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trussplot.py
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trussplot.py
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# Enrico Stragiotti 10/2021
import numpy as np
import math
import matplotlib
import matplotlib.pyplot as plt
import matplotlib.colors as colors
from matplotlib import collections as mc
from mpl_toolkits.mplot3d.art3d import Line3DCollection
import plotly.graph_objects as go
from itertools import product, combinations, compress
import glob
import imageio
import os
import tikzplotlib
import scipy.sparse as sp
# import bpy
#matplotlib.use("pgf")
matplotlib.rcParams.update({
"pgf.texsystem": "pdflatex",
'font.family': 'serif',
'text.usetex': True,
'pgf.rcfonts': False,
})
sample = 8
norm = matplotlib.colors.Normalize(vmin=0, vmax=sample-1) #normalize item number values to colormap
cmap = matplotlib.cm.get_cmap('coolwarm')
accent_b_1 = colors.rgb2hex((cmap(norm(0))), keep_alpha=True)
accent_b_2 = colors.rgb2hex((cmap(norm(1))), keep_alpha=True)
accent_b_3 = colors.rgb2hex((cmap(norm(2))), keep_alpha=True)
accent_b_4 = colors.rgb2hex((cmap(norm(3))), keep_alpha=True)
accent_r_1 = colors.rgb2hex((cmap(norm(7))), keep_alpha=True)
accent_r_2 = colors.rgb2hex((cmap(norm(6))), keep_alpha=True)
accent_r_3 = colors.rgb2hex((cmap(norm(5))), keep_alpha=True)
accent_r_4 = colors.rgb2hex((cmap(norm(4))), keep_alpha=True)
# Create custom colormaps
def truncate_colormap(cmap, minval=0.0, maxval=1.0, n=256):
new_cmap = colors.LinearSegmentedColormap.from_list(
'trunc({n},{a:.2f},{b:.2f})'.format(n=cmap.name, a=minval, b=maxval),
cmap(np.linspace(minval, maxval, n)))
return new_cmap
# Blue
cmap_original = plt.get_cmap('coolwarm')
cmap_original_r = plt.get_cmap('coolwarm_r')
Blue_mono = truncate_colormap(cmap_original_r, 0.5, 1)
# Red
Red_mono = truncate_colormap(cmap, 0.5, 1)
############################
# 2D plotting
############################
class plot2D():
#Visualize truss
@staticmethod
def plotTruss(myBCs, a, forces, threshold, vol, tk, foldername=False):
""" Plot the ground stucture optimization solution """
nodes = myBCs.nodes
candidates = myBCs.ground_structure
fig = plt.figure()
plt.clf()
plt.axis('off')
plt.axis('equal')
plt.title("Final Structure - Vol = %.3f" % (vol))
candidates = myBCs.ground_structure[a >= threshold,:]
q = forces[a >= threshold]
a = a[a >= threshold]
c = np.empty(a.size, dtype = object)
tol = np.max(q) * 1e-04
c[:] = 'grey' # no force
c[q>tol] = accent_r_1 # tension
c[q<-tol] = accent_b_1 # compression
linewidth = a * tk
# boundaries
if not myBCs.isLshape:
plt.plot([0,0], [0, myBCs.L[1]], 'lightgray', linestyle="dotted", linewidth=0.2)
plt.plot([0, myBCs.L[0]], [myBCs.L[1], myBCs.L[1]], 'lightgray', linestyle="dotted", linewidth=0.2)
plt.plot([myBCs.L[0], myBCs.L[0]], [myBCs.L[1], 0], 'lightgray', linestyle="dotted", linewidth=0.2)
plt.plot([myBCs.L[0], 0], [0,0], 'lightgray', linestyle="dotted", linewidth=0.2)
# optimized beams
for i in range(len(a)):
pos = nodes[candidates[i, [0, 1]].astype(int), :]
plt.plot(pos[:, 0], pos[:, 1], c[i], linewidth = linewidth[i])
# plt.scatter(pos[:, 0], pos[:, 1], c = 'black', marker = 'o', edgecolors = 'none', zorder=2, s=5) # enforce the scatter plot after the plot
fig.tight_layout()
if foldername == False:
plt.show()
else:
# tikzplotlib.save(foldername+'fig1-Topology.tex')
# plt.savefig(foldername+'fig1-Topology.pgf')
plt.savefig(foldername+'fig1-Topology.pdf')
#Visualize deformed truss
@staticmethod
def plotTrussDeformation(myBCs, a, q, u, threshold, magnitude, tk, foldername, axis):
""" Plot the ground stucture optimization solution """
nodes = myBCs.nodes
u = u.reshape(-1,2)
candidates = myBCs.ground_structure[a >= threshold,:]
q = q[a >= threshold]
a = a[a >= threshold]
fig = plt.figure()
plt.clf()
plt.axis('off')
plt.axis('equal')
plt.title("Final Structure deformation - Magnitude %i" % (magnitude))
if not myBCs.isLshape:
plt.plot([0,0], [0, myBCs.L[1]], 'lightgray')
plt.plot([0, myBCs.L[0]], [myBCs.L[1], myBCs.L[1]], 'lightgray')
plt.plot([myBCs.L[0], myBCs.L[0]], [myBCs.L[1], 0], 'lightgray')
plt.plot([myBCs.L[0], 0], [0,0], 'lightgray')
# optimized beams
for i in [i for i in range(len(a)) if a[i] >= threshold]:
c = 'black'
pos = nodes[candidates[i, [0, 1]].astype(int), :] + magnitude * u[candidates[i, [0, 1]].astype(int), :]
