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<a name = "hj-top"> </a><table class = "table1" id = "table11"><tr><td><table class = "DocHeader"><tr><td class = "DocHeader1" colspan = "2"><h1>About Cluster Groups</h1></td></tr><tr><td class = "DocHeader4" colspan = "2"/></tr><tr><td class = "DocHeader3" colspan = "2"><table class = "DocThemeIntro" id = "table12"><tr><td class = "Intro1Only"><p class = "shortdesc">
    For sensitivity-based topology optimization, elements can be clustered to have equal pseudo densities in certain areas during the optimization (<code class = "ph codeph">CHECK_TYPE = CLUSTER_GROUPS</code>).
  
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  <div class = "body conbody">
    <p>Define a cluster group as follows:</p>

<pre class = "codeblock">
<code class = "ph codeph">DVCON_TOPO</code>
<code class = "ph codeph">  ID_NAME    = DVCON_CLUSTER</code>
<code class = "ph codeph">  EL_GROUP   = CLUSTER_1</code>
<code class = "ph codeph">  EL_GROUP   = CLUSTER_2</code>
<code class = "ph codeph">  EL_GROUP   = CLUSTER_3</code>
<code class = "ph codeph">  EL_GROUP   = CLUSTER_4</code>
<code class = "ph codeph">  ...</code>
<code class = "ph codeph">  ...</code>
<code class = "ph codeph">  EL_GROUP   = CLUSTER_143</code>
<code class = "ph codeph">  EL_GROUP   = CLUSTER_144</code>
<code class = "ph codeph">  CHECK_TYPE = CLUSTER_GROUPS</code>
<code class = "ph codeph">END_</code>
</pre>

    <p><div class = "note"><span class = "run-in.note">Note:
			</span><span class = "notecontent">
      Elements within one referred element group will have the same values for pseudo densities.
      But two different element groups will have different values for pseudo densities.
    </span></div>
</p>

    <p>
      Reference the <code class = "ph codeph">DVCON_TOPO</code> ID name in the <code class = "ph codeph">OPTIMIZE</code>
      command in order to activate this restriction:
    </p>

<pre class = "codeblock">
<code class = "ph codeph">OPTIMIZE</code>
<code class = "ph codeph">  ID_NAME = ...</code>
<code class = "ph codeph">  ...</code>
<code class = "ph codeph">  DVCON   = DVCON_CLUSTER</code>
<code class = "ph codeph">  ...</code>
<code class = "ph codeph">END_</code>
</pre>

    <p>To give an example the following model is considered:</p>

    <table class = "table" id = "tso-c-user-TopOpt-DesArea-clustering-gui__table_BEC3E735C8AA49B5A2F4BA07CAA2B62A"><caption/><colgroup><col style = "width:33.33333333333333%"/><col style = "width:33.33333333333333%"/><col style = "width:33.33333333333333%"/></colgroup><thead class = "thead">
          <tr class = "row">
            <th class = "entry" id = "tso-c-user-TopOpt-DesArea-clustering-gui__table_BEC3E735C8AA49B5A2F4BA07CAA2B62A__entry__1"> Model </th>
            <th class = "entry" id = "tso-c-user-TopOpt-DesArea-clustering-gui__table_BEC3E735C8AA49B5A2F4BA07CAA2B62A__entry__2"> Displacements </th>
            <th class = "entry" id = "tso-c-user-TopOpt-DesArea-clustering-gui__table_BEC3E735C8AA49B5A2F4BA07CAA2B62A__entry__3"> Stresses </th>
          </tr>
        </thead><tbody class = "tbody">
          <tr class = "row">
            <td class = "entry" headers = "tso-c-user-TopOpt-DesArea-clustering-gui__table_BEC3E735C8AA49B5A2F4BA07CAA2B62A__entry__1"><br/><img class = "image" id = "tso-c-user-TopOpt-DesArea-clustering-gui__image_D71257A5A05C49DAB9A1AC4875863FB6" src = "../TsoUserImages/topo_clusters_example_model.png" height = "227"/><br/></td>
            <td class = "entry" headers = "tso-c-user-TopOpt-DesArea-clustering-gui__table_BEC3E735C8AA49B5A2F4BA07CAA2B62A__entry__2"><br/><img class = "image" id = "tso-c-user-TopOpt-DesArea-clustering-gui__image_98DF890CF7C64354BFC586DB2EED42E8" src = "../TsoUserImages/topo_clusters_example_displ.png" height = "189"/><br/></td>
            <td class = "entry" headers = "tso-c-user-TopOpt-DesArea-clustering-gui__table_BEC3E735C8AA49B5A2F4BA07CAA2B62A__entry__3"><br/><img class = "image" id = "tso-c-user-TopOpt-DesArea-clustering-gui__image_69267BC5D04B47CC8497DA7848EF74D5" src = "../TsoUserImages/topo_clusters_example_stress.png" height = "189"/><br/></td>
          </tr>
        </tbody></table>

