.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "examples\02-tbrom_examples\06-TBROM_FEA_static_structural_optimization.py"
.. LINE NUMBERS ARE GIVEN BELOW.

.. only:: html

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

        :ref:`Go to the end <sphx_glr_download_examples_02-tbrom_examples_06-TBROM_FEA_static_structural_optimization.py>`
        to download the full example code.

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

.. _sphx_glr_examples_02-tbrom_examples_06-TBROM_FEA_static_structural_optimization.py:

.. _ref_example_TBROM_FEA_static_structural_optimization:

Static structural analysis and optimization using 3D field ROM
--------------------------------------------------------------

This example shows how PyTwin can be used to perform different types of static structural analysis using 3D field ROM.
A static structural model of a dog bone is created with Ansys Mechanical. A fixed support is applied on the right hand
side, while a remote force is supplied on the left hand side. A non-linear structural analysis with plastic material
behavior (using steel) is performed to compute the resulting stress field and associated displacement. A static ROM
has been generated out of the original 3D model, so that the resulting Twin model can be evaluated using PyTwin,
giving the possibilities to evaluate multiple configurations and operating conditions quickly, while keeping
predictions accuracy similar to original 3D FEA model. The PyTwin worklow illustrates different APIs usage to evaluate
the models at different conditions, visualize 3D detailed field results, as well as performing optimization and
inverse problems.

.. GENERATED FROM PYTHON SOURCE LINES 40-43

.. image:: /_static/TBROM_FEA_static_structural_optimization.png
  :width: 400pt
  :align: center

.. GENERATED FROM PYTHON SOURCE LINES 43-46

.. code-block:: Python


    # sphinx_gallery_thumbnail_path = '_static/TBROM_FEA_static_structural_optimization.png'








.. GENERATED FROM PYTHON SOURCE LINES 47-49

.. note::
  This example uses similar functionalities and requirements as :ref:`ref_example_TBROM_FEA_mesh_projection`

