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Solve a 2D short cantilever 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 = "Short_Cantilever"
Define the number of elements in the x- and y- directions:
n_x = 50
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_memeber_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_memeber_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 - 10:43:04:
INFO - 10:43:04: *** Start MDOScenario execution ***
INFO - 10:43:04: MDOScenario
INFO - 10:43:04: Disciplines: DensityFilter FiniteElementAnalysis MaterialModelInterpolation VolumeFraction
INFO - 10:43:04: MDO formulation: DisciplinaryOpt
INFO - 10:43:04: Optimization problem:
INFO - 10:43:04: minimize compliance(x)
INFO - 10:43:04: with respect to x
INFO - 10:43:04: subject to constraints:
INFO - 10:43:04: volume fraction(x) <= 0.3
INFO - 10:43:04: Solving optimization problem with algorithm NLOPT_MMA:
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INFO - 10:43:12: 96%|█████████▋| 193/200 [00:07<00:00, 25.55 it/sec, obj=137]
INFO - 10:43:12: 97%|█████████▋| 194/200 [00:07<00:00, 25.55 it/sec, obj=137]
INFO - 10:43:12: 98%|█████████▊| 195/200 [00:07<00:00, 25.55 it/sec, obj=137]
INFO - 10:43:12: 98%|█████████▊| 196/200 [00:07<00:00, 25.56 it/sec, obj=137]
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INFO - 10:43:12: 100%|██████████| 200/200 [00:07<00:00, 25.64 it/sec, obj=137]
INFO - 10:43:12: Optimization result:
INFO - 10:43:12: Optimizer info:
INFO - 10:43:12: Status: None
INFO - 10:43:12: Message: Maximum number of iterations reached. GEMSEO stopped the driver.
INFO - 10:43:12: Number of calls to the objective function by the optimizer: 201
INFO - 10:43:12: Solution:
INFO - 10:43:12: The solution is feasible.
INFO - 10:43:12: Objective: 136.56123312100124
INFO - 10:43:12: Standardized constraints:
INFO - 10:43:12: [volume fraction-0.3] = -1.9140380946858215e-09
INFO - 10:43:12: *** End MDOScenario execution (time: 0:00:07.815885) ***
{'max_iter': 200, 'algo': 'NLOPT_MMA'}
Results¶
Post-process the optimization history:
scenario.post_process(
"BasicHistory", variable_names=["compliance"], show=True, save=False
)
/home/docs/checkouts/readthedocs.org/user_builds/gemseo/envs/develop/lib/python3.9/site-packages/gemseo/datasets/dataset.py:483: 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 0x7f130619c070>
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 0x7f130657d160>
Total running time of the script: (0 minutes 8.641 seconds)