.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "examples/topology_optimization/plot_topology_optimization_short_cantilever.py"
.. LINE NUMBERS ARE GIVEN BELOW.

.. only:: html

    .. note::
        :class: sphx-glr-download-link-note

        :ref:`Go to the end <sphx_glr_download_examples_topology_optimization_plot_topology_optimization_short_cantilever.py>`
        to download the full example code.

.. rst-class:: sphx-glr-example-title

.. _sphx_glr_examples_topology_optimization_plot_topology_optimization_short_cantilever.py:


Solve a 2D short cantilever topology optimization problem
=========================================================

.. GENERATED FROM PYTHON SOURCE LINES 23-31

.. code-block:: Python


    from __future__ import annotations

    from gemseo import create_scenario
    from gemseo.problems.topology_optimization.topopt_initialize import (
        initialize_design_space_and_discipline_to,
    )








.. GENERATED FROM PYTHON SOURCE LINES 32-35

Setup the topology optimization problem
---------------------------------------
Define the target volume fraction:

.. GENERATED FROM PYTHON SOURCE LINES 35-37

.. code-block:: Python

    volume_fraction = 0.3








.. GENERATED FROM PYTHON SOURCE LINES 38-39

Define the problem type:

.. GENERATED FROM PYTHON SOURCE LINES 39-41

.. code-block:: Python

    problem_name = "Short_Cantilever"








.. GENERATED FROM PYTHON SOURCE LINES 42-43

Define the number of elements in the x- and y- directions:

.. GENERATED FROM PYTHON SOURCE LINES 43-46

.. code-block:: Python

    n_x = 50
    n_y = 25








.. GENERATED FROM PYTHON SOURCE LINES 47-48

Define the full material Young's modulus and Poisson's ratio:

.. GENERATED FROM PYTHON SOURCE LINES 48-51

.. code-block:: Python

    e0 = 1
    nu = 0.3








.. GENERATED FROM PYTHON SOURCE LINES 52-53

Define the penalty of the SIMP approach:

.. GENERATED FROM PYTHON SOURCE LINES 53-55

.. code-block:: Python

    penalty = 3








.. GENERATED FROM PYTHON SOURCE LINES 56-57

Define the minimum member size in the solution:

.. GENERATED FROM PYTHON SOURCE LINES 57-59

.. code-block:: Python

    min_member_size = 1.5








.. GENERATED FROM PYTHON SOURCE LINES 60-61

Instantiate the :class:`.DesignSpace` and the disciplines:

.. GENERATED FROM PYTHON SOURCE LINES 61-73

.. code-block:: Python


    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,
    )








.. GENERATED FROM PYTHON SOURCE LINES 74-77

Solve the topology optimization problem
---------------------------------------
Generate an :class:`.MDOScenario`:

.. GENERATED FROM PYTHON SOURCE LINES 77-84

.. code-block:: Python

    scenario = create_scenario(
        disciplines,
        "compliance",
        design_space,
        formulation_name="DisciplinaryOpt",
    )








.. GENERATED FROM PYTHON SOURCE LINES 85-86

Add the volume fraction constraint to the scenario:

.. GENERATED FROM PYTHON SOURCE LINES 86-90

.. code-block:: Python

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








.. GENERATED FROM PYTHON SOURCE LINES 91-92

Generate the XDSM:

.. GENERATED FROM PYTHON SOURCE LINES 92-94

.. code-block:: Python

    scenario.xdsmize(save_html=False)






