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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>Correction of Defects in Topology Optimization Results</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 = "header"><p class = "abstract">
<span class = "shortdesc">In some cases, the topology optimization results contain small
irregularities that are generally not desired. In order to deal with
them, the filtering of the material distribution as well as the possibility
to remove small unconnected components are implemented.</span>

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<div class = "body conbody">

<table class = "table" id = "tso-c-usr-validation-smooth-defectsTopo__ah681694"><caption/><colgroup><col/><col/><col/><col/><col/><col/><col/></colgroup><thead class = "thead">
<tr class = "row">
<th class = "entry" id = "tso-c-usr-validation-smooth-defectsTopo__ah681694__entry__1" colspan = "6"><p>Filtering and repair parameters
of <span class = "ph">Tosca Structure.smooth</span></p></th>
</tr>
<tr class = "row">
<th class = "entry" id = "tso-c-usr-validation-smooth-defectsTopo__ah681694__entry__2" rowspan = "2"><p>Parameter</p></th>
<th class = "entry" id = "tso-c-usr-validation-smooth-defectsTopo__ah681694__entry__3" rowspan = "2"><p>Value</p></th>
<th class = "entry" id = "tso-c-usr-validation-smooth-defectsTopo__ah681694__entry__4" rowspan = "2"><p>Description</p></th>
<th class = "entry" id = "tso-c-usr-validation-smooth-defectsTopo__ah681694__entry__5" colspan = "3"><p>Supported by</p></th>
</tr>
<tr class = "row">
<th class = "entry" id = "tso-c-usr-validation-smooth-defectsTopo__ah681694__entry__6"><p>GUI-TS.pre </p></th>
<th class = "entry" id = "tso-c-usr-validation-smooth-defectsTopo__ah681694__entry__7"><p>GUI-TS.smooth</p></th>
<th class = "entry" id = "tso-c-usr-validation-smooth-defectsTopo__ah681694__entry__8"><p>TExt</p></th>
</tr>
</thead><tbody class = "tbody">
<tr class = "row">
<td class = "entry" headers = "tso-c-usr-validation-smooth-defectsTopo__ah681694__entry__1 tso-c-usr-validation-smooth-defectsTopo__ah681694__entry__2"><p><span class = "ph">RESULT_FILTERING</span></p></td>
<td class = "entry" headers = "tso-c-usr-validation-smooth-defectsTopo__ah681694__entry__1 tso-c-usr-validation-smooth-defectsTopo__ah681694__entry__3"><p><span class = "ph">off</span><span class = "ph">: </span>  no filtering</p><p><span class = "ph">moderate: </span>
 one filtering cycle</p><p><span class = "ph">full: </span>  5 filtering cycles</p><p>default:
<span class = "ph">off</span></p></td>
<td class = "entry" headers = "tso-c-usr-validation-smooth-defectsTopo__ah681694__entry__1 tso-c-usr-validation-smooth-defectsTopo__ah681694__entry__4"><p>Defines the number of filtering cycles that
are applied in order to make the material distribution homogeneous</p></td>
<td class = "entry" headers = "tso-c-usr-validation-smooth-defectsTopo__ah681694__entry__1 tso-c-usr-validation-smooth-defectsTopo__ah681694__entry__5 tso-c-usr-validation-smooth-defectsTopo__ah681694__entry__6"><p>x</p></td>
<td class = "entry" headers = "tso-c-usr-validation-smooth-defectsTopo__ah681694__entry__1 tso-c-usr-validation-smooth-defectsTopo__ah681694__entry__5 tso-c-usr-validation-smooth-defectsTopo__ah681694__entry__7"><p>x</p></td>
<td class = "entry" headers = "tso-c-usr-validation-smooth-defectsTopo__ah681694__entry__1 tso-c-usr-validation-smooth-defectsTopo__ah681694__entry__5 tso-c-usr-validation-smooth-defectsTopo__ah681694__entry__8"><p>-</p></td>
</tr>
<tr class = "row">
<td class = "entry" headers = "tso-c-usr-validation-smooth-defectsTopo__ah681694__entry__1 tso-c-usr-validation-smooth-defectsTopo__ah681694__entry__2"><p><span class = "ph">COMPONENT_LIMITING_SIZE</span></p></td>
<td class = "entry" headers = "tso-c-usr-validation-smooth-defectsTopo__ah681694__entry__1 tso-c-usr-validation-smooth-defectsTopo__ah681694__entry__3"><p>Real value between 0 and 0.5</p><p>Default:
0</p></td>
<td class = "entry" headers = "tso-c-usr-validation-smooth-defectsTopo__ah681694__entry__1 tso-c-usr-validation-smooth-defectsTopo__ah681694__entry__4"><p>Defines the minimal allowed relative size of
a connected component (calculated using its number of faces). All components
with the relative size below this value are removed. Default: 0</p></td>
<td class = "entry" headers = "tso-c-usr-validation-smooth-defectsTopo__ah681694__entry__1 tso-c-usr-validation-smooth-defectsTopo__ah681694__entry__5 tso-c-usr-validation-smooth-defectsTopo__ah681694__entry__6"><p>x</p></td>
<td class = "entry" headers = "tso-c-usr-validation-smooth-defectsTopo__ah681694__entry__1 tso-c-usr-validation-smooth-defectsTopo__ah681694__entry__5 tso-c-usr-validation-smooth-defectsTopo__ah681694__entry__7"><p>x</p></td>
<td class = "entry" headers = "tso-c-usr-validation-smooth-defectsTopo__ah681694__entry__1 tso-c-usr-validation-smooth-defectsTopo__ah681694__entry__5 tso-c-usr-validation-smooth-defectsTopo__ah681694__entry__8"><p>x</p></td>
</tr>

