Note
Click here to download the full example code
Solve a 2D short cantilever topology optimization problem¶
import matplotlib.pyplot as plt
from gemseo.api import configure_logger
from gemseo.api import create_scenario
from gemseo.problems.topo_opt.topopt_initialize import (
initialize_design_space_and_discipline_to,
)
from matplotlib import colors
configure_logger()
Out:
<RootLogger root (INFO)>
Setup the topology optimization problem¶
Define the target volume fraction:
volume_fraction = 0.3
Define the problem type:
problem_name = "Short_Cantilever"
Define the number of elements in the x- and y- directions:
n_x = 50
n_y = 25
Define the full material Young’s modulus and Poisson’s ratio:
e0 = 1
nu = 0.3
Define the penalty of the SIMP approach:
penalty = 3
Define the minimum member size in the solution:
min_memeber_size = 1.5
Instantiate the DesignSpace and the disciplines:
design_space, disciplines = initialize_design_space_and_discipline_to(
problem=problem_name,
n_x=n_x,
n_y=n_y,
e0=e0,
nu=nu,
penalty=penalty,
min_member_size=min_memeber_size,
vf0=volume_fraction,
)
Solve the topology optimization problem¶
Generate a MDOScenario:
scenario = create_scenario(
disciplines,
formulation="DisciplinaryOpt",
objective_name="compliance",
design_space=design_space,
)
Add the volume fraction constraint to the scenario:
scenario.add_constraint("volume fraction", "ineq", value=volume_fraction)
Generate the XDSM:
scenario.xdsmize()
Out:
INFO - 07:15:36: Generating HTML XDSM file in : xdsm.html
Execute the scenario:
scenario.execute(input_data={"max_iter": 200, "algo": "NLOPT_MMA"})
Out:
INFO - 07:15:36:
INFO - 07:15:36: *** Start MDOScenario execution ***
INFO - 07:15:36: MDOScenario
INFO - 07:15:36: Disciplines: DensityFilter MaterialModelInterpolation FininiteElementAnalysis VolumeFraction
INFO - 07:15:36: MDO formulation: DisciplinaryOpt
INFO - 07:15:36: Optimization problem:
INFO - 07:15:36: minimize compliance(x)
INFO - 07:15:36: with respect to x
INFO - 07:15:36: subject to constraints:
INFO - 07:15:36: volume fraction(x) <= 0.3
INFO - 07:15:36: Solving optimization problem with algorithm NLOPT_MMA:
INFO - 07:15:36: ... 0%| | 0/200 [00:00<?, ?it]
INFO - 07:15:36: ... 1%| | 2/200 [00:00<00:00, 972.27 it/sec]
INFO - 07:15:37: ... 2%|▏ | 3/200 [00:00<00:00, 647.99 it/sec]
INFO - 07:15:37: ... 2%|▎ | 5/200 [00:00<00:00, 403.33 it/sec]
INFO - 07:15:37: ... 4%|▎ | 7/200 [00:00<00:00, 293.32 it/sec]
INFO - 07:15:37: ... 4%|▍ | 9/200 [00:00<00:00, 231.64 it/sec]
INFO - 07:15:37: ... 6%|▌ | 11/200 [00:01<00:00, 191.12 it/sec]
INFO - 07:15:37: ... 6%|▋ | 13/200 [00:01<00:01, 162.78 it/sec]
INFO - 07:15:38: ... 8%|▊ | 15/200 [00:01<00:01, 142.06 it/sec]
INFO - 07:15:38: ... 8%|▊ | 17/200 [00:01<00:01, 126.10 it/sec]
INFO - 07:15:38: ... 10%|▉ | 19/200 [00:01<00:01, 113.37 it/sec]
INFO - 07:15:38: ... 10%|█ | 21/200 [00:01<00:01, 103.06 it/sec]
INFO - 07:15:38: ... 12%|█▏ | 23/200 [00:02<00:01, 94.67 it/sec]
INFO - 07:15:39: ... 12%|█▎ | 25/200 [00:02<00:02, 87.43 it/sec]
INFO - 07:15:39: ... 14%|█▎ | 27/200 [00:02<00:02, 81.19 it/sec]
INFO - 07:15:39: ... 14%|█▍ | 29/200 [00:02<00:02, 75.97 it/sec]
INFO - 07:15:39: ... 16%|█▌ | 31/200 [00:02<00:02, 71.42 it/sec]
INFO - 07:15:39: ... 16%|█▋ | 33/200 [00:02<00:02, 67.40 it/sec]
INFO - 07:15:39: ... 18%|█▊ | 35/200 [00:03<00:02, 63.77 it/sec]