    <p>To obtain an extrudable profile as the optimization result cluster groups are utilized:</p>

    <table class = "table" id = "tso-c-user-TopOpt-DesArea-clustering-gui__table_1217D5D230804F96A9597A9CB891EDCC"><caption/><colgroup><col style = "width:50%"/><col style = "width:50%"/></colgroup><thead class = "thead">
          <tr class = "row">
            <th class = "entry" id = "tso-c-user-TopOpt-DesArea-clustering-gui__table_1217D5D230804F96A9597A9CB891EDCC__entry__1"> Mesh </th>
            <th class = "entry" id = "tso-c-user-TopOpt-DesArea-clustering-gui__table_1217D5D230804F96A9597A9CB891EDCC__entry__2"> Clustering groups </th>
          </tr>
        </thead><tbody class = "tbody">
          <tr class = "row">
            <td class = "entry" headers = "tso-c-user-TopOpt-DesArea-clustering-gui__table_1217D5D230804F96A9597A9CB891EDCC__entry__1"><br/><img class = "image" id = "tso-c-user-TopOpt-DesArea-clustering-gui__image_8900C79DD8914823922FB870396009B8" src = "../TsoUserImages/topo_clusters_example_mesh.png" height = "189"/><br/></td>
            <td class = "entry" headers = "tso-c-user-TopOpt-DesArea-clustering-gui__table_1217D5D230804F96A9597A9CB891EDCC__entry__2"><br/><img class = "image" id = "tso-c-user-TopOpt-DesArea-clustering-gui__image_1CC1D6BDC6AA473AA480BD924C5E8E4B" src = "../TsoUserImages/topo_clusters_example_clustering.png" height = "189"/><br/></td>
          </tr>
        </tbody></table>

    <p>The corresponding optimized structures are shown in the following figures:</p>

    <table class = "table" id = "tso-c-user-TopOpt-DesArea-clustering-gui__table_780A8D93092643F2A112C3B7F5153C8A"><caption/><colgroup><col style = "width:50%"/><col style = "width:50%"/></colgroup><thead class = "thead">
          <tr class = "row">
            <th class = "entry" id = "tso-c-user-TopOpt-DesArea-clustering-gui__table_780A8D93092643F2A112C3B7F5153C8A__entry__1"> Optimization without clustering </th>
            <th class = "entry" id = "tso-c-user-TopOpt-DesArea-clustering-gui__table_780A8D93092643F2A112C3B7F5153C8A__entry__2"> Optimization with clustering groups </th>
          </tr>
        </thead><tbody class = "tbody">
          <tr class = "row">
            <td class = "entry" headers = "tso-c-user-TopOpt-DesArea-clustering-gui__table_780A8D93092643F2A112C3B7F5153C8A__entry__1"><br/><img class = "image" id = "tso-c-user-TopOpt-DesArea-clustering-gui__image_838A91190F7E43B798F666027A11560A" src = "../TsoUserImages/topo_clusters_example_default_optim.png" height = "189"/><br/></td>
            <td class = "entry" headers = "tso-c-user-TopOpt-DesArea-clustering-gui__table_780A8D93092643F2A112C3B7F5153C8A__entry__2"><br/><img class = "image" id = "tso-c-user-TopOpt-DesArea-clustering-gui__image_387A880B345C403D88D8D96E2028469E" src = "../TsoUserImages/topo_clusters_example_clustered_optim.png" height = "189"/><br/></td>
          </tr>
        </tbody></table>
  </div>

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