plt.plot(pos[:, 0], pos[:, 1], c, linewidth = a[i] * tk)
plt.scatter(pos[:, 0], pos[:, 1], c = 'black', marker = 'o', edgecolors = 'none', zorder=2) # enforce the scatter plot after the plot
fig.tight_layout()
if not axis:
plt.title(' ')
if foldername == False:
plt.show()
else:
# tikzplotlib.save(foldername+'fig6-U_NoAxis-Mag={0}.tex'.format(magnitude))
plt.savefig(foldername+'fig5-U_NoAxis-Mag={0}.pdf'.format(magnitude))
# plt.savefig(foldername+'fig6-U_NoAxis-Mag={0}.pgf'.format(magnitude))
else:
plt.title(' ')
if foldername == False:
plt.show()
else:
# tikzplotlib.save(foldername+'fig6-U_Axis-Mag={0}.tex'.format(magnitude))
plt.savefig(foldername+'fig6-U_Axis-Mag={0}.pdf'.format(magnitude))
# plt.savefig(foldername+'fig6-U_Axis-Mag={0}.pgf'.format(magnitude))
@staticmethod
def plotTrussRF(myBCs, a, q, threshold, stress_t, stress_c, tk, foldername=False):
""" Plot the ground stucture optimization solution efficency, defined as the percentage of the max charge """
nodes = myBCs.nodes
candidates = myBCs.ground_structure[a >= threshold]
fig, ax = plt.subplots()
plt.axis('off')
plt.axis('equal')
plt.title("Reserve Factor")
q[abs(q) < max(abs(q)) * 10e-3] = 0 # eliminates 0/0 cases
efficency = q[a >= threshold]/a[a >= threshold]
efficency[efficency > 0] /= stress_t
efficency[efficency < 0] /= stress_c
points = nodes[candidates[:, [0, 1]].astype(int), :].reshape(-1, 1, 2)
segments = np.concatenate([points[:-1:2], points[1::2]], axis=1)
ax.set_xlim(np.min(nodes[:,0]), np.max(nodes[:,0]+0.05*np.max(nodes[:,0])))
ax.set_ylim(np.min(nodes[:,1]), np.max(nodes[:,1]+0.05*np.max(nodes[:,1])))
norm = plt.Normalize(efficency.min(), efficency.max())
lc = mc.LineCollection(segments, cmap=Blue_mono, norm=norm)
lc.set_array(efficency)
lc.set_linewidth(a[a >= threshold] * tk)
line = ax.add_collection(lc)
fig.colorbar(line, ax=[ax], location='bottom', orientation="horizontal")
fig.tight_layout()
# optimized beams
if foldername == False:
plt.show()
else:
# tikzplotlib.save(foldername+'fig7-safety.tex')
plt.savefig(foldername+'fig7-safety.pdf')
# plt.savefig(foldername+'fig7-safety.pgf')
@staticmethod
def plotTrussStress(myBCs, a, q, threshold, s_t, s_c, tk, foldername=False):
""" Plot the ground stucture optimization solution stress """
nodes = myBCs.nodes
candidates = myBCs.ground_structure[a >= threshold]
fig, ax = plt.subplots()
plt.axis('off')
plt.axis('equal')
plt.title("ABS stress")
q = q[a >= threshold]
a = a[a >= threshold]
stress = q/a
# Round to a specified number of significant digits
significant_digits = 4
decimals = significant_digits - int(math.floor(math.log10(np.abs(np.max(stress))))) - 1
stress = np.around(stress, decimals=decimals)
points = nodes[candidates[:, [0, 1]].astype(int), :].reshape(-1, 1, 2)
segments = np.concatenate([points[:-1:2], points[1::2]], axis=1)
ax.set_xlim(np.min(nodes[:,0]), np.max(nodes[:,0]+0.05*np.max(nodes[:,0])))
ax.set_ylim(np.min(nodes[:,1]), np.max(nodes[:,1]+0.05*np.max(nodes[:,1])))
norm = plt.Normalize(s_c, s_t)
lc = mc.LineCollection(segments, cmap='coolwarm', norm=norm)
lc.set_array(stress[a >= threshold])
lc.set_linewidth(a[a >= threshold] * tk)
line = ax.add_collection(lc)
fig.colorbar(line, ax=[ax], location='bottom', orientation="horizontal")
if foldername == False:
plt.show()
else:
# tikzplotlib.save(foldername+'fig2-stress.tex')
plt.savefig(foldername+'fig2-stress.pdf')
# plt.savefig(foldername+'fig2-stress.pgf')
#Visualize initial truss
@staticmethod
def plotGroundStructure(myBCs, plot_nodes=False, foldername=False, load_case = -1, mag=0.1):
nodes = myBCs.nodes
candidates = myBCs.ground_structure
fig, ax = plt.subplots()
plt.axis('off')
plt.axis('equal')
plt.title("Starting Ground Structure - N. Elements = " + str(len(candidates)))
points = nodes[candidates[:, [0, 1]].astype(int), :].reshape(-1, 1, 2)
segments = np.concatenate([points[:-1:2], points[1::2]], axis=1)
lc = mc.LineCollection(segments, colors=accent_b_2)
ax.add_collection(lc)
if plot_nodes:
for i in range(len(segments)):
pos = nodes[candidates[i, [0, 1]].astype(int), :]
plt.scatter(pos[:, 0], pos[:, 1], c = accent_r_1, marker = 'o', edgecolors = 'none', zorder=100000, s=5) # enforce the scatter plot after the plot
ax.set_xlim(np.min(nodes[:,0]), np.max(nodes[:,0]+0.05*np.max(nodes[:,0])))
ax.set_ylim(np.min(nodes[:,1]), np.max(nodes[:,1]+0.05*np.max(nodes[:,1])))
