Note
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Solve a 2D MBB topology optimization problem#
from __future__ import annotations
from gemseo import create_scenario
from gemseo.problems.topology_optimization.topopt_initialize import (
initialize_design_space_and_discipline_to,
)
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)
Execute the scenario
scenario.execute(algo_name="NLOPT_MMA", max_iter=200)
INFO - 16:23:58: *** Start MDOScenario execution ***
INFO - 16:23:58: MDOScenario
INFO - 16:23:58: Disciplines: DensityFilter FiniteElementAnalysis MaterialModelInterpolation VolumeFraction
INFO - 16:23:58: MDO formulation: DisciplinaryOpt
INFO - 16:23:58: Optimization problem:
INFO - 16:23:58: minimize compliance(x)
INFO - 16:23:58: with respect to x
INFO - 16:23:58: under the inequality constraints
INFO - 16:23:58: volume fraction(x) <= 0.3
INFO - 16:23:58: Solving optimization problem with algorithm NLOPT_MMA:
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INFO - 16:24:01: 92%|█████████▎| 185/200 [00:02<00:00, 63.00 it/sec, feas=True, obj=170]
INFO - 16:24:01: 93%|█████████▎| 186/200 [00:02<00:00, 63.02 it/sec, feas=True, obj=170]
INFO - 16:24:01: 94%|█████████▎| 187/200 [00:02<00:00, 63.03 it/sec, feas=True, obj=170]
INFO - 16:24:01: 94%|█████████▍| 188/200 [00:02<00:00, 63.05 it/sec, feas=True, obj=170]
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INFO - 16:24:01: 95%|█████████▌| 190/200 [00:03<00:00, 63.07 it/sec, feas=True, obj=170]
INFO - 16:24:01: 96%|█████████▌| 191/200 [00:03<00:00, 63.08 it/sec, feas=True, obj=170]
INFO - 16:24:01: 96%|█████████▌| 192/200 [00:03<00:00, 63.09 it/sec, feas=True, obj=170]
INFO - 16:24:01: 96%|█████████▋| 193/200 [00:03<00:00, 63.10 it/sec, feas=True, obj=170]
INFO - 16:24:01: 97%|█████████▋| 194/200 [00:03<00:00, 63.11 it/sec, feas=True, obj=170]
INFO - 16:24:01: 98%|█████████▊| 195/200 [00:03<00:00, 63.14 it/sec, feas=True, obj=170]
INFO - 16:24:01: 98%|█████████▊| 196/200 [00:03<00:00, 63.15 it/sec, feas=True, obj=170]
INFO - 16:24:01: 98%|█████████▊| 197/200 [00:03<00:00, 63.18 it/sec, feas=True, obj=170]
INFO - 16:24:01: 99%|█████████▉| 198/200 [00:03<00:00, 63.21 it/sec, feas=True, obj=170]
INFO - 16:24:01: 100%|█████████▉| 199/200 [00:03<00:00, 63.24 it/sec, feas=True, obj=170]
INFO - 16:24:01: 100%|██████████| 200/200 [00:03<00:00, 63.27 it/sec, feas=True, obj=170]
INFO - 16:24:01: Optimization result:
INFO - 16:24:01: Optimizer info:
INFO - 16:24:01: Status: None
INFO - 16:24:01: Message: Maximum number of iterations reached. GEMSEO stopped the driver.
INFO - 16:24:01: Solution:
INFO - 16:24:01: The solution is feasible.
INFO - 16:24:01: Objective: 169.89100281948836
INFO - 16:24:01: Standardized constraints:
INFO - 16:24:01: [volume fraction-0.3] = 6.224782465036327e-07
INFO - 16:24:01: *** End MDOScenario execution ***
Results#
Post-process the optimization history:
scenario.post_process(
post_name="BasicHistory", variable_names=["compliance"], show=True, save=False
)
<gemseo.post.basic_history.BasicHistory object at 0x7c2f6caa3320>
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 0x7c2f8fab6420>
Total running time of the script: (0 minutes 4.079 seconds)