INFO - 07:15:40: ... 18%|█▊ | 37/200 [00:03<00:02, 60.57 it/sec]
INFO - 07:15:40: ... 20%|█▉ | 39/200 [00:03<00:02, 57.62 it/sec]
INFO - 07:15:40: ... 20%|██ | 41/200 [00:03<00:02, 54.94 it/sec]
INFO - 07:15:40: ... 22%|██▏ | 43/200 [00:03<00:02, 52.53 it/sec]
INFO - 07:15:40: ... 22%|██▎ | 45/200 [00:03<00:03, 50.32 it/sec]
INFO - 07:15:40: ... 24%|██▎ | 47/200 [00:04<00:03, 48.26 it/sec]
INFO - 07:15:41: ... 24%|██▍ | 49/200 [00:04<00:03, 46.35 it/sec]
INFO - 07:15:41: ... 26%|██▌ | 51/200 [00:04<00:03, 44.58 it/sec]
INFO - 07:15:41: ... 26%|██▋ | 53/200 [00:04<00:03, 42.97 it/sec]
INFO - 07:15:41: ... 28%|██▊ | 55/200 [00:04<00:03, 41.47 it/sec]
INFO - 07:15:41: ... 28%|██▊ | 57/200 [00:04<00:03, 40.08 it/sec]
INFO - 07:15:41: ... 30%|██▉ | 59/200 [00:05<00:03, 38.78 it/sec]
INFO - 07:15:42: ... 30%|███ | 61/200 [00:05<00:03, 37.56 it/sec]
INFO - 07:15:42: ... 32%|███▏ | 63/200 [00:05<00:03, 36.42 it/sec]
INFO - 07:15:42: ... 32%|███▎ | 65/200 [00:05<00:03, 35.34 it/sec]
INFO - 07:15:42: ... 34%|███▎ | 67/200 [00:05<00:03, 34.32 it/sec]
INFO - 07:15:42: ... 34%|███▍ | 69/200 [00:05<00:03, 33.38 it/sec]
INFO - 07:15:42: ... 36%|███▌ | 71/200 [00:06<00:03, 32.47 it/sec]
INFO - 07:15:43: ... 36%|███▋ | 73/200 [00:06<00:04, 31.61 it/sec]
INFO - 07:15:43: ... 38%|███▊ | 75/200 [00:06<00:04, 30.79 it/sec]
INFO - 07:15:43: ... 38%|███▊ | 77/200 [00:06<00:04, 30.02 it/sec]
INFO - 07:15:43: ... 40%|███▉ | 79/200 [00:06<00:04, 29.28 it/sec]
INFO - 07:15:43: ... 40%|████ | 81/200 [00:06<00:04, 28.58 it/sec]
INFO - 07:15:43: ... 42%|████▏ | 83/200 [00:07<00:04, 27.91 it/sec]
INFO - 07:15:44: ... 42%|████▎ | 85/200 [00:07<00:04, 27.28 it/sec]
INFO - 07:15:44: ... 44%|████▎ | 87/200 [00:07<00:04, 26.66 it/sec]
INFO - 07:15:44: ... 44%|████▍ | 89/200 [00:07<00:04, 26.09 it/sec]
INFO - 07:15:44: ... 46%|████▌ | 91/200 [00:07<00:04, 25.53 it/sec]
INFO - 07:15:44: ... 46%|████▋ | 93/200 [00:08<00:04, 25.00 it/sec]
INFO - 07:15:44: ... 48%|████▊ | 95/200 [00:08<00:04, 24.48 it/sec]
INFO - 07:15:45: ... 48%|████▊ | 97/200 [00:08<00:04, 23.99 it/sec]
INFO - 07:15:45: ... 50%|████▉ | 99/200 [00:08<00:04, 23.52 it/sec]
INFO - 07:15:45: ... 50%|█████ | 101/200 [00:08<00:04, 23.07 it/sec]
INFO - 07:15:45: ... 52%|█████▏ | 103/200 [00:08<00:04, 22.63 it/sec]
INFO - 07:15:45: ... 52%|█████▎ | 105/200 [00:09<00:04, 22.20 it/sec]
INFO - 07:15:45: ... 54%|█████▎ | 107/200 [00:09<00:04, 21.79 it/sec]
INFO - 07:15:46: ... 55%|█████▍ | 109/200 [00:09<00:04, 21.40 it/sec]
INFO - 07:15:46: ... 56%|█████▌ | 111/200 [00:09<00:04, 21.03 it/sec]
INFO - 07:15:46: ... 56%|█████▋ | 113/200 [00:09<00:04, 20.67 it/sec]
INFO - 07:15:46: ... 57%|█████▊ | 115/200 [00:09<00:04, 20.33 it/sec]
INFO - 07:15:46: ... 58%|█████▊ | 117/200 [00:10<00:04, 19.99 it/sec]
INFO - 07:15:46: ... 60%|█████▉ | 119/200 [00:10<00:04, 19.66 it/sec]
INFO - 07:15:47: ... 60%|██████ | 121/200 [00:10<00:04, 19.34 it/sec]
INFO - 07:15:47: ... 62%|██████▏ | 123/200 [00:10<00:04, 19.03 it/sec]
INFO - 07:15:47: ... 62%|██████▎ | 125/200 [00:10<00:04, 18.74 it/sec]
INFO - 07:15:47: ... 64%|██████▎ | 127/200 [00:10<00:03, 18.45 it/sec]
INFO - 07:15:47: ... 64%|██████▍ | 129/200 [00:11<00:03, 18.17 it/sec]
INFO - 07:15:47: ... 66%|██████▌ | 131/200 [00:11<00:03, 17.90 it/sec]
INFO - 07:15:48: ... 66%|██████▋ | 133/200 [00:11<00:03, 17.63 it/sec]