# BCs
fixed_nodes = np.unique(myBCs.fixed_dofs // 2)
x,y = myBCs.nodes[fixed_nodes,:][:,[0,1]].T
ax.scatter(x,y, s=15, c=accent_b_1, alpha=1, zorder=2)
# Loads
if load_case != -1:
load_nodes = np.nonzero(myBCs.R[:,load_case])[0] // 2
x,y = myBCs.nodes[load_nodes,:][:,[0,1]].T
R = myBCs.R[:,load_case].copy()
else:
load_nodes = np.nonzero(myBCs.R)[0] // 2
x,y = myBCs.nodes[load_nodes,:][:,[0,1]].T
R = myBCs.R.copy()
magnit = R[R!=0]
direction = myBCs.force_dofs % 2
v = np.zeros((load_nodes.shape[0],2))
v[range(load_nodes.shape[0]),direction] = magnit
# normalization of v
v_norm = np.max(np.abs(myBCs.R))
v = v/v_norm * mag * np.max(myBCs.L)
ax.quiver(x, y, v[:,0], v[:,1], color='red', zorder=30, linewidth = 0.7)
fig.tight_layout()
if foldername == False:
plt.show()
else:
if load_case != -1:
plt.savefig(foldername+'fig0-GS-LC{:03d}.pdf'.format(load_case+1))
else:
plt.savefig(foldername+'fig0-GS.pdf')
@staticmethod
def plotTrussBucklingCheck(myBCs, a, forces, threshold, s_buck, tk, foldername=False):
""" Plot the ground stucture optimization solution """
nodes = myBCs.nodes
candidates = myBCs.ground_structure[a >= threshold,:]
q = forces[a >= threshold]
# Critical force
q_crit = -s_buck*a[a >= threshold]**2/myBCs.ground_structure_length[a >= threshold]**2
a = a[a >= threshold]
color = np.empty(a.size, dtype = object)
color[q<q_crit*1.01] = accent_r_1 # Buckled
color[q>q_crit*1.01] = 'grey' # Ok
fig, ax = plt.subplots()
plt.axis('off')
plt.axis('equal')
plt.title("Buckling check")
points = nodes[candidates[:, [0, 1]].astype(int), :].reshape(-1, 1, 2)
segments = np.concatenate([points[:-1:2], points[1::2]], axis=1)
# boundaries
if not myBCs.isLshape:
ax.set_xlim(np.min(nodes[:,0]), np.max(nodes[:,0]+0.05*np.max(nodes[:,0])))
ax.set_ylim(np.min(nodes[:,1]), np.max(nodes[:,1]+0.05*np.max(nodes[:,1])))
lc = mc.LineCollection(segments, colors = color)
lc.set_linewidth(a[a >= threshold] * tk)
ax.add_collection(lc)
fig.tight_layout()
if foldername == False:
plt.show()
else:
plt.savefig(foldername+'fig3-B_check.pdf')
@staticmethod
def plotTrussBuckling(myBCs, a, forces, threshold, s_buck, tk, foldername=False):
""" Plot the ground stucture optimization solution """
nodes = myBCs.nodes
candidates = myBCs.ground_structure[a >= threshold,:]
q = forces[a >= threshold]
# Critical force
q_crit = -s_buck*a[a >= threshold]**2/myBCs.ground_structure_length[a >= threshold]**2
buck = q/q_crit
buck[buck<0] = 0 # Member in tension cannot buckle
fig, ax = plt.subplots()
plt.axis('off')
plt.axis('equal')
plt.title("Buckling SF")
# boundaries
if not myBCs.isLshape:
ax.set_xlim(np.min(nodes[:,0]), np.max(nodes[:,0]+0.05*np.max(nodes[:,0])))
ax.set_ylim(np.min(nodes[:,1]), np.max(nodes[:,1]+0.05*np.max(nodes[:,1])))
points = nodes[candidates[:, [0, 1]].astype(int), :].reshape(-1, 1, 2)
segments = np.concatenate([points[:-1:2], points[1::2]], axis=1)
ax.set_xlim(np.min(nodes[:,0]), np.max(nodes[:,0]*1.05))
ax.set_ylim(np.min(nodes[:,1]), np.max(nodes[:,1]*1.05))
norm = plt.Normalize(0,1)
lc = mc.LineCollection(segments, cmap=Blue_mono, norm=norm)
lc.set_array(buck)
lc.set_linewidth(a[a >= threshold] * tk)
line = ax.add_collection(lc)
fig.colorbar(line, ax=[ax], location='bottom', orientation="horizontal")
fig.tight_layout()
if foldername == False:
plt.show()
else:
plt.savefig(foldername+'fig4-B.pdf')
########### Multiload
#Visualize truss
@staticmethod
def plotTruss_ML(myBCs, a, forces, threshold, vol, tk, foldername=False):
""" Plot the ground stucture optimization solution """
nodes = myBCs.nodes
candidates = myBCs.ground_structure
fig = plt.figure()
plt.clf()
plt.axis('off')
plt.axis('equal')
plt.title("Final Structure - Vol = %.3f" % (vol))
candidates = myBCs.ground_structure[a >= threshold,:]
q = forces[a >= threshold,:]
grey = np.prod(forces, axis=1)[a >= threshold]
a = a[a >= threshold]
c = np.empty(a.size, dtype = object)
tol = np.max(q) * 1e-04
c[:] = 'grey' # no force
c[(q[:,0]>tol) & (grey>tol)] = accent_r_1 # tension
c[(q[:,0]<-tol)& (grey>tol)] = accent_b_1 # compression
linewidth = a * tk
# boundaries
if not myBCs.isLshape:
plt.plot([0,0], [0, myBCs.L[1]], 'lightgray', linestyle="dotted", linewidth=0.2)
plt.plot([0, myBCs.L[0]], [myBCs.L[1], myBCs.L[1]], 'lightgray', linestyle="dotted", linewidth=0.2)
plt.plot([myBCs.L[0], myBCs.L[0]], [myBCs.L[1], 0], 'lightgray', linestyle="dotted", linewidth=0.2)
