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

pv.set_plot_theme('document')
pv.set_jupyter_backend('panel')

[2]:

vm_mesh = pylife.vmap.VMAPImport("plate_with_hole.vmap")
mesh = (vm_mesh.make_mesh('1', 'STATE-2')
        .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 = .9 # 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	1734	14.897208	5.269875	0.0	33.996987	0
	1582	14.555333	5.355806	0.0	33.399850	0
	1596	14.630658	4.908741	0.0	54.777007	0
	4923	14.726271	5.312840	0.0	33.446991	0
	4924	14.592996	5.132274	0.0	44.070962	0
...	...	...	...	...	...	...
4770	3812	-13.189782	-5.691876	0.0	43.577209	0
	12418	-13.560289	-5.278386	0.0	39.903508	0
	14446	-13.673285	-5.569107	0.0	40.478974	0
	14614	-13.389065	-5.709927	0.0	42.140169	0
	14534	-13.276068	-5.419206	0.0	41.143837	0

37884 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(window_size=[1920, 1080])
plotter.add_mesh(grid, scalars=mesh.groupby('element_id')['hotspot'].first().to_numpy(),
                show_edges=True, cmap='prism_r')
plotter.add_scalar_bar()
plotter.show()

First hotspot

[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
456	5	0.0	6.3	0.0	300.899658	30.574533	0.0	-7.081042	0.0	0.0	1.365477e-35	-0.005435	0.0	287.099222	1

[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
2852	9	0.0	-6.3	0.0	284.085327	30.704277	0.0	3.546472	0.0	0.0	1.400164e-35	0.005436	0.0	270.115389	2

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