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<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 = "For shape optimization, restrictions are defined as boundary conditions that limit the potential area of the node displacement. A design variable constraint is a restriction that directly affects the individual design variables, here, the individual design nodes. Since the nodes in the mesh smoothing area (see MESH_SMOOTH) can be interpreted as second order design nodes, there is also the possibility to apply the restrictions (to a limited degree) to the nodes of the mesh smoothing area. Compared to geometrical optimization based on a few parameters, Tosca Structure.shape allows every design node to be displaced ‘independently’ from other design nodes."/><meta name = "description" content = "For shape optimization, restrictions are defined as boundary conditions that limit the potential area of the node displacement. A design variable constraint is a restriction that directly affects the individual design variables, here, the individual design nodes. Since the nodes in the mesh smoothing area (see MESH_SMOOTH) can be interpreted as second order design nodes, there is also the possibility to apply the restrictions (to a limited degree) to the nodes of the mesh smoothing area. Compared to geometrical optimization based on a few parameters, Tosca Structure.shape allows every design node to be displaced ‘independently’ from other design nodes."/><meta name = "DC.relation" scheme = "URI" content = "../TsoCmdMap/tso-r-cmd-dvconShape.htm#tso-r-cmd-dvconShape"/><meta name = "DC.format" content = "HTML5"/><meta name = "DC.identifier" content = "tso-c-usr-shape-desArea-dvcOvw"/><meta name = "DC.language" content = "en"/><link rel = "stylesheet" type = "text/css" href = "../DSDocUI_XML34.css"/><title>Restrictions (DVCON_SHAPE) Overview</title>
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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>Restrictions (DVCON_SHAPE) Overview</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">
For shape optimization, restrictions are defined as boundary
conditions that limit the potential area of the node displacement. A
design variable constraint is a restriction that directly affects the
individual design variables, here, the individual design nodes. Since
the nodes in the mesh smoothing area (see <code class = "ph codeph">MESH_SMOOTH</code>)
can be interpreted as second order design nodes, there is also the possibility
to apply the restrictions (to a limited degree) to the nodes of the mesh
smoothing area. Compared to geometrical optimization based on a few parameters,
<span class = "ph">Tosca Structure.shape</span>
allows every design node to be displaced ‘independently’ from other
design nodes.
</span>

</p>
<p>This page discusses: </p><ul><li><a href = "#tso-c-usr-shape-desArea-dvcOvw__tso-c-usr-shape-desArea-restr-defGui" id = "toc_rg" title = "">Definition in <span class = "ph">Tosca Structure.gui</span></a></li><li><a href = "#tso-c-usr-shape-desArea-dvcOvw__tso-c-usr-shape-desArea-restr-defCmd" id = "toc_rg" title = ""> Command Syntax</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 restrictions of the design variables in shape optimization." href = "../TsoCmdMap/tso-r-cmd-dvconShape.htm#tso-r-cmd-dvconShape">DVCON_SHAPE</a></td></tr></table></td></tr></table>




<div class = "body conbody">
<p>
To meet functional and manufacturing requirements, it is usually necessary
to limit the solution area and therefore the independence of the design
nodes. Unrestricted shape optimization can produce trivial results. For
example, if the shape of a shaft shoulder under axial tensile stress
is optimized without restricting the design nodes, a smooth beam will
arise that will not be able to fulfill the original function.</p><p>To achieve
the best results the rule "As much flexibility as possible, as few
restrictions as necessary!" should be followed. The possible restrictions
are the specification of an allowed displacement area by limiting the
directional amount of optimization displacement and the specification
of variation and frozen areas. It is also possible to influence the allowed
displacement direction by limiting the displacement to specific coordinate
directions. In addition, the optimization displacement of a node can
be made dependent on the optimization displacement of another node. The
definition of the design variable constraints for shape optimization
is done with the <code class = "ph codeph">DVCON_SHAPE</code> command.</p>
<p>The following restrictions are available for shape optimization, but not all are applicable for both optimization attempts:</p>
<ul class = "ul" id = "tso-c-usr-shape-desArea-dvcOvw__ul_4CF874A3E9DD4CC0A829248ACC69E102">
<li class = "li">Restriction of the amount of displacement </li>
<li class = "li">Maximum and minimum member size </li>
<li class = "li">Displacement check against solids </li>
<li class = "li">Displacement check against elements of an element group </li>
<li class = "li">Restriction of the displacement direction</li>
<li class = "li">Restricting the displacement to a slide surface</li>
<li class = "li">Assignment of a coupling condition</li>
</ul>
<p>
You are free to use the nonapplicable design variable constraints for sensitivity-based shape optimization as well. 
But in that case the geometry is changed without letting the optimization module acknowledge this change which might or might not lead to convergence problem for (complex) models.</p>
    