plt.plot([myBCs.L[0], 0], [0,0], 'lightgray', linestyle="dotted", linewidth=0.2)
# optimized beams
for i in range(len(a)):
pos = nodes[candidates[i, [0, 1]].astype(int), :]
plt.plot(pos[:, 0], pos[:, 1], c[i], linewidth = linewidth[i])
plt.scatter(pos[:, 0], pos[:, 1], c = 'black', marker = 'o', edgecolors = 'none', zorder=2) # enforce the scatter plot after the plot
fig.tight_layout()
if foldername == False:
plt.show()
else:
# tikzplotlib.save(foldername+'fig1-Topology.tex')
plt.savefig(foldername+'fig1-Topology.pgf')
plt.savefig(foldername+'fig1-Topology.pdf')
@staticmethod
def plotTrussMulti_ML(myBCs, a_unred, forces, threshold, tk, foldername=False):
""" Plot the ground stucture optimization solution stress """
nodes = myBCs.nodes
candidates = myBCs.ground_structure[a_unred >= threshold]
n_load_cases = forces.shape[-1]
for i in range(n_load_cases):
fig, ax = plt.subplots()
plt.axis('off')
plt.axis('equal')
q = forces[:,i]
q = q[a_unred >= threshold]
a = a_unred[a_unred >= threshold]
c = np.empty(a.size, dtype = object)
c[:] = 'darkgrey' # no force
c[(q>1e-5*max(q))] = accent_r_1 # tension
c[(q<1e-5*min(q))] = accent_b_1 # compression
linewidth = a * tk
points = nodes[candidates[:, [0, 1]].astype(int), :].reshape(-1, 1, 2)
segments = np.concatenate([points[:-1:2], points[1::2]], axis=1)
ax.set_xlim(np.min(nodes[:,0]), np.max(nodes[:,0]+0.05*np.max(nodes[:,0])))
ax.set_ylim(np.min(nodes[:,1]), np.max(nodes[:,1]+0.05*np.max(nodes[:,1])))
lc = mc.LineCollection(segments, colors=c)
lc.set_linewidth(linewidth)
line = ax.add_collection(lc)
if foldername == False:
plt.show()
else:
plt.savefig(foldername+'fig1-Topology-LC{:03d}.pdf'.format(i+1))
@staticmethod
def plotTrussStress_ML(myBCs, a_unred, forces, threshold, s_t, s_c, tk, foldername=False):
""" Plot the ground stucture optimization solution stress """
nodes = myBCs.nodes
candidates = myBCs.ground_structure[a_unred >= threshold]
n_load_cases = forces.shape[-1]
for i in range(n_load_cases):
fig, ax = plt.subplots()
plt.axis('off')
plt.axis('equal')
plt.title("ABS stress")
q = forces[:,i]
q = q[a_unred >= threshold]
a = a_unred[a_unred >= threshold]
stress = q/a
# Round to a specified number of significant digits
significant_digits = 4
decimals = significant_digits - int(math.floor(math.log10(np.abs(np.max(stress))))) - 1
stress = np.around(stress, decimals=decimals)
points = nodes[candidates[:, [0, 1]].astype(int), :].reshape(-1, 1, 2)
segments = np.concatenate([points[:-1:2], points[1::2]], axis=1)
ax.set_xlim(np.min(nodes[:,0]), np.max(nodes[:,0]+0.05*np.max(nodes[:,0])))
ax.set_ylim(np.min(nodes[:,1]), np.max(nodes[:,1]+0.05*np.max(nodes[:,1])))
norm = plt.Normalize(s_c, s_t)
lc = mc.LineCollection(segments, cmap='coolwarm', norm=norm)
lc.set_array(stress[a >= threshold])
lc.set_linewidth(a[a >= threshold] * tk)
line = ax.add_collection(lc)
fig.colorbar(line, ax=[ax], location='bottom', orientation="horizontal")
if foldername == False:
plt.show()
else:
plt.savefig(foldername+'fig2-stress-LC{:03d}.pdf'.format(i+1))
@staticmethod
def plotTrussBuckling_ML(myBCs, a_unred, forces, threshold, s_buck, tk, foldername=False):
""" Plot the ground stucture optimization solution stress """
nodes = myBCs.nodes
candidates = myBCs.ground_structure[a_unred >= threshold]
n_load_cases = forces.shape[-1]
for i in range(n_load_cases):
fig, ax = plt.subplots()
plt.axis('off')
plt.axis('equal')
plt.title("Buckling SF")
# Critical force
q = forces[:,i]
q = q[a_unred >= threshold]
a = a_unred[a_unred >= threshold]
q_crit = -s_buck*a**2/myBCs.ground_structure_length[a_unred >= threshold]**2
buck = q/q_crit
buck[buck<0] = 0 # Member in tension cannot buckle
points = nodes[candidates[:, [0, 1]].astype(int), :].reshape(-1, 1, 2)
segments = np.concatenate([points[:-1:2], points[1::2]], axis=1)
ax.set_xlim(np.min(nodes[:,0]), np.max(nodes[:,0]+0.05*np.max(nodes[:,0])))
ax.set_ylim(np.min(nodes[:,1]), np.max(nodes[:,1]+0.05*np.max(nodes[:,1])))
norm = plt.Normalize(0,1)
lc = mc.LineCollection(segments, cmap=Blue_mono, norm=norm)
lc.set_array(buck)
lc.set_linewidth(a * tk)
line = ax.add_collection(lc)
fig.colorbar(line, ax=[ax], location='bottom', orientation="horizontal")
if foldername == False:
plt.show()
else:
plt.savefig(foldername+'fig4-B-LC{:03d}.pdf'.format(i+1))
@classmethod
