# Solve a 2D L-shape 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 fractio:

volume_fraction = 0.3


Define the problem type:

problem_name = "L-Shape"


Define the number of elements in the x- and y- directions:

n_x = 25
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_member_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_member_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 - 07:15:20: Generating HTML XDSM file in : xdsm.html


Execute the scenario

scenario.execute({"max_iter": 200, "algo": "NLOPT_MMA"})


Out:

    INFO - 07:15:20:
INFO - 07:15:20: *** Start MDOScenario execution ***
INFO - 07:15:20: MDOScenario
INFO - 07:15:20:    Disciplines: DensityFilter MaterialModelInterpolation FininiteElementAnalysis VolumeFraction
INFO - 07:15:20:    MDO formulation: DisciplinaryOpt
INFO - 07:15:20: Optimization problem:
INFO - 07:15:20:    minimize compliance(x)
INFO - 07:15:20:    with respect to x
INFO - 07:15:20:    subject to constraints:
INFO - 07:15:20:       volume fraction(x) <= 0.3
INFO - 07:15:20: Solving optimization problem with algorithm NLOPT_MMA:
INFO - 07:15:20: ...   0%|          | 0/200 [00:00<?, ?it]
INFO - 07:15:20: ...   1%|          | 2/200 [00:00<00:00, 1956.06 it/sec]
INFO - 07:15:20: ...   2%|▎         | 5/200 [00:00<00:00, 861.65 it/sec]
INFO - 07:15:20: ...   4%|▍         | 8/200 [00:00<00:00, 547.03 it/sec]
INFO - 07:15:21: ...   6%|▌         | 11/200 [00:00<00:00, 400.46 it/sec]
INFO - 07:15:21: ...   7%|▋         | 14/200 [00:00<00:00, 317.42 it/sec]
INFO - 07:15:21: ...   8%|▊         | 17/200 [00:00<00:00, 263.79 it/sec]
INFO - 07:15:21: ...  10%|█         | 20/200 [00:00<00:00, 226.18 it/sec]
INFO - 07:15:21: ...  12%|█▏        | 23/200 [00:01<00:00, 198.04 it/sec]
INFO - 07:15:21: ...  13%|█▎        | 26/200 [00:01<00:00, 176.22 it/sec]
INFO - 07:15:21: ...  14%|█▍        | 29/200 [00:01<00:01, 158.82 it/sec]
INFO - 07:15:21: ...  16%|█▌        | 32/200 [00:01<00:01, 144.60 it/sec]
INFO - 07:15:22: ...  18%|█▊        | 35/200 [00:01<00:01, 132.89 it/sec]
INFO - 07:15:22: ...  19%|█▉        | 38/200 [00:01<00:01, 122.85 it/sec]
INFO - 07:15:22: ...  20%|██        | 41/200 [00:01<00:01, 114.17 it/sec]
INFO - 07:15:22: ...  22%|██▏       | 44/200 [00:01<00:01, 106.56 it/sec]
INFO - 07:15:22: ...  24%|██▎       | 47/200 [00:02<00:01, 99.96 it/sec]
INFO - 07:15:22: ...  25%|██▌       | 50/200 [00:02<00:01, 94.39 it/sec]
INFO - 07:15:22: ...  26%|██▋       | 53/200 [00:02<00:01, 89.29 it/sec]
INFO - 07:15:22: ...  28%|██▊       | 56/200 [00:02<00:01, 84.65 it/sec]
INFO - 07:15:23: ...  30%|██▉       | 59/200 [00:02<00:01, 80.50 it/sec]
INFO - 07:15:23: ...  31%|███       | 62/200 [00:02<00:01, 76.74 it/sec]
INFO - 07:15:23: ...  32%|███▎      | 65/200 [00:02<00:01, 73.30 it/sec]
INFO - 07:15:23: ...  34%|███▍      | 68/200 [00:02<00:01, 70.15 it/sec]
INFO - 07:15:23: ...  36%|███▌      | 71/200 [00:02<00:01, 67.22 it/sec]
INFO - 07:15:23: ...  37%|███▋      | 74/200 [00:03<00:01, 64.59 it/sec]
INFO - 07:15:23: ...  38%|███▊      | 77/200 [00:03<00:01, 62.18 it/sec]
INFO - 07:15:23: ...  40%|████      | 80/200 [00:03<00:02, 59.94 it/sec]
INFO - 07:15:24: ...  42%|████▏     | 83/200 [00:03<00:02, 57.87 it/sec]
INFO - 07:15:24: ...  43%|████▎     | 86/200 [00:03<00:02, 55.88 it/sec]
INFO - 07:15:24: ...  44%|████▍     | 89/200 [00:03<00:02, 54.07 it/sec]
INFO - 07:15:24: ...  46%|████▌     | 92/200 [00:03<00:02, 52.38 it/sec]
INFO - 07:15:24: ...  48%|████▊     | 95/200 [00:03<00:02, 50.80 it/sec]
INFO - 07:15:24: ...  49%|████▉     | 98/200 [00:04<00:02, 49.31 it/sec]
INFO - 07:15:24: ...  50%|█████     | 101/200 [00:04<00:02, 47.91 it/sec]
INFO - 07:15:24: ...  52%|█████▏    | 104/200 [00:04<00:02, 46.57 it/sec]
INFO - 07:15:24: ...  54%|█████▎    | 107/200 [00:04<00:02, 45.30 it/sec]
INFO - 07:15:25: ...  55%|█████▌    | 110/200 [00:04<00:02, 44.10 it/sec]
INFO - 07:15:25: ...  56%|█████▋    | 113/200 [00:04<00:02, 42.96 it/sec]
INFO - 07:15:25: ...  58%|█████▊    | 116/200 [00:04<00:02, 41.87 it/sec]
INFO - 07:15:25: ...  60%|█████▉    | 119/200 [00:04<00:01, 40.84 it/sec]
INFO - 07:15:25: ...  61%|██████    | 122/200 [00:05<00:01, 39.87 it/sec]
INFO - 07:15:25: ...  62%|██████▎   | 125/200 [00:05<00:01, 38.93 it/sec]
INFO - 07:15:25: ...  64%|██████▍   | 128/200 [00:05<00:01, 38.04 it/sec]
INFO - 07:15:25: ...  64%|██████▍   | 129/200 [00:05<00:01, 37.72 it/sec]
INFO - 07:15:25: Optimization result:
INFO - 07:15:25:    Optimizer info:
INFO - 07:15:25:       Status: None
INFO - 07:15:25:       Message: Successive iterates of the objective function are closer than ftol_rel or ftol_abs. GEMSEO Stopped the driver
INFO - 07:15:25:       Number of calls to the objective function by the optimizer: 129
INFO - 07:15:25:    Solution:
INFO - 07:15:25:       The solution is feasible.
INFO - 07:15:25:       Objective: 151.62873248988768
INFO - 07:15:25:       Standardized constraints:
INFO - 07:15:25:          volume fraction - 0.3 = 1.0969287427831098e-06
INFO - 07:15:25: *** End MDOScenario execution (time: 0:00:05.316237) ***

{'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 0x7f28f0e720d0>


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 5.832 seconds)

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