<?xml version='1.0' encoding='UTF-8' ?>
<!DOCTYPE html
  SYSTEM "about:legacy-compat">
<html xmlns:mml = "http://www.w3.org/1998/Math/MathML" lang = "en"><head><meta charset = "UTF-8"/><meta name = "copyright" content = "(C) Copyright 2020"/><meta name = "DC.rights.owner" content = "(C) Copyright 2020"/><meta name = "DC.type" content = "concept"/><meta name = "abstract" content = "Couple design nodes that are symmetric to a plane - for arbitrary meshes."/><meta name = "description" content = "Couple design nodes that are symmetric to a plane - for arbitrary meshes."/><meta name = "DC.relation" scheme = "URI" content = "../TsoCmdMap/tso-r-cmd-linkShape.htm"/><meta name = "DC.format" content = "HTML5"/><meta name = "DC.identifier" content = "tso-c-usr-shape-desArea-lsSPlaneSym"/><meta name = "DC.language" content = "en"/><link rel = "stylesheet" type = "text/css" href = "../DSDocUI_XML34.css"/><title>Plane Symmetry for Nonsymmetric Meshes (SURF_PLANE_SYM)</title>
<script type = "text/javascript" src = "../DSDocUI_Highlight34.js">
  	/* */
  	</script></head><body onLoad = "highlightSearchTerms();" id = "tso-c-usr-shape-desArea-lsSPlaneSym">
<a name = "hj-top"> </a><table class = "table1" id = "table11"><tr><td><table class = "DocHeader"><tr><td class = "DocHeader1" colspan = "2"><h1>Plane Symmetry for Nonsymmetric Meshes (SURF_PLANE_SYM)</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 = "header"><p class = "abstract">
<span class = "shortdesc">Couple design nodes that are symmetric to a plane - for arbitrary meshes.</span>

</p>
<ul><li><a href = "#tso-c-usr-shape-desArea-lsSPlaneSym__tso-c-usr-shape-desArea-lsSPlaneSym-sens" id = "toc_rg" title = "">Special Considerations when using Shape Sensitivity</a></li></ul>
</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 link conditions (coupling conditions) for nodes in shape optimization." href = "../TsoCmdMap/tso-r-cmd-linkShape.htm">LINK_SHAPE</a></td></tr></table></td></tr></table>




<div class = "body conbody">

<p>
<table class = "table" id = "tso-c-usr-shape-desArea-lsSPlaneSym__table_D2AB300D6AAC47A2B0C3A7C359D8BAC7"><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-usr-shape-desArea-lsSPlaneSym__table_D2AB300D6AAC47A2B0C3A7C359D8BAC7__entry__1">CLIENT / Applicable for</th>
<th class = "entry align-center" id = "tso-c-usr-shape-desArea-lsSPlaneSym__table_D2AB300D6AAC47A2B0C3A7C359D8BAC7__entry__2">SHAPE_CONTROLLER</th>
<th class = "entry align-center" id = "tso-c-usr-shape-desArea-lsSPlaneSym__table_D2AB300D6AAC47A2B0C3A7C359D8BAC7__entry__3">SHAPE_SENSITIVITY</th>
</tr>
</thead><tbody class = "tbody">
<tr class = "row">
<td class = "entry" headers = "tso-c-usr-shape-desArea-lsSPlaneSym__table_D2AB300D6AAC47A2B0C3A7C359D8BAC7__entry__1">SURF_PLANE_SYM</td>
<td class = "entry align-center" headers = "tso-c-usr-shape-desArea-lsSPlaneSym__table_D2AB300D6AAC47A2B0C3A7C359D8BAC7__entry__2">OK</td>
<td class = "entry align-center" headers = "tso-c-usr-shape-desArea-lsSPlaneSym__table_D2AB300D6AAC47A2B0C3A7C359D8BAC7__entry__3">OK</td>
</tr>
</tbody></table>
</p>


