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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>Settings of the Mesh Filter</h1></td></tr><tr><td class = "DocHeader4" colspan = "2"/></tr><tr><td class = "DocHeader3"><table class = "DocHeaderIntro" id = "table12"><tr><td class = "Intro1Only"><p class = "shortdesc">To obtain a mesh-independent result from the optimization, 
  <span class = "ph">SIMULIA Tosca Structure</span> 
 has a filter technique implemented to avoid mesh dependence. 
</p></td></tr></table></td><td class = "DocHeader2"><table class = "DocTopicsSeeAlso" id = "table13"><tr><td class = "TopicsTitle">See Also</td></tr></table><table class = "DocTopicsInOtherGuides" id = "table14"><tr><td height = "8px"/></tr><tr><td class = "TopicsTitleNormal">In Other Guides</td></tr><tr><td><a title = "Defines parameters to control optimization." href = "../TsoCmdMap/tso-r-cmd-optParam.htm#tso-r-cmd-optParam">OPT_PARAM</a></td></tr></table></td></tr></table>
  

  

<div class = "body conbody"><p>The result of the optimization of a bending beam, see the following
figure, shows a numerical instability effect. The structure contains
checkerboard-like areas with soft (void) and hard elements. In a structure
like this, many hard elements have only the point contact to other hard
elements. This result is not a valid design because the checkerboard
effect is a numerical instability. This effect has been analyzed by BENDSØE
and SIGMUND (M. P. Bendsøe, O. Sigmund, Topology Optimization Theory,
Methods and Applications Springer-Verlag 2003) and references therein.</p>
<p>The following figure shows a checkerboard effect for a bending beam:</p>
<p><br/><img border = "1" class = "image" id = "tso-c-user-TopOpt-Sett-Sensi-MF__image_8ABB643B4862482C94A87991F8699753" src = "../TsoUserImages/ag097c1b.jpg" width = "210"/><br/></p>
<p> This checkerboard effect depends on the mesh and the discretization, which is obvious in the next figure. The mesh is refined in parts of the model.</p>
<p><br/><img border = "1" class = "image" id = "tso-c-user-TopOpt-Sett-Sensi-MF__image_FED93E8FB456413B937D90FF4943EFF5" src = "../TsoUserImages/topo_checkerboard_effect_2.png" width = "210"/><br/></p>
<p> Checkerboard structures cannot be manufactured in practice. The user
also wants to obtain a mesh-independent result from the optimization.
Due to these demands, <span class = "ph">SIMULIA Tosca Structure</span>
has a filter technique implemented to avoid mesh dependence. A specification
of a filter radius (<code class = "ph codeph">FILTER_RADIUS</code> parameter) is necessary
for applying the filter. If the radius of the filter is not specified,
the optimization is performed using a filter having a default radius.
This radius might be too large for coarse meshes. </p>
<p><table class = "Remark" id = "table132"><tr><td class = "Remark"><span class = "run-in.important">Important:
				</span><span class = "notecontent">If the radius is too
large, the optimization result will not show a detailed structure. A
small value of the radius leads to a fine structure.  <p>It is recommended to choose the filter radius equal to twice the mean
element edge length.</p></span></td></tr></table>
</p>
<p>The filter radius is defined in <code class = "ph codeph">OPT_PARAM</code> command as follows:</p>
<pre class = "codeblock">
<code class = "ph codeph">
OPT_PARAM
 ID_NAME = optimization_control
 OPTIMIZE = id_of_optimize
 ...
 FILTER_RADIUS = 5.
END_
</code>
</pre>
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