<table class = "table" id = "tso-c-usr-shape-desArea-dvcOvw__ae231537"><caption/><colgroup><col/></colgroup><tbody class = "tbody">
<tr class = "row">
<td class = "entry">
<br/><img class = "image" id = "tso-c-usr-shape-desArea-dvcOvw__image_77736F00BE574B3397F47AB1D4203A96" src = "../TsoUserImages/ae038884.jpg" width = "450"/><br/>
</td>
</tr>
</tbody></table>

<div class = "note"><span class = "run-in.note">Note:
			</span><span class = "notecontent"><p><ul class = "ul" id = "tso-c-usr-shape-desArea-dvcOvw__ul_019B692D79C6496C9E47ABB290414004">
<li class = "li">
Some of the design variable constraints for shape optimization can be
interpreted as side constraints or bounds (design variable boundaries)
in the same way these terms are used in standard optimization nomenclature.</li>
<li class = "li">
Some of the design variable constraints for shape optimization relate
not only to the design variable itself but also to the corresponding
optimization displacement vectors (or the design coordinates). The term
‘design variable constraint’ in this case should be interpreted
in a more general sense.</li>
<li class = "li">
In contrast to the <code class = "ph codeph">DVCON_SHAPE</code> parameter, which
has a direct effect on the individual design variables, the <code class = "ph codeph">CONSTRAINT</code>
parameter defines a constraint for the optimization job that affects
the functional relationships of several design variables (for example, volume
constraint).</li>
<li class = "li">
The activated <code class = "ph codeph">DVCON_SHAPE</code> entries are executed in
the order in which they are referenced in the <code class = "ph codeph">OPTIMIZE</code>
command.
The individual <code class = "ph codeph">DVCON_SHAPE</code> entries are checked independent
of one another, that is , a <code class = "ph codeph">DVCON_SHAPE</code> entry always overrides
the preceding <code class = "ph codeph">DVCON_SHAPE</code> entry. If mutually independent
restrictions are declared all restrictions are observed. If mutually
dependent restrictions are declared the user must select an order of
execution that is logical and specific for the problem.</li>
<li class = "li">
The restricted nodes are checked at the beginning and the execution
stops if the defined constraint is not fulfilled (<code class = "ph codeph">CHECK_SLIDE</code>,
<code class = "ph codeph">CHECK_LINK</code>). This behavior can be switched off with
the parameter <code class = "ph codeph">FEASIBLE_START=NO</code>. But for example if
the surface described node group is not stampable and this check is switched
off the restriction enforces the stampable surface.
</li>
</ul></p></span></div>

  
<div class = "section" id = "tso-c-usr-shape-desArea-dvcOvw__tso-c-usr-shape-desArea-restr-rem1">
<p>
This section only contained a general overview of the command forms without
going into detail about the exact syntax and operations of the individual
restrictions. In the following sections, the individual restrictions are
described in more detail.</p>
</div>


<div class = "section" id = "tso-c-usr-shape-desArea-dvcOvw__tso-c-usr-shape-desArea-restr-defGui"><h2 class = "title sectiontitle">Definition in <span class = "ph">Tosca Structure.gui</span></h2>

<ol class = "ol">
<li class = "li">Choose <span class = "ph menucascade"><span class = "ph uicontrol">Command</span><abbr title = "and then"> &gt; </abbr><span class = "ph uicontrol">DVCON_SHAPE</span></span> in  
<span class = "ph">Tosca Structure.pre</span>.</li>
<li class = "li">In the DVCON_SHAPE dialog, choose the node group for the restrictions and define further settings:</li>
</ol>
<table class = "table" id = "tso-c-usr-shape-desArea-dvcOvw__ae377532"><caption/><colgroup><col/></colgroup><tbody class = "tbody">
<tr class = "row">
<td class = "entry">
<br/><img class = "image" id = "tso-c-usr-shape-desArea-dvcOvw__image_14FA7DCB3AD74C9BB7253724FA93577A" src = "../TsoUserImages/shape_DVCON_SHAPE_gui1.png" width = "450"/><br/>
</td>
</tr>
</tbody></table>

</div>

<div class = "section" id = "tso-c-usr-shape-desArea-dvcOvw__tso-c-usr-shape-desArea-restr-defCmd"><p><map name = "FPMap1"><area href = "#hj-top" title = "Back to Top" shape = "rect" coords = "416, 0, 435, 10"/></map><span class = "itemsprite"/></p><h2 class = "title sectiontitle"> Command Syntax</h2>