</tbody></table>

<p>The result filtering averages the material values ("densities") in
the places where it affects the isosurface most, and therefore it may
account for large changes of the surface geometry.</p><p>See the following
figures for the influence of the result filtering on the geometry in
various cases.</p>
<table class = "table" id = "tso-c-usr-validation-smooth-defectsTopo__ah730917"><caption/><colgroup><col/><col/><col/><col/></colgroup><tbody class = "tbody">
<tr class = "row">
<td class = "entry"><p>No result filtering (left)</p></td>
<td class = "entry"><p>moderate result filtering (one cycle) (right)</p></td>
<td class = "entry"/>
</tr>
<tr class = "row">
<td class = "entry" colspan = "2"><br/><img class = "image" src = "../TsoUserImages/smooth_result_filter1.png" width = "350"/><br/></td>
<td class = "entry"><p>Small isolated components are removed</p></td>
</tr>
<tr class = "row">
<td class = "entry" colspan = "2"><br/><img class = "image" src = "../TsoUserImages/smooth_result_filter2.png" width = "350"/><br/></td>
<td class = "entry"><p>Narrow "bridges" are removed</p></td>
</tr>
<tr class = "row">
<td class = "entry" colspan = "2"><br/><img class = "image" src = "../TsoUserImages/smooth_result_filter3.png" width = "350"/><br/></td>
<td class = "entry"><p>Narrow caverns and small holes (including the
holes inside the model) are removed</p></td>
</tr>
</tbody></table>

<p>When the parameter <code class = "ph codeph">COMPONENT_LIMITING_SIZE</code> is set
to a positive number, all connected components with the number of faces
below the product <code class = "ph codeph">&lt;number of all faces&gt; * COMPONENT_LIMITING_SIZE</code>
are removed. By definition, in a connected component, each two faces
can be connected by a chain of other faces, so that two consequent faces
in the chain have a common side.</p><table class = "Remark" id = "table132"><tr><td class = "Remark"><span class = "run-in.important">Important:
				</span><span class = "notecontent"><p>Note that only the connectivity of the
surface is checked; a hole inside the model that is completely surrounded
by material is considered as a separate connected component. The removal
of small connected components takes place directly after the isocut.</p></span></td></tr></table>

<p>If more than one connected component remains, the user gets a message:</p><table class = "table" id = "tso-c-usr-validation-smooth-defectsTopo__ah705301"><caption/><colgroup><col/></colgroup><tbody class = "tbody">
<tr class = "row">
<td class = "entry"><br/><img class = "image" src = "../TsoUserImages/f1100.png" width = "400"/><br/></td>
</tr>
</tbody></table>

<p>where <code class = "ph codeph">N</code> is the number of remaining connected components (each
inner hole counts as a component as well).</p>
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