Note
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Solve a 2D MBB topology optimization problem#
from __future__ import annotations
from gemseo import configure_logger
from gemseo import create_scenario
from gemseo.problems.topology_optimization.topopt_initialize import (
initialize_design_space_and_discipline_to,
)
configure_logger()
<RootLogger root (INFO)>
Setup the topology optimization problem#
Define the target volume fraction:
volume_fraction = 0.3
Define the problem type:
problem_name = "MBB"
Define the number of elements in x- and y- directions:
n_x = 50
n_y = 25
Define the full material Young's modulus and the 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 an MDOScenario
scenario = create_scenario(
disciplines,
"compliance",
design_space,
formulation_name="DisciplinaryOpt",
)
Add the volume fraction constraint to the scenario:
scenario.add_constraint(
"volume fraction", constraint_type="ineq", value=volume_fraction
)
Generate the XDSM
scenario.xdsmize(save_html=False, pdf_build=False)
Execute the scenario
scenario.execute(algo_name="NLOPT_MMA", max_iter=200)
INFO - 08:37:58:
INFO - 08:37:58: *** Start MDOScenario execution ***
INFO - 08:37:58: MDOScenario
INFO - 08:37:58: Disciplines: DensityFilter FiniteElementAnalysis MaterialModelInterpolation VolumeFraction
INFO - 08:37:58: MDO formulation: DisciplinaryOpt
INFO - 08:37:58: Optimization problem:
INFO - 08:37:58: minimize compliance(x)
INFO - 08:37:58: with respect to x
INFO - 08:37:58: subject to constraints:
INFO - 08:37:58: volume fraction(x) <= 0.3
INFO - 08:37:58: Solving optimization problem with algorithm NLOPT_MMA:
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INFO - 08:38:03: 92%|█████████▏| 183/200 [00:04<00:00, 38.94 it/sec, obj=170]
INFO - 08:38:03: 92%|█████████▏| 184/200 [00:04<00:00, 38.95 it/sec, obj=170]
INFO - 08:38:03: 92%|█████████▎| 185/200 [00:04<00:00, 38.97 it/sec, obj=170]
INFO - 08:38:03: 93%|█████████▎| 186/200 [00:04<00:00, 38.99 it/sec, obj=170]
INFO - 08:38:03: 94%|█████████▎| 187/200 [00:04<00:00, 39.00 it/sec, obj=170]
INFO - 08:38:03: 94%|█████████▍| 188/200 [00:04<00:00, 39.00 it/sec, obj=170]
INFO - 08:38:03: 94%|█████████▍| 189/200 [00:04<00:00, 39.01 it/sec, obj=170]
INFO - 08:38:03: 95%|█████████▌| 190/200 [00:04<00:00, 39.02 it/sec, obj=170]
INFO - 08:38:03: 96%|█████████▌| 191/200 [00:04<00:00, 39.03 it/sec, obj=170]
INFO - 08:38:03: 96%|█████████▌| 192/200 [00:04<00:00, 39.04 it/sec, obj=170]
INFO - 08:38:03: 96%|█████████▋| 193/200 [00:04<00:00, 39.05 it/sec, obj=170]
INFO - 08:38:03: 97%|█████████▋| 194/200 [00:04<00:00, 39.05 it/sec, obj=170]
INFO - 08:38:03: 98%|█████████▊| 195/200 [00:04<00:00, 39.06 it/sec, obj=170]
INFO - 08:38:03: 98%|█████████▊| 196/200 [00:05<00:00, 39.06 it/sec, obj=170]
INFO - 08:38:03: 98%|█████████▊| 197/200 [00:05<00:00, 39.07 it/sec, obj=170]
INFO - 08:38:03: 99%|█████████▉| 198/200 [00:05<00:00, 39.07 it/sec, obj=170]
INFO - 08:38:03: 100%|█████████▉| 199/200 [00:05<00:00, 39.08 it/sec, obj=170]
INFO - 08:38:03: 100%|██████████| 200/200 [00:05<00:00, 39.24 it/sec, obj=170]
INFO - 08:38:03: Optimization result:
INFO - 08:38:03: Optimizer info:
INFO - 08:38:03: Status: None
INFO - 08:38:03: Message: Maximum number of iterations reached. GEMSEO stopped the driver.
INFO - 08:38:03: Number of calls to the objective function by the optimizer: 201
INFO - 08:38:03: Solution:
INFO - 08:38:03: The solution is feasible.
INFO - 08:38:03: Objective: 169.89161468983534
INFO - 08:38:03: Standardized constraints:
INFO - 08:38:03: [volume fraction-0.3] = -4.312432086428508e-07
INFO - 08:38:03: *** End MDOScenario execution (time: 0:00:05.102675) ***
Results#
Post-process the optimization history:
scenario.post_process(
post_name="BasicHistory", variable_names=["compliance"], show=True, save=False
)
/home/docs/checkouts/readthedocs.org/user_builds/gemseo/envs/6.0.0/lib/python3.9/site-packages/gemseo/datasets/dataset.py:482: PerformanceWarning: DataFrame is highly fragmented. This is usually the result of calling `frame.insert` many times, which has poor performance. Consider joining all columns at once using pd.concat(axis=1) instead. To get a de-fragmented frame, use `newframe = frame.copy()`
self[columns] = value
<gemseo.post.basic_history.BasicHistory object at 0x7f6dc829b310>
Plot the solution
scenario.post_process(post_name="TopologyView", n_x=n_x, n_y=n_y, show=True, save=False)
<gemseo.post.topology_view.TopologyView object at 0x7f6dc829b850>
Total running time of the script: (0 minutes 5.968 seconds)