Hotspot calculation demo
This notebook detects and classifies hotspots of the von Mises stress in a connected FEM mesh. Each element/node entry of the mesh receives a number of the hotspot it is member of. “0” means the element/node is not part of any hotspots. “1” means that the element/node is part of the hotspot with the highes peak, “2” the same for the second highest peak and so forth.
See module documentation further details.
[1]:
import numpy as np
import pylife
import pandas as pd
import scipy.stats as stats
import pylife.stress.equistress
import pylife.strength.meanstress
import pylife.mesh.meshsignal
import pylife.mesh.hotspot
import pylife.vmap
import pyvista as pv
[2]:
vm_mesh = pylife.vmap.VMAPImport("two_notched_beam.vmap")
mesh = (vm_mesh.make_mesh('beam', 'STATE-1')
.join_coordinates()
.join_variable('STRESS_CAUCHY')
.join_variable('DISPLACEMENT')
.to_frame())
Equivalent stress calculation
[3]:
mesh['mises'] = mesh.equistress.mises()
Hot spot Calculation
[4]:
threshold = .3 # factor of the maximum local value
mesh['hotspot'] = mesh.hotspot.calc("mises", threshold)
display(mesh[['x', 'y', 'z', 'mises', 'hotspot']])
| x | y | z | mises | hotspot | ||
|---|---|---|---|---|---|---|
| element_id | node_id | |||||
| 1 | 352 | -43.969048 | 23.989227 | 0.0 | 1296.278948 | 0 |
| 359 | -42.955109 | 24.005196 | 0.0 | 1296.278948 | 0 | |
| 215 | -43.000000 | 25.000000 | 0.0 | 1296.278948 | 0 | |
| 216 | -44.000000 | 25.000000 | 0.0 | 1296.278948 | 0 | |
| 1271 | -43.969048 | 23.989227 | 1.0 | 1296.278948 | 0 | |
| ... | ... | ... | ... | ... | ... | ... |
| 8340 | 9186 | -35.655140 | 17.474123 | 9.0 | 1508.430170 | 0 |
| 10106 | -36.133118 | 17.862680 | 10.0 | 1508.430170 | 0 | |
| 9903 | -36.538712 | 17.142405 | 10.0 | 1508.430170 | 0 | |
| 9796 | -35.728638 | 16.920214 | 10.0 | 1508.430170 | 0 | |
| 10105 | -35.655140 | 17.474123 | 10.0 | 1508.430170 | 0 |
66720 rows × 5 columns
[5]:
print("%d hotspots found over the threshold" % mesh['hotspot'].max())
3 hotspots found over the threshold
[6]:
grid = pv.UnstructuredGrid(*mesh.mesh.vtk_data())
plotter = pv.Plotter()
plotter.add_mesh(grid, scalars=mesh.groupby('element_id')['hotspot'].first().to_numpy(), show_edges=True)
plotter.add_scalar_bar()
plotter.show()
Hotspots
[7]:
first_hotspot = mesh[mesh['hotspot'] == 1]
display(first_hotspot)
| x | y | z | S11 | S22 | S33 | S12 | S13 | S23 | dx | dy | dz | mises | hotspot | ||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| element_id | node_id | ||||||||||||||
| 11 | 11 | -29.798346 | 15.728621 | 0.0 | 6272.631348 | 2563.831787 | 451.533936 | -180.307007 | -238.394638 | 134.026550 | 1.154036e-07 | -1.756874e-07 | 4.878709e-08 | 5135.465212 | 1 |
| 293 | -30.003225 | 15.085076 | 0.0 | 6272.631348 | 2563.831787 | 451.533936 | -180.307007 | -238.394638 | 134.026550 | 6.027405e-08 | -1.652169e-07 | 3.857556e-08 | 5135.465212 | 1 | |
| 298 | -29.560358 | 14.704604 | 0.0 | 6272.631348 | 2563.831787 | 451.533936 | -180.307007 | -238.394638 | 134.026550 | 4.464848e-08 | -1.967865e-07 | 3.022250e-08 | 5135.465212 | 1 | |
