Note
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Solve a 2D short cantilever 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 = "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_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 - 16:24:02: *** Start MDOScenario execution ***
INFO - 16:24:02: MDOScenario
INFO - 16:24:02: Disciplines: DensityFilter FiniteElementAnalysis MaterialModelInterpolation VolumeFraction
INFO - 16:24:02: MDO formulation: DisciplinaryOpt
INFO - 16:24:02: Optimization problem:
INFO - 16:24:02: minimize compliance(x)
INFO - 16:24:02: with respect to x
INFO - 16:24:02: under the inequality constraints
INFO - 16:24:02: volume fraction(x) <= 0.3
INFO - 16:24:02: Solving optimization problem with algorithm NLOPT_MMA:
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INFO - 16:24:05: 95%|█████████▌| 190/200 [00:02<00:00, 64.89 it/sec, feas=True, obj=137]
INFO - 16:24:05: 96%|█████████▌| 191/200 [00:02<00:00, 64.90 it/sec, feas=True, obj=137]
INFO - 16:24:05: 96%|█████████▌| 192/200 [00:02<00:00, 64.91 it/sec, feas=True, obj=137]
INFO - 16:24:05: 96%|█████████▋| 193/200 [00:02<00:00, 64.92 it/sec, feas=True, obj=137]
INFO - 16:24:05: 97%|█████████▋| 194/200 [00:02<00:00, 64.93 it/sec, feas=True, obj=137]
INFO - 16:24:05: 98%|█████████▊| 195/200 [00:03<00:00, 64.94 it/sec, feas=True, obj=137]
INFO - 16:24:05: 98%|█████████▊| 196/200 [00:03<00:00, 64.98 it/sec, feas=True, obj=137]
INFO - 16:24:05: Optimization result:
INFO - 16:24:05: Optimizer info:
INFO - 16:24:05: Status: None
INFO - 16:24:05: Message: Successive iterates of the objective function are closer than ftol_rel or ftol_abs. GEMSEO stopped the driver.
INFO - 16:24:05: Solution:
INFO - 16:24:05: The solution is feasible.
INFO - 16:24:05: Objective: 136.5612552177233
INFO - 16:24:05: Standardized constraints:
INFO - 16:24:05: [volume fraction-0.3] = -6.272737218537827e-09
INFO - 16:24:05: *** 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 0x7c2f70c66360>
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 0x7c2f7175d070>
Total running time of the script: (0 minutes 3.932 seconds)