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Solve a 2D MBB topology optimization problem

import matplotlib.pyplot as plt
from gemseo.api import configure_logger
from gemseo.api import create_scenario
from gemseo.problems.topo_opt.topopt_initialize import (
    initialize_design_space_and_discipline_to,
)
from matplotlib import colors

configure_logger()

Out:

<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 a MDOScenario

scenario = create_scenario(
    disciplines,
    formulation="DisciplinaryOpt",
    objective_name="compliance",
    design_space=design_space,
)

Add the volume fraction constraint to the scenario:

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

Generate the XDSM

scenario.xdsmize()

Out:

INFO - 10:03:24: Generating HTML XDSM file in : xdsm.html

Execute the scenario

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

Out:

    INFO - 10:03:24:
    INFO - 10:03:24: *** Start MDOScenario execution ***
    INFO - 10:03:24: MDOScenario
    INFO - 10:03:24:    Disciplines: DensityFilter MaterialModelInterpolation FininiteElementAnalysis VolumeFraction
    INFO - 10:03:24:    MDO formulation: DisciplinaryOpt
    INFO - 10:03:24: Optimization problem:
    INFO - 10:03:24:    minimize compliance(x)
    INFO - 10:03:24:    with respect to x
    INFO - 10:03:24:    subject to constraints:
    INFO - 10:03:24:       volume fraction(x) <= 0.3
    INFO - 10:03:24: Solving optimization problem with algorithm NLOPT_MMA:
    INFO - 10:03:24: ...   0%|          | 0/200 [00:00<?, ?it]
    INFO - 10:03:24: ...   1%|          | 2/200 [00:00<00:00, 1010.68 it/sec]
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    INFO - 10:03:34: ...  53%|█████▎    | 106/200 [00:09<00:04, 21.63 it/sec]
    INFO - 10:03:34: Optimization result:
    INFO - 10:03:34:    Optimizer info:
    INFO - 10:03:34:       Status: None
    INFO - 10:03:34:       Message: Successive iterates of the objective function are closer than ftol_rel or ftol_abs. GEMSEO Stopped the driver
    INFO - 10:03:34:       Number of calls to the objective function by the optimizer: 106
    INFO - 10:03:34:    Solution:
    INFO - 10:03:34:       The solution is feasible.
    INFO - 10:03:34:       Objective: 170.90194735674362
    INFO - 10:03:34:       Standardized constraints:
    INFO - 10:03:34:          volume fraction - 0.3 = -1.5002556197907246e-06
    INFO - 10:03:34: *** End MDOScenario execution (time: 0:00:09.263465) ***

{'max_iter': 200, 'algo': 'NLOPT_MMA'}

Results

Post-process the optmization history:

scenario.post_process(
    "BasicHistory",
    variable_names=["compliance"],
    save=True,
    show=False,
    file_name=problem_name + "_history.png",
)

Out:

<gemseo.post.basic_history.BasicHistory object at 0x7fdbfb433b80>
../../_images/MBB_history.png

Plot the solution

plt.ion()  # Ensure that redrawing is possible
fig, ax = plt.subplots()
im = ax.imshow(
    -scenario.optimization_result.x_opt.reshape((n_x, n_y)).T,
    cmap="gray",
    interpolation="none",
    norm=colors.Normalize(vmin=-1, vmax=0),
)
fig.show()
im.set_array(-scenario.optimization_result.x_opt.reshape((n_x, n_y)).T)
fig.canvas.draw()
plt.savefig(problem_name + "_solution.png")
topology optimization MBB../../_images/MBB_solution.png

Total running time of the script: ( 0 minutes 9.865 seconds)

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