.. raw:: html

    <div class="output_subarea output_html rendered_html output_result">

        <script type="text/javascript">
            document.addEventListener('DOMContentLoaded', () => {
              const mdo = {
      "root": {
        "nodes": [
          {
            "id": "Opt",
            "name": "Optimizer",
            "type": "optimization",
            "status": "DONE"
          },
          {
            "id": "Dis1",
            "name": "DensityFilter",
            "type": "analysis",
            "status": "DONE"
          },
          {
            "id": "Dis2",
            "name": "MaterialModelInterpolation",
            "type": "analysis",
            "status": "DONE"
          },
          {
            "id": "Dis3",
            "name": "FiniteElementAnalysis",
            "type": "analysis",
            "status": "DONE"
          },
          {
            "id": "Dis4",
            "name": "VolumeFraction",
            "type": "analysis",
            "status": "DONE"
          }
        ],
        "edges": [
          {
            "from": "_U_",
            "to": "Opt",
            "name": "x^(0)"
          },
          {
            "from": "Opt",
            "to": "_U_",
            "name": "compliance^*, [volume fraction-0.3]^*"
          },
          {
            "from": "Opt",
            "to": "Dis1",
            "name": "x"
          },
          {
            "from": "Dis3",
            "to": "Opt",
            "name": "compliance"
          },
          {
            "from": "Dis4",
            "to": "Opt",
            "name": "volume fraction"
          },
          {
            "from": "Dis1",
            "to": "_U_",
            "name": "xPhys^*"
          },
          {
            "from": "Dis2",
            "to": "_U_",
            "name": "rho^*, E^*"
          },
          {
            "from": "Dis3",
            "to": "Opt",
            "name": "compliance"
          },
          {
            "from": "Dis4",
            "to": "Opt",
            "name": "volume fraction"
          },
          {
            "from": "Dis1",
            "to": "Dis2",
            "name": "xPhys"
          },
          {
            "from": "Dis2",
            "to": "Dis3",
            "name": "E"
          },
          {
            "from": "Dis2",
            "to": "Dis4",
            "name": "rho"
          }
        ],
        "workflow": [
          "_U_",
          [
            "Opt",
            [
              "Dis1",
              "Dis2",
              "Dis3",
              "Dis4"
            ]
          ]
        ],
        "optpb": ""
      }
    };
              const config = {
                labelizer: {
                    ellipsis: 5,
                    subSupScript: false,
                    showLinkNbOnly: false,
                },
                layout: {
                    origin: { x: 50, y: 20 },
                    cellsize: { w: 150, h: 50 },
                    padding: 10,
                },
                withDefaultDriver: true,
                withTitleTooltip: true,
              };
              xdsmjs.XDSMjs(config).createXdsm(mdo);
            });
        </script>
        <div class='xdsm-toolbar'></div><div class='xdsm2'></div>
    </div>
    <br />
    <br />

.. GENERATED FROM PYTHON SOURCE LINES 95-96

Execute the scenario:

.. GENERATED FROM PYTHON SOURCE LINES 96-98

.. code-block:: Python

    scenario.execute(algo_name="NLOPT_MMA", max_iter=200)





