau 8: **Comparaison des** **déplacements et rotations** **à la suite de la combinaison modale** +-----------+----------------+-----------+----------------+-----------------+ | **Noeud** | **Composante** | **NUREG** | **Code_Aster** | **NUREG/ASTER** | +-----------+----------------+-----------+----------------+-----------------+ | PT_6 | N (N) | 6743.17 | 8247.25 | 2.23052E+01 | | +----------------+-----------+----------------+-----------------+ | | VY (N) | 1573.70 | 1794.48 | 1.40295E+01 | | +----------------+-----------+----------------+-----------------+ | | VZ (N) | 1392.22 | 2077.35 | 4.92115E+01 | | +----------------+-----------+----------------+-----------------+ | | MT (N.m) | 2525.21 | 2858.02 | 1.31794E+01 | | +----------------+-----------+----------------+-----------------+ | | MFY (N.m) | 13806.74 | 16882.75 | 2.22790E+01 | | +----------------+-----------+----------------+-----------------+ | | MFZ (N.m) | 14925.29 | 18142.38 | 2.15546E+01 | +-----------+----------------+-----------+----------------+-----------------+ | PT_17 | N (N) | 4817.18 | 5897.12 | 2.24185E+01 | | +----------------+-----------+----------------+-----------------+ | | VY (N) | 3804.82 | 4481.16 | 1.77757E+01 | | +----------------+-----------+----------------+-----------------+ | | VZ (N) | 3581.53 | 4810.00 | 3.43000E+01 | | +----------------+-----------+----------------+-----------------+ | | MT (N.m) | 2451.77 | 2876.85 | 1.73377E+01 | | +----------------+-----------+----------------+-----------------+ | | MFY (N.m) | 11693.93 | 14773.87 | 2.63379E+01 | | +----------------+-----------+----------------+-----------------+ | | MFZ (N.m) | 10816.04 | 14481.66 | 3.38905E+01 | +-----------+----------------+-----------+----------------+-----------------+ | PT_28 | N (N) | 4510.27 | 5323.58 | 1.80325E+01 | | +----------------+-----------+----------------+-----------------+ | | VY (N) | 8820.38 | 8717.52 | 1.16611E+00 | | +----------------+-----------+----------------+-----------------+ | | VZ (N) | 5177.47 | 5578.23 | 7.74039E+00 | | +----------------+-----------+----------------+-----------------+ | | MT (N.m) | 1005.45 | 1050.75 | 4.50534E+00 | | +----------------+-----------+----------------+-----------------+ | | MFY (N.m) | 5992.72 | 6793.32 | 1.33595E+01 | | +----------------+-----------+----------------+-----------------+ | | MFZ (N.m) | 19218.72 | 19054.19 | 8.56075E-01 | +-----------+----------------+-----------+----------------+-----------------+ | PT_36 | N (N) | 6351.74 | 6569.42 | 3.42716E+00 | | +----------------+-----------+----------------+-----------------+ | | VY (N) | 4132.19 | 4061.34 | 1.71447E+00 | | +----------------+-----------+----------------+-----------------+ | | VZ (N) | 2994.84 | 3114.78 | 4.00505E+00 | | +----------------+-----------+----------------+-----------------+ | | MT (N.m) | 8676.11 | 8437.24 | 2.75314E+00 | | +----------------+-----------+----------------+-----------------+ | | MFY (N.m) | 12597.81 | 13209.77 | 4.85770E+00 | | +----------------+-----------+----------------+-----------------+ | | MFZ (N.m) | 12213.66 | 12343.87 | 1.06609E+00 | +-----------+----------------+-----------+----------------+-----------------+ Tableau 9: **Comparaison des** **efforts** **à la suite de la combinaison modale** Remarques --------- Pour cette étude, les unités de départ sont en impérial (lb, inch, psi), une conversion en unité S.I a été réalisée. Certains écarts sont de l’ordre de 30% sont notamment liés à la formulation entre les éléments poutres courbées utilisés dans le logiciel EPIPE de NUREG et les éléments poutres droites de aster. Incertitudes sur la solution ---------------------------- Conversion des unités, Méthode de combinaison, lecture des données (document NUREG peu lisible).