| 294 | -29.171230 | 15.177115 | 0.0 | 6272.631348 | 2563.831787 | 451.533936 | -180.307007 | -238.394638 | 134.026550 | 8.558990e-08 | -2.332368e-07 | 3.184098e-08 | 5135.465212 | 1 | |
| 930 | -29.798346 | 15.728621 | 1.0 | 6272.631348 | 2563.831787 | 451.533936 | -180.307007 | -238.394638 | 134.026550 | 1.209642e-07 | -1.854055e-07 | 3.053447e-08 | 5135.465212 | 1 | |
| ... | ... | ... | ... | ... | ... | ... | ... | ... | ... | ... | ... | ... | ... | ... | ... |
| 8305 | 8564 | -30.003225 | 15.085076 | 9.0 | 3100.241699 | 3297.122559 | 107.299477 | 309.390259 | -129.906067 | -215.895401 | 5.984818e-08 | -1.767131e-07 | -2.791749e-08 | 3172.277492 | 1 |
| 10016 | -30.398149 | 15.265852 | 10.0 | 3100.241699 | 3297.122559 | 107.299477 | 309.390259 | -129.906067 | -215.895401 | 7.019130e-08 | -1.394186e-07 | -3.904580e-08 | 3172.277492 | 1 | |
| 9487 | -30.526169 | 14.907959 | 10.0 | 3100.241699 | 3297.122559 | 107.299477 | 309.390259 | -129.906067 | -215.895401 | 4.688527e-08 | -1.422961e-07 | -3.277479e-08 | 3172.277492 | 1 | |
| 10022 | -30.299625 | 14.657948 | 10.0 | 3100.241699 | 3297.122559 | 107.299477 | 309.390259 | -129.906067 | -215.895401 | 3.804261e-08 | -1.504318e-07 | -2.902902e-08 | 3172.277492 | 1 | |
| 9483 | -30.003225 | 15.085076 | 10.0 | 3100.241699 | 3297.122559 | 107.299477 | 309.390259 | -129.906067 | -215.895401 | 6.027405e-08 | -1.652169e-07 | -3.857556e-08 | 3172.277492 | 1 |
1296 rows × 14 columns
[8]:
second_hotspot = mesh[mesh['hotspot'] == 2]
display(second_hotspot)
| x | y | z | S11 | S22 | S33 | S12 | S13 | S23 | dx | dy | dz | mises | hotspot | ||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| element_id | node_id | ||||||||||||||
| 9 | 376 | -32.057991 | 10.855629 | 0.0 | -4764.971191 | 22.753010 | -25.855721 | 329.925690 | -65.013237 | 15.423181 | -1.413637e-07 | -1.010070e-07 | -2.588431e-08 | 4799.154854 | 2 |
| 307 | -33.038311 | 10.866936 | 0.0 | -4764.971191 | 22.753010 | -25.855721 | 329.925690 | -65.013237 | 15.423181 | -1.208426e-07 | -7.387519e-08 | -2.458061e-08 | 4799.154854 | 2 | |
| 263 | -33.000000 | 10.000000 | 0.0 | -4764.971191 | 22.753010 | -25.855721 | 329.925690 | -65.013237 | 15.423181 | -1.472568e-07 | -8.075897e-08 | -3.334923e-08 | 4799.154854 | 2 | |
| 54 | -32.000000 | 10.000000 | 0.0 | -4764.971191 | 22.753010 | -25.855721 | 329.925690 | -65.013237 | 15.423181 | -1.743098e-07 | -1.092242e-07 | -3.636057e-08 | 4799.154854 | 2 | |
| 1295 | -32.057991 | 10.855629 | 1.0 | -4764.971191 | 22.753010 | -25.855721 | 329.925690 | -65.013237 | 15.423181 | -1.405872e-07 | -1.109971e-07 | -1.996358e-08 | 4799.154854 | 2 | |
| ... | ... | ... | ... | ... | ... | ... | ... | ... | ... | ... | ... | ... | ... | ... | ... |
| 7943 | 8578 | -33.038311 | 10.866936 | 9.0 | -3235.834717 | 12.813469 | -20.089951 | 846.806335 | 9.251723 | -42.739223 | -1.200192e-07 | -8.246292e-08 | 1.906615e-08 | 3550.335991 | 2 |
