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 - 16:13:46: *** Start MDOScenario execution ***
INFO - 16:13:46: MDOScenario
INFO - 16:13:46:    Disciplines: DensityFilter FiniteElementAnalysis MaterialModelInterpolation VolumeFraction
INFO - 16:13:46:    MDO formulation: DisciplinaryOpt
INFO - 16:13:46: Optimization problem:
INFO - 16:13:46:    minimize compliance(x)
INFO - 16:13:46:    with respect to x
INFO - 16:13:46:    under the inequality constraints
INFO - 16:13:46:       volume fraction(x) <= 0.3
INFO - 16:13:46: Solving optimization problem with algorithm NLOPT_MMA:
INFO - 16:13:46:      1%|          | 2/200 [00:00<00:05, 37.95 it/sec, feas=True, obj=1.46e+3]
INFO - 16:13:46:      2%|▏         | 3/200 [00:00<00:04, 41.09 it/sec, feas=True, obj=1.45e+3]
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INFO - 16:13:46:      4%|▍         | 8/200 [00:00<00:04, 44.75 it/sec, feas=True, obj=1.36e+3]
INFO - 16:13:46:      4%|▍         | 9/200 [00:00<00:04, 44.75 it/sec, feas=True, obj=1.2e+3]
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INFO - 16:13:49:     95%|█████████▌| 190/200 [00:03<00:00, 55.31 it/sec, feas=True, obj=137]
INFO - 16:13:49:     96%|█████████▌| 191/200 [00:03<00:00, 55.34 it/sec, feas=True, obj=137]
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INFO - 16:13:49:     97%|█████████▋| 194/200 [00:03<00:00, 55.39 it/sec, feas=True, obj=137]
INFO - 16:13:49:     98%|█████████▊| 195/200 [00:03<00:00, 55.39 it/sec, feas=True, obj=137]
INFO - 16:13:49:     98%|█████████▊| 196/200 [00:03<00:00, 55.41 it/sec, feas=True, obj=137]
INFO - 16:13:49:     98%|█████████▊| 197/200 [00:03<00:00, 55.44 it/sec, feas=True, obj=137]
INFO - 16:13:49:     99%|█████████▉| 198/200 [00:03<00:00, 55.46 it/sec, feas=True, obj=137]
INFO - 16:13:49:    100%|█████████▉| 199/200 [00:03<00:00, 55.47 it/sec, feas=True, obj=137]
INFO - 16:13:49:    100%|██████████| 200/200 [00:03<00:00, 55.50 it/sec, feas=True, obj=137]
INFO - 16:13:49: Optimization result:
INFO - 16:13:49:    Optimizer info:
INFO - 16:13:49:       Status: None
INFO - 16:13:49:       Message: Maximum number of iterations reached. GEMSEO stopped the driver.
INFO - 16:13:49:    Solution:
INFO - 16:13:49:       The solution is feasible.
INFO - 16:13:49:       Objective: 136.5606526095802
INFO - 16:13:49:       Standardized constraints:
INFO - 16:13:49:          [volume fraction-0.3] = 1.0310935563140333e-06
INFO - 16:13:49: *** End MDOScenario execution ***

Results#

Post-process the optimization history:

scenario.post_process(
    post_name="BasicHistory", variable_names=["compliance"], show=True, save=False
)
History plot
<gemseo.post.basic_history.BasicHistory object at 0x7b1d43d4b740>

Plot the solution

scenario.post_process(post_name="TopologyView", n_x=n_x, n_y=n_y, show=True, save=False)
plot topology optimization short cantilever
<gemseo.post.topology_view.TopologyView object at 0x7b1d50a05ca0>

Total running time of the script: (0 minutes 4.778 seconds)

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