.. rst-class:: sphx-glr-script-out

 .. code-block:: none

        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]
        INFO - 16:13:46:      2%|▏         | 4/200 [00:00<00:04, 43.15 it/sec, feas=True, obj=1.45e+3]
        INFO - 16:13:46:      2%|▎         | 5/200 [00:00<00:04, 43.68 it/sec, feas=True, obj=1.45e+3]
        INFO - 16:13:46:      3%|▎         | 6/200 [00:00<00:04, 44.11 it/sec, feas=True, obj=1.43e+3]
        INFO - 16:13:46:      4%|▎         | 7/200 [00:00<00:04, 44.65 it/sec, feas=True, obj=1.4e+3]
        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]
        INFO - 16:13:46:      5%|▌         | 10/200 [00:00<00:04, 45.05 it/sec, feas=True, obj=1.01e+3]
        INFO - 16:13:46:      6%|▌         | 11/200 [00:00<00:04, 45.31 it/sec, feas=True, obj=756]
        INFO - 16:13:46:      6%|▌         | 12/200 [00:00<00:04, 45.49 it/sec, feas=True, obj=573]
        INFO - 16:13:46:      6%|▋         | 13/200 [00:00<00:04, 45.73 it/sec, feas=True, obj=509]
        INFO - 16:13:46:      7%|▋         | 14/200 [00:00<00:04, 45.95 it/sec, feas=True, obj=448]
        INFO - 16:13:46:      8%|▊         | 15/200 [00:00<00:04, 46.17 it/sec, feas=True, obj=399]
        INFO - 16:13:46:      8%|▊         | 16/200 [00:00<00:03, 46.38 it/sec, feas=True, obj=360]
        INFO - 16:13:46:      8%|▊         | 17/200 [00:00<00:03, 46.57 it/sec, feas=True, obj=329]
        INFO - 16:13:46:      9%|▉         | 18/200 [00:00<00:03, 46.71 it/sec, feas=True, obj=304]
        INFO - 16:13:46:     10%|▉         | 19/200 [00:00<00:03, 47.04 it/sec, feas=True, obj=278]
        INFO - 16:13:46:     10%|█         | 20/200 [00:00<00:03, 47.22 it/sec, feas=True, obj=251]
        INFO - 16:13:46:     10%|█         | 21/200 [00:00<00:03, 47.43 it/sec, feas=True, obj=231]
        INFO - 16:13:46:     11%|█         | 22/200 [00:00<00:03, 47.61 it/sec, feas=True, obj=213]
        INFO - 16:13:46:     12%|█▏        | 23/200 [00:00<00:03, 47.71 it/sec, feas=True, obj=193]
        INFO - 16:13:46:     12%|█▏        | 24/200 [00:00<00:03, 47.84 it/sec, feas=True, obj=175]
        INFO - 16:13:46:     12%|█▎        | 25/200 [00:00<00:03, 47.99 it/sec, feas=True, obj=161]
        INFO - 16:13:46:     13%|█▎        | 26/200 [00:00<00:03, 48.17 it/sec, feas=True, obj=153]
        INFO - 16:13:46:     14%|█▎        | 27/200 [00:00<00:03, 48.36 it/sec, feas=True, obj=148]
        INFO - 16:13:46:     14%|█▍        | 28/200 [00:00<00:03, 48.51 it/sec, feas=True, obj=145]
        INFO - 16:13:46:     14%|█▍        | 29/200 [00:00<00:03, 48.70 it/sec, feas=True, obj=143]
        INFO - 16:13:46:     15%|█▌        | 30/200 [00:00<00:03, 48.88 it/sec, feas=True, obj=142]
        INFO - 16:13:46:     16%|█▌        | 31/200 [00:00<00:03, 49.04 it/sec, feas=True, obj=141]
        INFO - 16:13:47:     16%|█▌        | 32/200 [00:00<00:03, 49.18 it/sec, feas=True, obj=140]
        INFO - 16:13:47:     16%|█▋        | 33/200 [00:00<00:03, 49.29 it/sec, feas=True, obj=140]
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        INFO - 16:13:47:     18%|█▊        | 35/200 [00:00<00:03, 49.63 it/sec, feas=True, obj=139]
        INFO - 16:13:47:     18%|█▊        | 36/200 [00:00<00:03, 49.79 it/sec, feas=True, obj=139]
        INFO - 16:13:47:     18%|█▊        | 37/200 [00:00<00:03, 49.92 it/sec, feas=True, obj=139]
        INFO - 16:13:47:     19%|█▉        | 38/200 [00:00<00:03, 50.08 it/sec, feas=True, obj=139]
        INFO - 16:13:47:     20%|█▉        | 39/200 [00:00<00:03, 50.25 it/sec, feas=True, obj=139]
        INFO - 16:13:47:     20%|██        | 40/200 [00:00<00:03, 50.40 it/sec, feas=True, obj=139]
        INFO - 16:13:47:     20%|██        | 41/200 [00:00<00:03, 50.55 it/sec, feas=True, obj=139]
        INFO - 16:13:47:     21%|██        | 42/200 [00:00<00:03, 50.65 it/sec, feas=True, obj=138]
        INFO - 16:13:47:     22%|██▏       | 43/200 [00:00<00:03, 50.77 it/sec, feas=True, obj=138]
        INFO - 16:13:47:     22%|██▏       | 44/200 [00:00<00:03, 50.89 it/sec, feas=True, obj=138]
        INFO - 16:13:47:     22%|██▎       | 45/200 [00:00<00:03, 51.03 it/sec, feas=True, obj=138]
        INFO - 16:13:47:     23%|██▎       | 46/200 [00:00<00:03, 51.17 it/sec, feas=True, obj=138]
        INFO - 16:13:47:     24%|██▎       | 47/200 [00:00<00:02, 51.26 it/sec, feas=True, obj=138]
        INFO - 16:13:47:     24%|██▍       | 48/200 [00:00<00:02, 51.36 it/sec, feas=True, obj=138]
        INFO - 16:13:47:     24%|██▍       | 49/200 [00:00<00:02, 51.48 it/sec, feas=True, obj=138]
        INFO - 16:13:47:     25%|██▌       | 50/200 [00:00<00:02, 51.57 it/sec, feas=True, obj=138]
        INFO - 16:13:47:     26%|██▌       | 51/200 [00:00<00:02, 51.66 it/sec, feas=True, obj=138]