| 9566 | -32.057991 | 10.855629 | 10.0 | -3235.834717 | 12.813469 | -20.089951 | 846.806335 | 9.251723 | -42.739223 | -1.413637e-07 | -1.010070e-07 | 2.588431e-08 | 3550.335991 | 2 | |
| 9658 | -32.109859 | 11.699945 | 10.0 | -3235.834717 | 12.813469 | -20.089951 | 846.806335 | 9.251723 | -42.739223 | -1.036564e-07 | -9.417452e-08 | 1.589893e-08 | 3550.335991 | 2 | |
| 9997 | -33.070908 | 11.748685 | 10.0 | -3235.834717 | 12.813469 | -20.089951 | 846.806335 | 9.251723 | -42.739223 | -9.047081e-08 | -7.002545e-08 | 1.569840e-08 | 3550.335991 | 2 | |
| 9497 | -33.038311 | 10.866936 | 10.0 | -3235.834717 | 12.813469 | -20.089951 | 846.806335 | 9.251723 | -42.739223 | -1.208426e-07 | -7.387519e-08 | 2.458061e-08 | 3550.335991 | 2 |
1504 rows × 14 columns
[9]:
third_hotspot = mesh[mesh['hotspot'] == 3]
display(third_hotspot)
| x | y | z | S11 | S22 | S33 | S12 | S13 | S23 | dx | dy | dz | mises | hotspot | ||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| element_id | node_id | ||||||||||||||
| 99 | 26 | -6.500000 | 16.000000 | 0.0 | 3004.292725 | 521.134766 | 64.611237 | -880.206421 | 60.812458 | -0.974387 | 2.934005e-07 | -0.000003 | 2.286925e-08 | 3137.434391 | 3 |
| 481 | -6.711311 | 15.297429 | 0.0 | 3004.292725 | 521.134766 | 64.611237 | -880.206421 | 60.812458 | -0.974387 | 2.026713e-07 | -0.000003 | 1.759673e-08 | 3137.434391 | 3 | |
| 117 | -5.611419 | 14.901155 | 0.0 | 3004.292725 | 521.134766 | 64.611237 | -880.206421 | 60.812458 | -0.974387 | 1.590093e-07 | -0.000003 | 1.773502e-08 | 3137.434391 | 3 | |
| 27 | -5.526631 | 15.597612 | 0.0 | 3004.292725 | 521.134766 | 64.611237 | -880.206421 | 60.812458 | -0.974387 | 2.583925e-07 | -0.000003 | 2.423010e-08 | 3137.434391 | 3 | |
| 945 | -6.500000 | 16.000000 | 1.0 | 3004.292725 | 521.134766 | 64.611237 | -880.206421 | 60.812458 | -0.974387 | 2.902192e-07 | -0.000003 | 1.753467e-08 | 3137.434391 | 3 | |
| ... | ... | ... | ... | ... | ... | ... | ... | ... | ... | ... | ... | ... | ... | ... | ... |
| 7606 | 8298 | -5.526631 | 15.597612 | 9.0 | 3324.102539 | 357.891479 | 100.239151 | -170.086090 | 44.371521 | -26.944239 | 2.571436e-07 | -0.000003 | -1.762701e-08 | 3118.319462 | 3 |
| 9307 | -5.611419 | 14.901155 | 10.0 | 3324.102539 | 357.891479 | 100.239151 | -170.086090 | 44.371521 | -26.944239 | 1.590093e-07 | -0.000003 | -1.773502e-08 | 3118.319462 | 3 | |
| 9792 | -4.326275 | 14.848801 | 10.0 | 3324.102539 | 357.891479 | 100.239151 | -170.086090 | 44.371521 | -26.944239 | 1.620271e-07 | -0.000003 | -1.573879e-08 | 3118.319462 | 3 | |
| 9218 | -4.473369 | 15.597612 | 10.0 | 3324.102539 | 357.891479 | 100.239151 | -170.086090 | 44.371521 | -26.944239 | 2.813164e-07 | -0.000003 | -2.211096e-08 | 3118.319462 | 3 | |
| 9217 | -5.526631 | 15.597612 | 10.0 | 3324.102539 | 357.891479 | 100.239151 | -170.086090 | 44.371521 | -26.944239 | 2.583925e-07 | -0.000003 | -2.423010e-08 | 3118.319462 | 3 |
160 rows × 14 columns
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