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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.topo_opt.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,
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()
Execute the scenario
scenario.execute(input_data={"max_iter": 200, "algo": "NLOPT_MMA"})
INFO - 10:56:23:
INFO - 10:56:23: *** Start MDOScenario execution ***
INFO - 10:56:23: MDOScenario
INFO - 10:56:23: Disciplines: DensityFilter FininiteElementAnalysis MaterialModelInterpolation VolumeFraction
INFO - 10:56:23: MDO formulation: DisciplinaryOpt
INFO - 10:56:23: Optimization problem:
INFO - 10:56:23: minimize compliance(x)
INFO - 10:56:23: with respect to x
INFO - 10:56:23: subject to constraints:
INFO - 10:56:23: volume fraction(x) <= 0.3
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INFO - 10:56:32: 92%|█████████▏| 184/200 [00:08<00:00, 21.79 it/sec, obj=170]
INFO - 10:56:32: 92%|█████████▎| 185/200 [00:08<00:00, 21.80 it/sec, obj=170]
INFO - 10:56:32: 93%|█████████▎| 186/200 [00:08<00:00, 21.80 it/sec, obj=170]
INFO - 10:56:32: 94%|█████████▎| 187/200 [00:08<00:00, 21.80 it/sec, obj=170]
INFO - 10:56:32: 94%|█████████▍| 188/200 [00:08<00:00, 21.81 it/sec, obj=170]
INFO - 10:56:32: 94%|█████████▍| 189/200 [00:08<00:00, 21.81 it/sec, obj=170]
INFO - 10:56:32: 95%|█████████▌| 190/200 [00:08<00:00, 21.81 it/sec, obj=170]
INFO - 10:56:32: 96%|█████████▌| 191/200 [00:08<00:00, 21.82 it/sec, obj=170]
INFO - 10:56:32: 96%|█████████▌| 192/200 [00:08<00:00, 21.82 it/sec, obj=170]
INFO - 10:56:32: 96%|█████████▋| 193/200 [00:08<00:00, 21.82 it/sec, obj=170]
INFO - 10:56:32: 97%|█████████▋| 194/200 [00:08<00:00, 21.82 it/sec, obj=170]
INFO - 10:56:32: 98%|█████████▊| 195/200 [00:08<00:00, 21.83 it/sec, obj=170]
INFO - 10:56:32: 98%|█████████▊| 196/200 [00:08<00:00, 21.83 it/sec, obj=170]
INFO - 10:56:32: 98%|█████████▊| 197/200 [00:09<00:00, 21.84 it/sec, obj=170]
INFO - 10:56:32: 99%|█████████▉| 198/200 [00:09<00:00, 21.84 it/sec, obj=170]
INFO - 10:56:32: 100%|█████████▉| 199/200 [00:09<00:00, 21.84 it/sec, obj=170]
INFO - 10:56:32: 100%|██████████| 200/200 [00:09<00:00, 21.92 it/sec, obj=170]
INFO - 10:56:32: Optimization result:
INFO - 10:56:32: Optimizer info:
INFO - 10:56:32: Status: None
INFO - 10:56:32: Message: Maximum number of iterations reached. GEMSEO Stopped the driver
INFO - 10:56:32: Number of calls to the objective function by the optimizer: 201
INFO - 10:56:32: Solution:
INFO - 10:56:32: The solution is feasible.
INFO - 10:56:32: Objective: 169.89161468983534
INFO - 10:56:32: Standardized constraints:
INFO - 10:56:32: [volume fraction-0.3] = -4.312432086428508e-07
INFO - 10:56:32: *** End MDOScenario execution (time: 0:00:09.142248) ***
{'max_iter': 200, 'algo': 'NLOPT_MMA'}
Results¶
Post-process the optimization history:
scenario.post_process(
"BasicHistory", variable_names=["compliance"], show=True, save=False
)
<gemseo.post.basic_history.BasicHistory object at 0x7efd2ecff5e0>
Plot the solution
scenario.post_process("TopologyView", n_x=n_x, n_y=n_y, show=True, save=False)
<gemseo.post.topology_view.TopologyView object at 0x7efd2a224220>
Total running time of the script: (0 minutes 9.489 seconds)