Solve a 2D MBB 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()

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()

Execute the scenario

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

Results

Post-process the optimization history:

scenario.post_process(
    "BasicHistory",
    variable_names=["compliance"],
    file_name=f"{problem_name}_history.png",
)

Plot the solution

scenario.post_process(
    "TopologyView",
    n_x=n_x,
    n_y=n_y,
    file_name=f"{problem_name}_solution.png",
)