<p>To couple nodal displacements symmetrically with respect to a plane, the symmetry plane must be
            defined in terms of position and orientation. This is supported for symmetric and
            unsymmetric meshes. The following four parameters are necessary for the definition of
            the link condition:</p>
<pre class = "codeblock">
<code class = "ph codeph">
CLIENT     = SURF_PLANE_SYM
CLIENT_DIR = &lt;X_1&gt;, &lt;X_2&gt;, &lt;X_3&gt;
CS         = name_of_coord_system
TOL        = tolerance_value
</code>
</pre>
<p>The origin of the coordinate system referenced by <code class = "ph codeph">CS</code> defines a point on the
            symmetry plane. The direction specified by the <code class = "ph codeph">CLIENT_DIR</code> parameter
            defines the normal of the plane. The tolerance value specified by <code class = "ph codeph">TOL</code>
            is used as absolute tolerance in intersection tests and can be used to influence the
            behavior on the border of the selected node group.</p>
<p>The symmetry of the nodes (assigned by <code class = "ph codeph">ND_GROUP</code> in the
                <code class = "ph codeph">DVCON_SHAPE</code> command) is checked against the symmetry plane. For
            each node, a reference displacement is calculated for its symmetric "counterpart". This
            counterpart is obtained by reflecting the node at the symmetry plane, that is, by
            intersecting a line through the node in the plane normal direction with the surface defined
            by all selected nodes. The reference displacement is obtained by interpolation of the
            optimization displacements of the adjacent nodes. The tolerance is required to find
            reference displacements at the border of the selected node group, where it will happen
            that nodes do not have an opposite face (with respect to the plane definition) and thus
            no intersection points in plane normal directions can be found.</p>
<p>Optional, a strategy to determine node position influence on the result
can be chosen:</p>
<pre class = "codeblock">
<code class = "ph codeph">
MAIN = MAX | MIN</code>
</pre>
<p>The symmetry is built up by using the maximum (default) or the minimum of the displacement of the selected node 
(d1 in the following figure) and the interpolated displacement of its plane
symmetric counter part (reference displacement d2 in the following
figure).</p>
<table class = "table" id = "tso-c-usr-shape-desArea-lsSPlaneSym__ae289478"><caption/><colgroup><col/></colgroup><tbody class = "tbody">
<tr class = "row">
<td class = "entry"><br/><img class = "image" id = "tso-c-usr-shape-desArea-lsSPlaneSym__image_F06E875D1D4243FAB027A7D72199D43A" src = "../TsoUserImages/ae046be3.jpg" width = "585" height = "293"/><br/></td>
</tr>
</tbody></table>

    
<p><table class = "Remark" id = "table132"><tr><td class = "Remark"><span class = "run-in.important">Important:
				</span><span class = "notecontent"><p><ul class = "ul" id = "tso-c-usr-shape-desArea-lsSPlaneSym__ul_5BC748E67FDC45739B513CF0B6CF83A1">
<li class = "li">
The coordinate system referenced by <code class = "ph codeph">CS</code> must be a Cartesian
coordinate system.</li>
<li class = "li">
Only the <code class = "ph codeph">MAIN=MAX</code> or <code class = "ph codeph">MAIN=MIN</code>
criteria are allowed for determination of the main node.</li>
</ul></p></span></td></tr></table>
</p>

<div class = "section" id = "tso-c-usr-shape-desArea-lsSPlaneSym__tso-c-usr-shape-desArea-lsSPlaneSym-sens"><h2 class = "title sectiontitle">Special Considerations when using Shape Sensitivity</h2>

<p>This coupling condition is applicable for sensitivity-based shape optimization. However, the two approaches work in different ways.
For the sensitivity-based optimization, the optimization problem is solved only on one halve of the symmetry group and the results (the design variable values) are transferred to the missing part.
     
<ul class = "ul" id = "tso-c-usr-shape-desArea-lsSPlaneSym__ul_1CA037D5DEC140BD90C25E9E8A89669F">
<li class = "li">The <code class = "ph codeph">MAIN</code> command is not evaluated. Instead the "active" part is determined by the direction of the plane normal:
The "active"/"main" lies on the side of the plane where the plane normal direction points to.          </li>
<li class = "li"> This is especially important when combining several
                        plane restrictions. The later restrictions must lie in the "active" area of
                        the previous restriction.</li>
<li class = "li">If the reflection of a node near the symmetry plane
                        lies in a face that is cut by the symmetry plane, then this node also
                        becomes part of the "active"/"main" area. This might lead to nonsymmetries
                        near the symmetry plane. These nonsymmetries can get distributed to
                        neighboring nodes through design variable filtering (which is activated by
                        default).</li>
</ul>
</p>
</div>

</div>

<div class = "related-links"/></td></tr></table><script type = "text/javascript" src = "../DSDocUI_Bottom34.js">/* */</script></body>
</html>
