Modeling A ============== Characteristics of modeling ----------------------------------- A modal analysis is carried out taking into account the masses and stiffness. Subsequently, the dynamic response is obtained by the operator "COMB_SISM_MODAL". For this study, the combination chosen is the combination with the 10% rule that is COMB_MODE/TYPE = 'DPC'. As a reminder, for this type of combination, the neighboring modes (whose frequencies are different by less than 10%) are first combined by summing the absolute values. The values resulting from this first combination are then combined quadratically. The combination selected according to the directions is the quadratic combination (COMB_DIRECTION/TYPE =' QUAD '). Characteristics of the mesh ---------------------------- The length of the elements is approximately 303 mm. The following table summarizes the elements present in the mesh: Table 6: General characteristics of the mesh .. csv-table:: "**PARAMÈTRE**", "**TYPE**", "**NOMBRE**" "Elements", "Beam (SEG2) Springs (SEG2) Point mass", "204 8 22" "", "Total items Total nodes", "**234** **21** 3" Tested sizes and results ------------------------------ The values tested are: * natural frequencies * movements and rotations at different nodes * efforts ('EFGE_ELNO') at different nodes .. csv-table:: "**Mode**", "**NUREG — Frequency (Hz)**", "**Code_Aster — Frequency (Hz)**", "Gap **(%)**" "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" Table 7: **Comparison of modal analysis results** +--------+-------------+---------+--------------+----------------+ |**Knot**|**Component**|**NUREG**|**Aster_code**|**Variance (%)**| +--------+-------------+---------+--------------+----------------+ |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 | +--------+-------------+---------+--------------+----------------+ Table 8: **Comparison** **displacements and rotations** **as a result of the modal combination** +--------+-------------+---------+--------------+---------------+ |**Knot**|**Component**|**NUREG**|**Aster_code**|**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 | +--------+-------------+---------+--------------+---------------+ Table 9: **Comparison** **efforts** **as a result of the modal combination** notes --------- For this study, the starting units are in imperial (lb, inch, psi), a conversion to an SI unit was carried out. Some differences are of the order of 30% and are in particular linked to the formulation between the curved beam elements used in the EPIPE NUREG software and the aster straight beam elements. Uncertainty about the solution ---------------------------- Unit conversion, Combination method, data reading (document NUREG not very readable).