def plotRoutine(cls, myBCs, a, q, U, vol, stress_tension_max, stress_compression_max, tol, s_buck, obj_hist, obj_hist_LP, cellsEquals, foldername, LP, GIF, a_cell=False):
thick = 5 / max(a)
tol *= max(a)
if LP:
folder = foldername + '/LP/'
if not os.path.isdir(folder):
os.makedirs(folder)
else:
folder = foldername + '/'
cls.plotGroundStructure(myBCs, False, folder)
cls.plotTruss(myBCs, a, q, max(a) * tol, vol, thick, folder)
cls.plotTrussStress(myBCs, a, q, max(a) * tol, stress_tension_max, stress_compression_max, thick, folder)
if sum(U) != 0:
cls.plotTrussDeformation(myBCs, a, q, U, max(a) * tol, 1, folder, axis=False)
cls.plotTrussRF(myBCs, a, q, max(a) * tol, stress_tension_max, stress_compression_max, thick, folder)
if np.any(obj_hist) != False:
plotObjHistory(obj_hist, folder)
if np.any(obj_hist_LP) != False:
plotObjHistory_combined(obj_hist, obj_hist_LP, folder)
if GIF:
generateGIF(folder,'animation')
@classmethod
def plotRoutineBuckling(cls, myBCs, a, q, U, vol, stress_tension_max, stress_compression_max, tol, s_buck, obj_hist, obj_hist_LP, cellsEquals, foldername, LP, GIF, a_cell=False):
thick = 5 / max(a)
if LP:
folder = foldername + '/LP/'
if not os.path.isdir(folder):
os.makedirs(folder)
else:
folder = foldername + '/'
cls.plotGroundStructure(myBCs, True, folder)
cls.plotTruss(myBCs, a, q, max(a) * tol, vol, thick, folder)
cls.plotTrussStress(myBCs, a, q, max(a) * tol, stress_tension_max, stress_compression_max, thick, folder)
cls.plotTrussBucklingCheck(myBCs, a, q, max(a) * tol, s_buck, thick, folder)
cls.plotTrussBuckling(myBCs, a, q, max(a) * tol, s_buck, thick, folder)
if sum(U) != 0:
cls.plotTrussDeformation(myBCs, a, q, U, max(a) * tol, 1, thick, folder, axis=False)
cls.plotTrussRF(myBCs, a, q, max(a) * tol, stress_tension_max, stress_compression_max, thick, folder)
if np.any(obj_hist) != False:
plotObjHistory(obj_hist, folder)
if np.any(obj_hist_LP) != False:
plotObjHistory_combined(obj_hist, obj_hist_LP, folder)
if GIF:
generateGIF(folder,'animation')
@classmethod
def plotRoutineBuckling_ML(cls, myBCs, a, q, U, vol, stress_tension_max, stress_compression_max, tol,
s_buck, obj_hist, foldername, LP, GIF, obj_hist_LP=False,
eq_hist=False, s_c_hist=False, s_t_hist=False, comp_hist=False, buck_hist=False):
thick = 5 / max(a)
tol *= max(a)
if LP:
folder = foldername + '/LP/'
if not os.path.isdir(folder):
os.makedirs(folder)
else:
folder = foldername + '/'
n_load_cases = myBCs.R.shape[1]
for i in range(n_load_cases):
cls.plotGroundStructure(myBCs, foldername=folder, load_case=i, mag=0.1)
cls.plotTruss_ML(myBCs, a, q, tol, vol, thick, foldername=folder)
cls.plotTrussMulti_ML(myBCs, a, q, tol, thick, foldername=folder)
cls.plotTrussStress_ML(myBCs, a, q, tol, stress_tension_max, stress_compression_max, thick, foldername=folder)
cls.plotTrussBuckling_ML(myBCs, a, q, tol, s_buck, thick, foldername=folder)
if np.sum(U[:]) != 0:
cls.plotTrussDeformation(myBCs, a, q, U, tol, 1, thick, foldername=folder, axis=False)
if np.any(obj_hist) != False:
plotObjHistory(obj_hist, foldername=folder)
if np.any(eq_hist) != False:
plotConstHistory(eq_hist, s_c_hist, s_t_hist, comp_hist, buck_hist, folder)
if np.any(obj_hist_LP) != False:
plotObjHistory_combined(obj_hist, obj_hist_LP, folder)
if GIF:
generateGIF(folder+'gif_tmp_top','topology')
############################
# 3D plotting
############################
class plot3D():
# Visualize truss
@staticmethod
def plotTruss(myBCs, a, forces, threshold, vol, tk, foldername = False, gif=False):
""" Plot the ground stucture optimization solution """
nodes = myBCs.nodes
candidates = myBCs.ground_structure[a >= threshold,:]
q = forces[a >= threshold]
a = a[a >= threshold]
color = np.empty(a.size, dtype = object)
fig = plt.figure()
ax = fig.add_subplot(projection='3d', proj_type = 'ortho')
plt.axis('off')
plt.title("Final Structure - Vol = %.3f" % (vol))
# optimized beams
tol = np.max(q) * 1e-04
color[:] = 'grey' # no force
color[q>tol] = accent_r_1 # tension
color[q<-tol] = accent_b_1 # compression
linewidth = a * tk
points = nodes[candidates[:, [0, 1]].astype(int), :][:,:,[0,1,2]].reshape(-1, 1, 3)
# Normalization to [0-Dim]
points[:,:,0] = (points[:,:,0] - np.min(points[:,:,0]))
points[:,:,1] = (points[:,:,1] - np.min(points[:,:,1]))
points[:,:,2] = (points[:,:,2] - np.min(points[:,:,2]))
segments = np.concatenate([points[:-1:2], points[1::2]], axis=1)
