# 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,
"DisciplinaryOpt",
"compliance",
design_space,
)


Add the volume fraction constraint to the scenario:

scenario.add_constraint(
"volume fraction", constraint_type="ineq", value=volume_fraction
)


Generate the XDSM

scenario.xdsmize()


Execute the scenario

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

    INFO - 13:57:26:
INFO - 13:57:26: *** Start MDOScenario execution ***
INFO - 13:57:26: MDOScenario
INFO - 13:57:26:    Disciplines: DensityFilter FininiteElementAnalysis MaterialModelInterpolation VolumeFraction
INFO - 13:57:26:    MDO formulation: DisciplinaryOpt
INFO - 13:57:26: Optimization problem:
INFO - 13:57:26:    minimize compliance(x)
INFO - 13:57:26:    with respect to x
INFO - 13:57:26:    subject to constraints:
INFO - 13:57:26:       volume fraction(x) <= 0.3
INFO - 13:57:26: Solving optimization problem with algorithm NLOPT_MMA:
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INFO - 13:57:33:     88%|████████▊ | 177/200 [00:07<00:00, 24.25 it/sec, obj=170]
INFO - 13:57:33:     89%|████████▉ | 178/200 [00:07<00:00, 24.25 it/sec, obj=170]
INFO - 13:57:34:     90%|████████▉ | 179/200 [00:07<00:00, 24.26 it/sec, obj=170]
INFO - 13:57:34:     90%|█████████ | 180/200 [00:07<00:00, 24.26 it/sec, obj=170]
INFO - 13:57:34:     90%|█████████ | 181/200 [00:07<00:00, 24.26 it/sec, obj=170]
INFO - 13:57:34:     91%|█████████ | 182/200 [00:07<00:00, 24.26 it/sec, obj=170]
INFO - 13:57:34:     92%|█████████▏| 183/200 [00:07<00:00, 24.26 it/sec, obj=170]
INFO - 13:57:34:     92%|█████████▏| 184/200 [00:07<00:00, 24.26 it/sec, obj=170]
INFO - 13:57:34:     92%|█████████▎| 185/200 [00:07<00:00, 24.27 it/sec, obj=170]
INFO - 13:57:34:     93%|█████████▎| 186/200 [00:07<00:00, 24.27 it/sec, obj=170]
INFO - 13:57:34:     94%|█████████▎| 187/200 [00:07<00:00, 24.28 it/sec, obj=170]
INFO - 13:57:34:     94%|█████████▍| 188/200 [00:07<00:00, 24.28 it/sec, obj=170]
INFO - 13:57:34:     94%|█████████▍| 189/200 [00:07<00:00, 24.28 it/sec, obj=170]
INFO - 13:57:34:     95%|█████████▌| 190/200 [00:07<00:00, 24.29 it/sec, obj=170]
INFO - 13:57:34:     96%|█████████▌| 191/200 [00:07<00:00, 24.29 it/sec, obj=170]
INFO - 13:57:34:     96%|█████████▌| 192/200 [00:07<00:00, 24.30 it/sec, obj=170]
INFO - 13:57:34:     96%|█████████▋| 193/200 [00:07<00:00, 24.30 it/sec, obj=170]
INFO - 13:57:34:     97%|█████████▋| 194/200 [00:07<00:00, 24.30 it/sec, obj=170]
INFO - 13:57:34:     98%|█████████▊| 195/200 [00:08<00:00, 24.30 it/sec, obj=170]
INFO - 13:57:34:     98%|█████████▊| 196/200 [00:08<00:00, 24.30 it/sec, obj=170]
INFO - 13:57:34:     98%|█████████▊| 197/200 [00:08<00:00, 24.31 it/sec, obj=170]
INFO - 13:57:34:     99%|█████████▉| 198/200 [00:08<00:00, 24.31 it/sec, obj=170]
INFO - 13:57:34:    100%|█████████▉| 199/200 [00:08<00:00, 24.32 it/sec, obj=170]
INFO - 13:57:34:    100%|██████████| 200/200 [00:08<00:00, 24.41 it/sec, obj=170]
INFO - 13:57:34: Optimization result:
INFO - 13:57:34:    Optimizer info:
INFO - 13:57:34:       Status: None
INFO - 13:57:34:       Message: Maximum number of iterations reached. GEMSEO Stopped the driver
INFO - 13:57:34:       Number of calls to the objective function by the optimizer: 201
INFO - 13:57:34:    Solution:
INFO - 13:57:34:       The solution is feasible.
INFO - 13:57:34:       Objective: 169.89161468983534
INFO - 13:57:34:       Standardized constraints:
INFO - 13:57:34:          [volume fraction-0.3] = -4.312432086428508e-07
INFO - 13:57:34: *** End MDOScenario execution (time: 0:00:08.212408) ***

{'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 0x7f28d00f14f0>


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 0x7f28cf641dc0>


Total running time of the script: (0 minutes 8.554 seconds)

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