.. GENERATED FROM PYTHON SOURCE LINES 51-55

Perform required imports
~~~~~~~~~~~~~~~~~~~~~~~~
Perform required imports, which include downloading and importing the input
files.

.. GENERATED FROM PYTHON SOURCE LINES 55-67

.. code-block:: Python


    import ansys.dpf.core as dpf
    import matplotlib.pyplot as plt
    import numpy as np
    import pandas as pd
    from pytwin import TwinModel, download_file
    import pyvista as pv
    from scipy.optimize import minimize

    twin_file = download_file("TwinDogBone.twin", "twin_files", force_download=True)
    fea_file = download_file("TwinDogBone.rst", "other_files", force_download=True)








.. GENERATED FROM PYTHON SOURCE LINES 68-71

Definition of the force values for which the model will be evaluated
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Define the force range and step size and create a simple design of experiments with uniformly space values.

.. GENERATED FROM PYTHON SOURCE LINES 71-79

.. code-block:: Python

    applied_force_min = 10.0
    applied_force_max = 920.0
    step = 5.0

    design_points = np.linspace(
        start=applied_force_min, stop=applied_force_max, num=int((applied_force_max - applied_force_min) / step + 1)
    )








.. GENERATED FROM PYTHON SOURCE LINES 80-83

Load the twin runtime and generate displacement and stress results for different forces applied.
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Load the twin runtime, initialize and extract ROM related information.

.. GENERATED FROM PYTHON SOURCE LINES 83-98

.. code-block:: Python

    print("Initializing the Twin")
    twin_model = TwinModel(twin_file)
    input_name = list(twin_model.inputs.keys())[0]
    results = []
    for dp in design_points:
        dp_input = {input_name: dp}
        twin_model.initialize_evaluation(inputs=dp_input)
        outputs = [dp]
        for item in twin_model.outputs:
            outputs.append(twin_model.outputs[item])
        results.append(outputs)
        if dp % 10 * step == 0.0:
            print("Simulating the model with input {}".format(dp))
    sim_results = pd.DataFrame(results, columns=[input_name] + list(twin_model.outputs), dtype=float)





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

 .. code-block:: none

    Initializing the Twin
    Simulating the model with input 10.0
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.. GENERATED FROM PYTHON SOURCE LINES 99-102

Results analysis (2D curves, as well as 3D visualization of field results)
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Plot the maximum displacement and stress computed with respect to supplied force

.. GENERATED FROM PYTHON SOURCE LINES 102-147

.. code-block:: Python

    x_ind = 0
    y0_ind = 1
    y1_ind = 3

    # Plot simulation results (outputs versus input)
    fig, ax = plt.subplots(ncols=1, nrows=1, figsize=(18, 7))

    fig.subplots_adjust(hspace=0.5)
    fig.set_tight_layout({"pad": 0.0})

    axes0 = ax
    axes1 = ax.twinx()

    sim_results.plot(x=x_ind, y=y0_ind, ax=axes0, color="g", ls="-.", label="{}".format("Max Displacement"))
    axes0.legend(loc="upper left")
    sim_results.plot(x=x_ind, y=y1_ind, ax=axes1, color="b", ls="-.", label="{}".format("Max Stress (Von Mises)"))
    axes1.legend(loc="upper right")

    axes0.set_xlabel(sim_results.columns[x_ind] + " [N]")
    axes0.set_ylabel("Max Displacement")
    axes1.set_ylabel("Max Stress (Von Mises)")

    # Show plot
    plt.show()

    # Plot the maximum stress with respect to maximum displacement
    y0_ind = 1
    y1_ind = 3

    # Plot simulation results (outputs versus input)
    fig, ax = plt.subplots(ncols=1, nrows=1, figsize=(18, 7))

    fig.subplots_adjust(hspace=0.5)
    fig.set_tight_layout({"pad": 0.0})

    axes0 = ax

    sim_results.plot(x=y0_ind, y=y1_ind, ax=axes0, color="g", ls="-.")

    axes0.set_xlabel("Max Displacement")
    axes0.set_ylabel("Max Stress (Von Mises)")

    # Show plot
    plt.show()




.. rst-class:: sphx-glr-horizontal


    *

      .. image-sg:: /examples/02-tbrom_examples/images/sphx_glr_06-TBROM_FEA_static_structural_optimization_001.png
         :alt: 06 TBROM FEA static structural optimization
         :srcset: /examples/02-tbrom_examples/images/sphx_glr_06-TBROM_FEA_static_structural_optimization_001.png
         :class: sphx-glr-multi-img

    *

      .. image-sg:: /examples/02-tbrom_examples/images/sphx_glr_06-TBROM_FEA_static_structural_optimization_002.png
         :alt: 06 TBROM FEA static structural optimization
         :srcset: /examples/02-tbrom_examples/images/sphx_glr_06-TBROM_FEA_static_structural_optimization_002.png
         :class: sphx-glr-multi-img





.. GENERATED FROM PYTHON SOURCE LINES 148-151

Extract the FEA mesh information for projection
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Load the Mechanical rst file through PyDPF and extract the mesh