        INFO - 16:13:47:     26%|██▌       | 52/200 [00:01<00:02, 51.72 it/sec, feas=True, obj=138]
        INFO - 16:13:47:     26%|██▋       | 53/200 [00:01<00:02, 51.80 it/sec, feas=True, obj=138]
        INFO - 16:13:47:     27%|██▋       | 54/200 [00:01<00:02, 51.84 it/sec, feas=True, obj=137]
        INFO - 16:13:47:     28%|██▊       | 55/200 [00:01<00:02, 51.92 it/sec, feas=True, obj=137]
        INFO - 16:13:47:     28%|██▊       | 56/200 [00:01<00:02, 52.01 it/sec, feas=True, obj=137]
        INFO - 16:13:47:     28%|██▊       | 57/200 [00:01<00:02, 52.09 it/sec, feas=True, obj=137]
        INFO - 16:13:47:     29%|██▉       | 58/200 [00:01<00:02, 52.17 it/sec, feas=True, obj=137]
        INFO - 16:13:47:     30%|██▉       | 59/200 [00:01<00:02, 52.24 it/sec, feas=True, obj=137]
        INFO - 16:13:47:     30%|███       | 60/200 [00:01<00:02, 52.34 it/sec, feas=True, obj=137]
        INFO - 16:13:47:     30%|███       | 61/200 [00:01<00:02, 52.41 it/sec, feas=True, obj=137]
        INFO - 16:13:47:     31%|███       | 62/200 [00:01<00:02, 52.49 it/sec, feas=True, obj=137]
        INFO - 16:13:47:     32%|███▏      | 63/200 [00:01<00:02, 52.58 it/sec, feas=True, obj=137]
        INFO - 16:13:47:     32%|███▏      | 64/200 [00:01<00:02, 52.66 it/sec, feas=True, obj=137]
        INFO - 16:13:47:     32%|███▎      | 65/200 [00:01<00:02, 52.74 it/sec, feas=True, obj=137]
        INFO - 16:13:47:     33%|███▎      | 66/200 [00:01<00:02, 52.79 it/sec, feas=True, obj=137]
        INFO - 16:13:47:     34%|███▎      | 67/200 [00:01<00:02, 52.90 it/sec, feas=True, obj=137]
        INFO - 16:13:47:     34%|███▍      | 68/200 [00:01<00:02, 52.95 it/sec, feas=True, obj=137]
        INFO - 16:13:47:     34%|███▍      | 69/200 [00:01<00:02, 53.01 it/sec, feas=True, obj=137]
        INFO - 16:13:47:     35%|███▌      | 70/200 [00:01<00:02, 53.04 it/sec, feas=True, obj=137]
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        INFO - 16:13:47:     38%|███▊      | 75/200 [00:01<00:02, 53.16 it/sec, feas=True, obj=137]
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        INFO - 16:13:47:     38%|███▊      | 77/200 [00:01<00:02, 53.26 it/sec, feas=True, obj=137]
        INFO - 16:13:47:     39%|███▉      | 78/200 [00:01<00:02, 53.27 it/sec, feas=True, obj=137]
        INFO - 16:13:47:     40%|███▉      | 79/200 [00:01<00:02, 53.29 it/sec, feas=True, obj=137]
        INFO - 16:13:47:     40%|████      | 80/200 [00:01<00:02, 53.32 it/sec, feas=True, obj=137]
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        INFO - 16:13:47:     42%|████▏     | 83/200 [00:01<00:02, 53.44 it/sec, feas=True, obj=137]
        INFO - 16:13:47:     42%|████▏     | 84/200 [00:01<00:02, 53.48 it/sec, feas=True, obj=137]
        INFO - 16:13:47:     42%|████▎     | 85/200 [00:01<00:02, 53.51 it/sec, feas=True, obj=137]
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        INFO - 16:13:47:     44%|████▎     | 87/200 [00:01<00:02, 53.54 it/sec, feas=True, obj=137]
        INFO - 16:13:48:     44%|████▍     | 88/200 [00:01<00:02, 53.57 it/sec, feas=True, obj=137]
        INFO - 16:13:48:     44%|████▍     | 89/200 [00:01<00:02, 53.59 it/sec, feas=True, obj=137]
        INFO - 16:13:48:     45%|████▌     | 90/200 [00:01<00:02, 53.60 it/sec, feas=True, obj=137]
        INFO - 16:13:48:     46%|████▌     | 91/200 [00:01<00:02, 53.63 it/sec, feas=True, obj=137]
        INFO - 16:13:48:     46%|████▌     | 92/200 [00:01<00:02, 53.68 it/sec, feas=True, obj=137]
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        INFO - 16:13:48:     47%|████▋     | 94/200 [00:01<00:01, 53.74 it/sec, feas=True, obj=137]
        INFO - 16:13:48:     48%|████▊     | 95/200 [00:01<00:01, 53.78 it/sec, feas=True, obj=137]
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        INFO - 16:13:48:     56%|█████▌    | 111/200 [00:02<00:01, 54.16 it/sec, feas=True, obj=137]
        INFO - 16:13:48:     56%|█████▌    | 112/200 [00:02<00:01, 54.19 it/sec, feas=True, obj=137]
        INFO - 16:13:48:     56%|█████▋    | 113/200 [00:02<00:01, 54.22 it/sec, feas=True, obj=137]
        INFO - 16:13:48:     57%|█████▋    | 114/200 [00:02<00:01, 54.25 it/sec, feas=True, obj=137]
        INFO - 16:13:48:     57%|█████▊    | 115/200 [00:02<00:01, 54.26 it/sec, feas=True, obj=137]
        INFO - 16:13:48:     58%|█████▊    | 116/200 [00:02<00:01, 54.28 it/sec, feas=True, obj=137]
        INFO - 16:13:48:     58%|█████▊    | 117/200 [00:02<00:01, 54.28 it/sec, feas=True, obj=137]
        INFO - 16:13:48:     59%|█████▉    | 118/200 [00:02<00:01, 54.32 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 ***




