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

.. only:: html

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

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

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

.. _sphx_glr_gallery_examples_verifications_make_cantilever_min_volume.py:


Minimize volume with maximum compliance
#######################################

.. GENERATED FROM PYTHON SOURCE LINES 7-9

This is a variation of the standart design optimisation problem where the minimum volume structure is seeked given a maximum compliance.
 It illustrate the modularity of how Functions is implemented in HydrOpTop and can be used either as a constrain or a main objective.

.. GENERATED FROM PYTHON SOURCE LINES 9-64

.. code-block:: Python


    import numpy as np

    from HydrOpTop.Functions.verification import Mechanical_Compliance, Volume_Percentage
    from HydrOpTop.Functions import Volume_Percentage
    from HydrOpTop.Materials import SIMP
    from HydrOpTop.Filters import Density_Filter, Heaviside_Filter
    from HydrOpTop.Crafter import Steady_State_Crafter
    from HydrOpTop.Solvers import Linear_Elasticity_2D

    #create solver simulation object
    sim = Linear_Elasticity_2D("cantilever")

    #get cell ids in the region to optimize and parametrize permeability
    #same name than in pflotran input file
    young_modulus = SIMP(cell_ids_to_parametrize="all", property_name="YOUNG_MODULUS", bounds=[0, 2000], power=3)

    #define cost function
    max_vol = Volume_Percentage("parametrized_cell")

    #define maximum compliance
    MC = Mechanical_Compliance(ids_to_consider="everywhere")
    MC.constraint_tol = 5e-2

    #define filter
    dfilter = Density_Filter(0.3)
    hfilter = Heaviside_Filter(0.5, 1)

    #craft optimization problem
    #i.e. create function to optimize, initiate IO array in classes...
    crafted_problem = Steady_State_Crafter(max_vol, sim, [young_modulus], [MC], filters=[dfilter, hfilter])
    crafted_problem.IO.output_every_iteration(2)
    crafted_problem.IO.define_output_format("vtu")

    #initialize optimizer
    p_ini = np.ones(crafted_problem.get_problem_size(),dtype='f8')

    #optimize in several pass to reach discrete distribution
    out = crafted_problem.optimize(optimizer="nlopt-mma", action="minimize", max_it=50, ftol=1e-10, initial_guess=p_ini)

    hfilter.stepness = 2
    out = crafted_problem.optimize(optimizer="nlopt-mma", action="minimize", 
                                   max_it=20, initial_guess=out.p_opt)
    hfilter.stepness = 4
    out = crafted_problem.optimize(optimizer="nlopt-mma", action="minimize", 
                                   max_it=20, initial_guess=out.p_opt)
    hfilter.stepness = 8
    out = crafted_problem.optimize(optimizer="nlopt-mma", action="minimize", 
                                   max_it=20, initial_guess=out.p_opt)
    hfilter.stepness = 20
    out = crafted_problem.optimize(optimizer="nlopt-mma", action="minimize", 
                                   max_it=30, initial_guess=out.p_opt)

    crafted_problem.IO.write_fields_to_file([out.p_opt_filtered], "./out.vtu", ["Filtered_density"])



.. _sphx_glr_download_gallery_examples_verifications_make_cantilever_min_volume.py:

.. only:: html

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

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

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

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

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


.. only:: html

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

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