INFO - 07:15:48: ... 68%|██████▊ | 135/200 [00:11<00:03, 17.38 it/sec]
INFO - 07:15:48: ... 68%|██████▊ | 137/200 [00:11<00:03, 17.13 it/sec]
INFO - 07:15:48: ... 70%|██████▉ | 139/200 [00:11<00:03, 16.89 it/sec]
INFO - 07:15:48: ... 70%|███████ | 141/200 [00:12<00:03, 16.65 it/sec]
INFO - 07:15:48: ... 72%|███████▏ | 143/200 [00:12<00:03, 16.43 it/sec]
INFO - 07:15:49: ... 72%|███████▎ | 145/200 [00:12<00:03, 16.21 it/sec]
INFO - 07:15:49: ... 74%|███████▎ | 147/200 [00:12<00:03, 15.99 it/sec]
INFO - 07:15:49: ... 74%|███████▍ | 149/200 [00:12<00:03, 15.78 it/sec]
INFO - 07:15:49: ... 76%|███████▌ | 151/200 [00:12<00:03, 15.58 it/sec]
INFO - 07:15:49: ... 76%|███████▋ | 153/200 [00:13<00:03, 15.38 it/sec]
INFO - 07:15:49: ... 78%|███████▊ | 155/200 [00:13<00:02, 15.19 it/sec]
INFO - 07:15:50: ... 78%|███████▊ | 157/200 [00:13<00:02, 15.00 it/sec]
INFO - 07:15:50: ... 80%|███████▉ | 159/200 [00:13<00:02, 14.81 it/sec]
INFO - 07:15:50: ... 80%|████████ | 161/200 [00:13<00:02, 14.63 it/sec]
INFO - 07:15:50: ... 82%|████████▏ | 163/200 [00:13<00:02, 14.45 it/sec]
INFO - 07:15:50: ... 82%|████████▎ | 165/200 [00:14<00:02, 14.28 it/sec]
INFO - 07:15:50: ... 84%|████████▎ | 167/200 [00:14<00:02, 14.12 it/sec]
INFO - 07:15:51: ... 84%|████████▍ | 169/200 [00:14<00:02, 13.95 it/sec]
INFO - 07:15:51: ... 86%|████████▌ | 171/200 [00:14<00:02, 13.80 it/sec]
INFO - 07:15:51: ... 86%|████████▋ | 173/200 [00:14<00:01, 13.64 it/sec]
INFO - 07:15:51: ... 88%|████████▊ | 175/200 [00:14<00:01, 13.49 it/sec]
INFO - 07:15:51: ... 88%|████████▊ | 177/200 [00:14<00:01, 13.34 it/sec]
INFO - 07:15:51: ... 90%|████████▉ | 179/200 [00:15<00:01, 13.20 it/sec]
INFO - 07:15:52: ... 90%|█████████ | 181/200 [00:15<00:01, 13.05 it/sec]
INFO - 07:15:52: ... 92%|█████████▏| 183/200 [00:15<00:01, 12.91 it/sec]
INFO - 07:15:52: ... 92%|█████████▎| 185/200 [00:15<00:01, 12.78 it/sec]
INFO - 07:15:52: ... 93%|█████████▎| 186/200 [00:15<00:01, 12.71 it/sec]
INFO - 07:15:52: Optimization result:
INFO - 07:15:52: Optimizer info:
INFO - 07:15:52: Status: None
INFO - 07:15:52: Message: Successive iterates of the objective function are closer than ftol_rel or ftol_abs. GEMSEO Stopped the driver
INFO - 07:15:52: Number of calls to the objective function by the optimizer: 186
INFO - 07:15:52: Solution:
INFO - 07:15:52: The solution is feasible.
INFO - 07:15:52: Objective: 136.56131771172448
INFO - 07:15:52: Standardized constraints:
INFO - 07:15:52: volume fraction - 0.3 = -1.0460364907594055e-08
INFO - 07:15:52: *** End MDOScenario execution (time: 0:00:15.758134) ***
{'max_iter': 200, 'algo': 'NLOPT_MMA'}
Results¶
Post-process the optimization history:
scenario.post_process(
"BasicHistory",
variable_names=["compliance"],
save=True,
show=False,
file_name=problem_name + "_history.png",
)
Out:
<gemseo.post.basic_history.BasicHistory object at 0x7f28f0dddf10>
Plot the solution:
plt.ion() # Ensure that redrawing is possible
fig, ax = plt.subplots()
im = ax.imshow(
-scenario.optimization_result.x_opt.reshape((n_x, n_y)).T,
cmap="gray",
interpolation="none",
norm=colors.Normalize(vmin=-1, vmax=0),
)
fig.show()
im.set_array(-scenario.optimization_result.x_opt.reshape((n_x, n_y)).T)
fig.canvas.draw()
plt.savefig(problem_name + "_solution.png")
Total running time of the script: ( 0 minutes 16.370 seconds)