lc = Line3DCollection(segments, colors = color)
lc.set_linewidth(linewidth)
ax.add_collection3d(lc, zs=nodes[:,2], zdir='z')
xx = myBCs.L[0]
yy = myBCs.L[1]
zz = myBCs.L[2]
#draw cube
r1 = [0, xx]
r2 = [0, yy]
r3 = [0, zz]
for s, e in combinations(np.array(list(product(r1,r2,r3))), 2):
s=np.array(s)
e=np.array(e)
if np.linalg.norm(s-e) == r1[1] or np.linalg.norm(s-e) == r2[1] or np.linalg.norm(s-e) == r3[1]:
ax.plot3D(*zip(s,e), color="lightgrey", linestyle="dotted", linewidth=0.2)
ax.set_xlim([0, myBCs.L[0]*1.05])
ax.set_ylim([0, myBCs.L[1]*1.05])
ax.set_zlim([0, myBCs.L[2]*1.05])
ax.set_box_aspect((myBCs.L[0]*1.05,myBCs.L[1]*1.05,myBCs.L[2]*1.05))
fig.tight_layout()
if foldername!=False:
plt.savefig(foldername+'fig1-Topology.pdf')
# Orthogonal views
plt.title(' ')
ax.view_init(azim=0, elev=0) # x-z plane
plt.savefig(foldername+'fig1-Topology_xz.pdf')
ax.view_init(azim=-90, elev=90) # x-y plane
plt.savefig(foldername+'fig1-Topology_xy.pdf')
ax.view_init(azim=-90, elev=0) # y-z plane
plt.savefig(foldername+'fig1-Topology_yz.pdf')
ax.view_init(azim=-70, elev=30) # view 1
plt.savefig(foldername+'fig1-Topology_ortho1.pdf')
ax.view_init(azim=70, elev=30) # view 1
plt.savefig(foldername+'fig1-Topology_ortho2.pdf')
else:
plt.show()
if gif:
fig.tight_layout()
plt.title(' ')
if not os.path.isdir(foldername+'/'+'gif_tmp_top'):
os.makedirs(foldername+'/'+'gif_tmp_top')
for ii in range(0,360,2):
ax.view_init(elev=25., azim=ii)
plt.savefig(foldername+'/'+'gif_tmp_top'+'/'+'gif{0:03d}.png'.format(ii), dpi=300)
# Visualize the reserve factor
@staticmethod
def plotTrussRF(myBCs, a, q, threshold, stress_t, stress_c, tk, foldername):
""" Plot the ground stucture optimization solution reserve factor, defined as the percentage of the max charge """
nodes = myBCs.nodes
candidates = myBCs.ground_structure[a >= threshold]
fig = plt.figure()
ax = fig.add_subplot(projection='3d')
plt.axis('off')
plt.title("Reserve factor")
q = q[a >= threshold]
a = a[a >= threshold]
q[abs(q) < max(abs(q)) * 10e-3] = 0 # eliminates 0/0 cases
efficency = q/a
efficency[efficency > 0] /= stress_t
efficency[efficency < 0] /= stress_c
points = nodes[candidates[:, [0, 1]].astype(int), :][:,:,[0,1,2]].reshape(-1, 1, 3)
segments = np.concatenate([points[:-1:2], points[1::2]], axis=1)
norm = plt.Normalize(efficency.min(), efficency.max())
lc = Line3DCollection(segments, cmap='RdYlGn', norm=norm)
lc.set_array(efficency[a >= threshold])
lc.set_linewidth(a[a >= threshold] * tk)
line = ax.add_collection(lc)
fig.colorbar(line, ax=ax)
ax.set_xlim([0, myBCs.L[0]*1.05])
ax.set_ylim([0, myBCs.L[1]*1.05])
ax.set_zlim([0, myBCs.L[2]*1.05])
ax.set_box_aspect((myBCs.L[0],myBCs.L[1],myBCs.L[2]))
fig.tight_layout()
# optimized beams
plt.savefig(foldername+'fig7-safety.pdf')
# Visualize the stress
@staticmethod
def plotTrussStress(myBCs, a, q, threshold, tk, foldername = False):
""" Plot the ground stucture optimization solution stress """
nodes = myBCs.nodes
candidates = myBCs.ground_structure[a >= threshold]
fig = plt.figure()
ax = fig.add_subplot(projection='3d', proj_type = 'ortho')
plt.axis('off')
plt.title("Stress plot [MPa]")
q = q[a >= threshold]
a = a[a >= threshold]
stress = q/a
# Round to a specified number of significant digits
significant_digits = 4
decimals = significant_digits - int(math.floor(math.log10(np.abs(np.max(stress))))) - 1
stress = np.around(stress, decimals=decimals)
points = nodes[candidates[:, [0, 1]].astype(int), :][:,:,[0,1,2]].reshape(-1, 1, 3)
segments = np.concatenate([points[:-1:2], points[1::2]], axis=1)
norm = plt.Normalize(stress.min(), stress.max())
lc = Line3DCollection(segments, cmap='coolwarm', norm=norm)
lc.set_array(stress)
lc.set_linewidth(a * tk)
line = ax.add_collection(lc)
fig.colorbar(line, ax=[ax], location='bottom', orientation="horizontal", fraction=0.046)
ax.set_xlim([0, myBCs.L[0]*1.05])
ax.set_ylim([0, myBCs.L[1]*1.05])
ax.set_zlim([0, myBCs.L[2]*1.05])
ax.set_box_aspect((myBCs.L[0],myBCs.L[1],myBCs.L[2]))
ax.view_init(azim=-70, elev=30) # view 1
# optimized beams
if foldername!=False:
plt.savefig(foldername+'fig2-stress.pdf')
else:
plt.show()
# Visualize only the different cell topologies
@staticmethod
def PlotTrussCellule(myBCs, a_cell, threshold, tk, foldername, axis, gif):
""" Plot the ground stucture optimization cell solution """
nodes = myBCs.nodes
