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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.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 = "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 - 13:11:42:
INFO - 13:11:42: *** Start MDOScenario execution ***
INFO - 13:11:42: MDOScenario
INFO - 13:11:42: Disciplines: DensityFilter FininiteElementAnalysis MaterialModelInterpolation VolumeFraction
INFO - 13:11:42: MDO formulation: DisciplinaryOpt
INFO - 13:11:42: Optimization problem:
INFO - 13:11:42: minimize compliance(x)
INFO - 13:11:42: with respect to x
INFO - 13:11:42: subject to constraints:
INFO - 13:11:42: volume fraction(x) <= 0.3
INFO - 13:11:42: Solving optimization problem with algorithm NLOPT_MMA:
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INFO - 13:11:51: 100%|█████████▉| 199/200 [00:08<00:00, 22.48 it/sec, obj=137]
INFO - 13:11:51: 100%|██████████| 200/200 [00:08<00:00, 22.57 it/sec, obj=137]
INFO - 13:11:51: Optimization result:
INFO - 13:11:51: Optimizer info:
INFO - 13:11:51: Status: None
INFO - 13:11:51: Message: Maximum number of iterations reached. GEMSEO Stopped the driver
INFO - 13:11:51: Number of calls to the objective function by the optimizer: 201
INFO - 13:11:51: Solution:
INFO - 13:11:51: The solution is feasible.
INFO - 13:11:51: Objective: 136.56123312100124
INFO - 13:11:51: Standardized constraints:
INFO - 13:11:51: [volume fraction-0.3] = -1.9140380946858215e-09
INFO - 13:11:51: *** End MDOScenario execution (time: 0:00:08.881037) ***
{'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/5.3.2/lib/python3.9/site-packages/gemseo/datasets/dataset.py:490: 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 0x7f8b9777f310>
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 0x7f8ba63c0ee0>
Total running time of the script: (0 minutes 9.684 seconds)