.. GENERATED FROM PYTHON SOURCE LINES 151-160

.. code-block:: Python

    print("Reading the FEA mesh")
    ds = dpf.DataSources()
    ds.set_result_file_path(fea_file)
    streams = dpf.operators.metadata.streams_provider(data_sources=ds)

    # extracting the grid associated to the fea model
    whole_mesh = dpf.operators.mesh.mesh_provider(streams_container=streams).eval()
    target_mesh = whole_mesh.grid





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

 .. code-block:: none

    Reading the FEA mesh




.. GENERATED FROM PYTHON SOURCE LINES 161-163

Project the deformation field ROM onto the targeted mesh, and visualize
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

.. GENERATED FROM PYTHON SOURCE LINES 163-172

.. code-block:: Python

    def_romname = twin_model.tbrom_names[0]  # 0 = Deformation ROM, 1 = Stress ROM
    # field_data = twin_model.get_tbrom_output_field(romname) # point cloud results
    def_field_data = twin_model.project_tbrom_on_mesh(def_romname, target_mesh, True)  # mesh based results
    def_plotter = pv.Plotter()
    def_plotter.set_background("white")
    def_plotter.add_axes()
    def_plotter.add_mesh(def_field_data, scalar_bar_args={"color": "black"})
    def_plotter.show()





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

 .. code-block:: none


      0%|          [00:00<?]
    Interpolating:   0%|          [00:00<?]
    Interpolating: 100%|██████████[00:00<?]
    Interpolating: 100%|██████████[00:00<?]




.. GENERATED FROM PYTHON SOURCE LINES 173-176

.. image:: /_static/TBROM_FEA_static_structural_optimization_postPro.png
  :width: 400pt
  :align: center

.. GENERATED FROM PYTHON SOURCE LINES 176-185

.. code-block:: Python


    stress_romname = twin_model.tbrom_names[1]  # 0 = Deformation ROM, 1 = Stress ROM
    stress_field_data = twin_model.project_tbrom_on_mesh(stress_romname, target_mesh, True)  # mesh based results
    stress_plotter = pv.Plotter()
    stress_plotter.set_background("white")
    stress_plotter.add_axes()
    stress_plotter.add_mesh(stress_field_data, scalar_bar_args={"color": "black"})
    stress_plotter.show()





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

 .. code-block:: none


      0%|          [00:00<?]
    Interpolating:   0%|          [00:00<?]
    Interpolating: 100%|██████████[00:00<00:00]
    Interpolating: 100%|██████████[00:00<00:00]




.. GENERATED FROM PYTHON SOURCE LINES 186-189

.. image:: /_static/TBROM_FEA_static_structural_optimization_postPro_stress.png
  :width: 400pt
  :align: center

.. GENERATED FROM PYTHON SOURCE LINES 191-195

Using the Twin and ROM for inverse problems
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
In this section, we are going to use a simple optimizer for inverse problems. For example, we want to determine what
should be the applied force to get a given maximum stress.

.. GENERATED FROM PYTHON SOURCE LINES 195-215

.. code-block:: Python


    stress_target = 4.8e8


    def example_optimize(input_force):
        input_name = list(twin_model.inputs.keys())[0]
        dp_input = {input_name: input_force}
        twin_model.initialize_evaluation(inputs=dp_input)
        max_stress_val = twin_model.outputs["max_stress"]

        return np.sqrt((max_stress_val - stress_target) ** 2)


    bounds = [(1, 920)]
    mymin = minimize(example_optimize, 100, bounds=bounds)
    print(f"Found solution : applied force = {mymin['x']}")
    input_name = list(twin_model.inputs.keys())[0]
    dp_input = {input_name: mymin["x"]}
    twin_model.initialize_evaluation(inputs=dp_input)
    print(f"Found solution : corresponding maximum stress = {twin_model.outputs['max_stress']}")




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

 .. code-block:: none

    Found solution : applied force = [893.22578833]
    Found solution : corresponding maximum stress = 479999999.99988663





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

   **Total running time of the script:** (0 minutes 18.091 seconds)


.. _sphx_glr_download_examples_02-tbrom_examples_06-TBROM_FEA_static_structural_optimization.py:

.. only:: html

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

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

      :download:`Download Jupyter notebook: 06-TBROM_FEA_static_structural_optimization.ipynb <06-TBROM_FEA_static_structural_optimization.ipynb>`

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

      :download:`Download Python source code: 06-TBROM_FEA_static_structural_optimization.py <06-TBROM_FEA_static_structural_optimization.py>`

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

      :download:`Download zipped: 06-TBROM_FEA_static_structural_optimization.zip <06-TBROM_FEA_static_structural_optimization.zip>`


.. only:: html

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

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