topol = a_cell.shape[0]
xx = myBCs.cell_size[0]
yy = myBCs.cell_size[1]
zz = myBCs.cell_size[2]
for i in np.arange(topol):
if not np.any(myBCs.ground_stucture_list_cell[i]):
continue
if myBCs.isReduced:
cellule = []
for l in myBCs.ground_stucture_list_cell[i]:
a = np.array(myBCs.ground_stucture_list_not_reduced).tolist() # neded because compatibility problem between iterators and lists
cellule.append(a.index(l))
mask = a_cell[i][:len(cellule)] >= threshold
candidates = myBCs.ground_structure_not_reduced[cellule][mask]
else:
cellule = [myBCs.ground_stucture_list.index(l) for l in myBCs.ground_stucture_list_cell]
candidates = myBCs.ground_structure[cellule][a_cell[i] >= threshold]
a_plot = a_cell[i][a_cell[i] >= threshold]
# checking whether Numpy array is empty
if not np.any(a_plot):
continue
color = np.empty(a_plot.size, dtype = object)
color[:] = 'black'
fig = plt.figure()
ax = fig.add_subplot(projection='3d', proj_type = 'ortho')
if not axis:
plt.axis('off')
else:
ax.set_xlabel('X axis [mm]',)
ax.set_ylabel('Y axis [mm]')
ax.set_zlabel('Z axis [mm]')
plt.title("Final cell topology {0}".format(i+1))
linewidth = a_plot * tk
if myBCs.isReduced:
points = myBCs.nodes_not_reduced[candidates[:, [0, 1]].astype(int), :][:,:,[0,1,2]].reshape(-1, 1, 3)
# Normalization to [0-cellDim]
points[:,:,0] = (points[:,:,0] - np.min(points[:,:,0])) * xx/np.max(points[:,:,0] - np.min(points[:,:,0]))
points[:,:,1] = (points[:,:,1] - np.min(points[:,:,1])) * yy/np.max(points[:,:,1] - np.min(points[:,:,1]))
points[:,:,2] = (points[:,:,2] - np.min(points[:,:,2])) * zz/np.max(points[:,:,2] - np.min(points[:,:,2]))
else:
points = nodes[candidates[:, [0, 1]].astype(int), :][:,:,[0,1,2]].reshape(-1, 1, 3)
# Normalization to [0-cellDim]
points[:,:,0] = (points[:,:,0] - np.min(points[:,:,0])) * xx/np.max(points[:,:,0] - np.min(points[:,:,0]))
points[:,:,1] = (points[:,:,1] - np.min(points[:,:,1])) * yy/np.max(points[:,:,1] - np.min(points[:,:,1]))
points[:,:,2] = (points[:,:,2] - np.min(points[:,:,2])) * zz/np.max(points[:,:,2] - np.min(points[:,:,2]))
segments = np.concatenate([points[:-1:2], points[1::2]], axis=1)
lc = Line3DCollection(segments, colors = color)
lc.set_linewidth(linewidth)
ax.add_collection3d(lc)
ax.set_frame_on(True)
ax.set_xlim([min(points[:,:,0]), max(points[:,:,0]*1.05)])
ax.set_ylim([min(points[:,:,1]), max(points[:,:,1]*1.05)])
ax.set_zlim([min(points[:,:,2]), max(points[:,:,2]*1.05)])
ax.set_box_aspect((xx,yy,zz))
#draw cube
r1 = [0, xx]
r2 = [0, yy]
r3 = [0, zz]
for s, e in combinations(np.array(list(product(r1,r2,r3))), 2):
s=np.array(s)
e=np.array(e)
if np.linalg.norm(s-e) == r1[1] or np.linalg.norm(s-e) == r2[1] or np.linalg.norm(s-e) == r3[1]:
ax.plot3D(*zip(s,e), color="lightblue", linestyle="dotted")
if not axis:
fig.tight_layout()
plt.savefig(foldername+'fig8-{:03d}_Cell-noAx.pdf'.format(i))
# Orthogonal views
plt.title(' ')
ax.view_init(azim=0, elev=0) # x-z plane
plt.savefig(foldername+'fig8-{:03d}_Cell_xz.pdf'.format(i))
ax.view_init(azim=-90, elev=90) # x-y plane
plt.savefig(foldername+'fig8-{:03d}_Cell_xy.pdf'.format(i))
ax.view_init(azim=-90, elev=0) # y-z plane
plt.savefig(foldername+'fig8-{:03d}_Cell_yz.pdf'.format(i))
ax.view_init(azim=-70, elev=30) # view 1
plt.savefig(foldername+'fig8-{:03d}_Cell_ortho1.pdf'.format(i))
ax.view_init(azim=70, elev=30) # view 2
plt.savefig(foldername+'fig8-{:03d}_Cell_ortho2.pdf'.format(i))
else:
plt.savefig(foldername+'fig9-{:03d}_Cell-Ax.pdf'.format(i))
if gif and not axis:
fig.tight_layout()
plt.title(' ')
if not os.path.isdir(foldername+'/'+'gif_tmp_cell_{:03d}'.format(i)):
os.makedirs(foldername+'/'+'gif_tmp_cell_{:03d}'.format(i))
for ii in range(0,360,2):
ax.view_init(elev=10., azim=ii)
plt.savefig(foldername+'/'+'gif_tmp_cell_{:03d}'.format(i)+'/'+'gif{0:03d}.png'.format(ii), dpi=300)
# Visualize only the different cell topologies
@staticmethod
def PlotTrussCellule_Free_form(myBCs, a, threshold, tk, foldername, axis, gif):
""" Plot the ground stucture optimization cell solution """
topologies = np.unique(myBCs.ground_structure[:,2]) # List the different types of topologies of the structure
for ID, top_ID in np.ndenumerate(topologies): # Evaluate the hull dimensions
ID = ID[0]
if top_ID == 1:
xx,yy,zz = myBCs.cell_size
elif top_ID == 2:
xx,yy,zz = myBCs.L
xx /= myBCs.number_section
elif top_ID == 3:
xx,yy,zz = myBCs.L
else:
break
# Evaluate the setions to plot
a_plot = a[(myBCs.ground_structure[:,2]==top_ID) & (myBCs.ground_structure[:,3]==0)]
a_plot = a_plot[a_plot>threshold]
candidates = myBCs.ground_structure[(myBCs.ground_structure[:,2]==top_ID) & (myBCs.ground_structure[:,3]==0),:2] # Start and end nodes of the candidates of the top_ID topology to plot
nodes = myBCs.nodes
points = nodes[candidates[:, [0, 1]].astype(int), :][:,:,[0,1,2]].reshape(-1, 1, 3)
# Normalization to [0-cellDim]
points[:,:,0] = (points[:,:,0] - np.min(points[:,:,0])) * xx/np.max(points[:,:,0] - np.min(points[:,:,0]))
points[:,:,1] = (points[:,:,1] - np.min(points[:,:,1])) * yy/np.max(points[:,:,1] - np.min(points[:,:,1]))
points[:,:,2] = (points[:,:,2] - np.min(points[:,:,2])) * zz/np.max(points[:,:,2] - np.min(points[:,:,2]))
segments = np.concatenate([points[:-1:2], points[1::2]], axis=1)
color = np.empty(a_plot.size, dtype = object)
color[:] = 'black'
fig = plt.figure()
ax = fig.add_subplot(projection='3d', proj_type = 'ortho')
if not axis:
plt.axis('off')
else:
ax.set_xlabel('X axis [mm]',)
ax.set_ylabel('Y axis [mm]')
ax.set_zlabel('Z axis [mm]')
plt.title("Final cell topology {0}".format(ID+1))
linewidth = a_plot * tk
lc = Line3DCollection(segments, colors = color)
lc.set_linewidth(linewidth)
ax.add_collection3d(lc)
ax.set_frame_on(True)
ax.set_xlim([min(points[:,:,0]), max(points[:,:,0]*1.05)])
ax.set_ylim([min(points[:,:,1]), max(points[:,:,1]*1.05)])
ax.set_zlim([min(points[:,:,2]), max(points[:,:,2]*1.05)])
ax.set_box_aspect((xx,yy,zz))
# Draw hull
r1 = [0, xx]
r2 = [0, yy]
r3 = [0, zz]
for s, e in combinations(np.array(list(product(r1,r2,r3))), 2):
s=np.array(s)
e=np.array(e)
if np.linalg.norm(s-e) == r1[1] or np.linalg.norm(s-e) == r2[1] or np.linalg.norm(s-e) == r3[1]:
ax.plot3D(*zip(s,e), color="lightblue", linestyle="dotted")
if not axis:
fig.tight_layout()
plt.savefig(foldername+'fig8-{:03d}_Cell-noAx.pdf'.format(ID))
# Orthogonal views
plt.title(' ')
ax.view_init(azim=0, elev=0) # x-z plane
plt.savefig(foldername+'fig8-{:03d}_Cell_xz.pdf'.format(ID))
ax.view_init(azim=-90, elev=90) # x-y plane
plt.savefig(foldername+'fig8-{:03d}_Cell_xy.pdf'.format(ID))
ax.view_init(azim=-90, elev=0) # y-z plane
plt.savefig(foldername+'fig8-{:03d}_Cell_yz.pdf'.format(ID))
ax.view_init(azim=-70, elev=30) # view 1
plt.savefig(foldername+'fig8-{:03d}_Cell_ortho1.pdf'.format(ID))
ax.view_init(azim=70, elev=30) # view 2
plt.savefig(foldername+'fig8-{:03d}_Cell_ortho2.pdf'.format(ID))
else:
plt.savefig(foldername+'fig9-{:03d}_Cell-Ax.pdf'.format(ID))
if gif and not axis:
fig.tight_layout()
plt.title(' ')
if not os.path.isdir(foldername+'/'+'gif_tmp_cell_{:03d}'.format(ID)):
os.makedirs(foldername+'/'+'gif_tmp_cell_{:03d}'.format(ID))
for ii in range(0,360,2):
ax.view_init(elev=10., azim=ii)
plt.savefig(foldername+'/'+'gif_tmp_cell_{:03d}'.format(ID)+'/'+'gif{0:03d}.png'.format(ii), dpi=300)
#Visualize initial truss
@staticmethod
def plotGroundStructure(myBCs, foldername, load_case = -1, mag=0.1):
nodes = myBCs.nodes
candidates = myBCs.ground_structure
fig = plt.figure()
ax = fig.add_subplot(projection='3d', computed_zorder=False)
plt.axis('off')
plt.title("Starting Ground Structure - N. Elements = " + str(len(candidates)))
points = nodes[candidates[:, [0, 1]].astype(int), :][:,:,[0,1,2]].reshape(-1, 1, 3)
segments = np.concatenate([points[:-1:2], points[1::2]], axis=1)
lc = Line3DCollection(segments, linewidths = 0.3)
ax.add_collection3d(lc, zs=nodes[:,2], zdir='z')
# BCs
fixed_nodes = np.unique(myBCs.fixed_dofs // 3)
x,y,z = myBCs.nodes[fixed_nodes,:][:,[0,1,2]].T
ax.scatter(x,y,z, s=10, c='black', alpha=1, zorder=0.5)
# Loads
load_nodes = myBCs.force_dofs // 3
x,y,z = myBCs.nodes[load_nodes,:][:,[0,1,2]].T
if load_case != -1:
R = myBCs.R[:,load_case].copy()
else:
R = myBCs.R.copy()
magnit = R[R!=0]
direction = myBCs.force_dofs % 3
v = np.zeros((load_nodes.shape[0],3))
v[range(load_nodes.shape[0]),direction] = magnit
# normalization of v
v_norm = np.max(np.abs(myBCs.R))
v = v/v_norm * mag * np.max(myBCs.L)
ax.quiver(x, y, z, v[:,0], v[:,1], v[:,2], color='red', zorder=30, linewidth = 0.7)
#ax.scatter(x, y, z, s=200, c="red", zorder=20)
ax.set_xlim([0, myBCs.L[0]*1.05])
ax.set_ylim([0, myBCs.L[1]*1.05])
ax.set_zlim([0, myBCs.L[2]*1.05])
ax.set_box_aspect((myBCs.L[0],myBCs.L[1],myBCs.L[2]))