.. GENERATED FROM PYTHON SOURCE LINES 99-102

Results
-------
Post-process the optimization history:

.. GENERATED FROM PYTHON SOURCE LINES 102-106

.. code-block:: Python

    scenario.post_process(
        post_name="BasicHistory", variable_names=["compliance"], show=True, save=False
    )




.. image-sg:: /examples/topology_optimization/images/sphx_glr_plot_topology_optimization_short_cantilever_001.png
   :alt: History plot
   :srcset: /examples/topology_optimization/images/sphx_glr_plot_topology_optimization_short_cantilever_001.png
   :class: sphx-glr-single-img


.. rst-class:: sphx-glr-script-out

 .. code-block:: none


    <gemseo.post.basic_history.BasicHistory object at 0x7b1d43d4b740>



.. GENERATED FROM PYTHON SOURCE LINES 107-108

Plot the solution

.. GENERATED FROM PYTHON SOURCE LINES 108-109

.. code-block:: Python

    scenario.post_process(post_name="TopologyView", n_x=n_x, n_y=n_y, show=True, save=False)



.. image-sg:: /examples/topology_optimization/images/sphx_glr_plot_topology_optimization_short_cantilever_002.png
   :alt: plot topology optimization short cantilever
   :srcset: /examples/topology_optimization/images/sphx_glr_plot_topology_optimization_short_cantilever_002.png
   :class: sphx-glr-single-img


.. rst-class:: sphx-glr-script-out

 .. code-block:: none


    <gemseo.post.topology_view.TopologyView object at 0x7b1d50a05ca0>




.. rst-class:: sphx-glr-timing

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


.. _sphx_glr_download_examples_topology_optimization_plot_topology_optimization_short_cantilever.py:

.. only:: html

  .. container:: sphx-glr-footer sphx-glr-footer-example

    .. container:: sphx-glr-download sphx-glr-download-jupyter

      :download:`Download Jupyter notebook: plot_topology_optimization_short_cantilever.ipynb <plot_topology_optimization_short_cantilever.ipynb>`

    .. container:: sphx-glr-download sphx-glr-download-python

      :download:`Download Python source code: plot_topology_optimization_short_cantilever.py <plot_topology_optimization_short_cantilever.py>`

    .. container:: sphx-glr-download sphx-glr-download-zip

      :download:`Download zipped: plot_topology_optimization_short_cantilever.zip <plot_topology_optimization_short_cantilever.zip>`


.. only:: html

 .. rst-class:: sphx-glr-signature

    `Gallery generated by Sphinx-Gallery <https://sphinx-gallery.github.io>`_