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Solve a 2D MBB topology optimization problem¶
from __future__ import annotations
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()
<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()
INFO - 17:19:45: Generating HTML XDSM file in : xdsm.html
Execute the scenario
scenario.execute(input_data={"max_iter": 200, "algo": "NLOPT_MMA"})
INFO - 17:19:45:
INFO - 17:19:45: *** Start MDOScenario execution ***
INFO - 17:19:45: MDOScenario
INFO - 17:19:45: Disciplines: DensityFilter FininiteElementAnalysis MaterialModelInterpolation VolumeFraction
INFO - 17:19:45: MDO formulation: DisciplinaryOpt
INFO - 17:19:45: Optimization problem:
INFO - 17:19:45: minimize compliance(x)
INFO - 17:19:45: with respect to x
INFO - 17:19:45: subject to constraints:
INFO - 17:19:45: volume fraction(x) <= 0.3
INFO - 17:19:45: Solving optimization problem with algorithm NLOPT_MMA:
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INFO - 17:20:11: Optimization result:
INFO - 17:20:11: Optimizer info:
INFO - 17:20:11: Status: None
INFO - 17:20:11: Message: Successive iterates of the objective function are closer than ftol_rel or ftol_abs. GEMSEO Stopped the driver
INFO - 17:20:11: Number of calls to the objective function by the optimizer: 165
INFO - 17:20:11: Solution:
INFO - 17:20:11: The solution is feasible.
INFO - 17:20:11: Objective: 169.90513692849225
INFO - 17:20:11: Standardized constraints:
INFO - 17:20:11: volume fraction - 0.3 = 2.1040097875069108e-07
INFO - 17:20:11: *** End MDOScenario execution (time: 0:00:25.824764) ***
{'max_iter': 200, 'algo': 'NLOPT_MMA'}
Results¶
Post-process the optimization history:
scenario.post_process(
"BasicHistory",
variable_names=["compliance"],
save=True,
show=False,
file_name=problem_name + "_history.png",
)
<gemseo.post.basic_history.BasicHistory object at 0x7fccf0500d60>
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")
Total running time of the script: ( 0 minutes 26.845 seconds)