<p>
Each <code class = "ph codeph">DVCON_SHAPE</code> definition has a name (<code class = "ph codeph">ID_NAME</code>
parameter) and references a previously defined node group (<code class = "ph codeph">ND_GROUP</code>
parameter). The name is required to subsequently activate the <code class = "ph codeph">DVCON_SHAPE</code>
definition when specifying the optimization job (see <code class = "ph codeph">OPTIMIZE</code>
command). The node group specifies the node area where the restriction
is in effect.</p>
<p>
The following parameters define the individual restrictions for shape
optimization:
</p>
<ul class = "ul" id = "tso-c-usr-shape-desArea-dvcOvw__ul_D53F49E56FC040F8A2F00D49DF4EA0C3">
<li class = "li">
<code class = "ph codeph">CHECK_GROW, CHECK_SHRINK</code>: Restriction of the amount
of displacement</li>
<li class = "li">
<code class = "ph codeph">CHECK_MAX_MEM, CHECK_MIN_MEM</code>: Definition of a maximum
and minimum member size</li>
<li class = "li">
<code class = "ph codeph">CHECK_SOLID</code>: Check the displacements against geometric
primitive solids</li>
<li class = "li">
<code class = "ph codeph">CHECK_ELGR</code>: Check the displacements against elements
of an element group</li>
<li class = "li">
<code class = "ph codeph">CHECK_BC, CHECK_DOF</code>: Restriction of the displacement
direction</li>
<li class = "li">
<code class = "ph codeph">CHECK_SLIDE</code>: Restricting the displacement to a
slide surface</li>
<li class = "li">
<code class = "ph codeph">CHECK_LINK</code>: Assignment of a coupling condition</li>
</ul>
<p>
A <code class = "ph codeph">DVCON_SHAPE</code> command using all individual restrictions
appears as follows:</p>
<pre class = "codeblock">
<code class = "ph codeph">
DVCON_SHAPE 
 ID_NAME        = name_of_dvcon_shape
 ND_GROUP       = name_of_node_group
 CHECK_GROW     = &lt;max_grow_value&gt;
 CHECK_SHRINK   = &lt;max_shrink_value&gt;
 CHECK_MAX_MEM  = &lt;radius&gt;
 CHECK_MIN_MEM  = &lt;radius&gt;
 CHECK_SOLID    = name_of_solid
 CHECK_ELGR     = name_of_element_group
 CHECK_BC       = [YES|NO]
 CHECK_DOF      = cs_name,[FREE|FIX],[FREE|FIX],[FREE|FIX]
 CHECK_SLIDE    = name_of_link_shape
 CHECK_LINK     = name_of_link_shape
 FEASIBLE_START = [YES|NO]
END_</code>
</pre>
      
<div class = "note"><span class = "run-in.note">Note:
			</span><span class = "notecontent"><p><ul class = "ul" id = "tso-c-usr-shape-desArea-dvcOvw__ul_B7CD6E3F00264400B7161F7F79B8944B">
<li class = "li">
It is possible to define several individual <code class = "ph codeph">CHECK_*</code>
restrictions within a <code class = "ph codeph">DVCON_SHAPE</code> command. The order
of the execution of the individual restrictions within a <code class = "ph codeph">DVCON_SHAPE</code>
command appears as follows: <code class = "ph codeph">
CHECK_GROW/ CHECK_SHRINK, CHECK_MAX_MEM,
CHECK_MIN_MEM, CHECK_SOLID, CHECK_ELGR, CHECK_BC, CHECK_DOF, CHECK_SLIDE,
CHECK_LINK
</code>. The individual restrictions are checked independent
of one another, thus, an individual restriction always overrides the
preceding restriction.</li>
<li class = "li">
It is possible to define several design variable constraints using
the <code class = "ph codeph">DVCON_SHAPE</code> command. Each <code class = "ph codeph">DVCON_SHAPE</code>
definition must have its own unique name.</li>
</ul>
</p></span></div>
<table class = "Remark" id = "table132"><tr><td class = "Remark"><span class = "run-in.important">Important:
				</span><span class = "notecontent"><p><ul class = "ul">
<li class = "li">
The <code class = "ph codeph">DVCON_SHAPE</code> definitions must be activated by
a reference in the  <code class = "ph codeph">OPTIMIZE</code> command. Nonactivated
definitions have no influence upon the optimization. The reference in
the <code class = "ph codeph">OPTIMIZE</code> command assigns the design variable constraints,
the design area (see <code class = "ph codeph">DV_SHAPE</code> command) and the area
for mesh smoothing (see <code class = "ph codeph">MESH_SMOOTH</code> command) to one
another. Therefore, it is important to ensure that the only node groups
referenced in the <code class = "ph codeph">DVCON_SHAPE</code> definitions are those
whose nodes are contained in the <code class = "ph codeph">MESH_SMOOTH</code> area.</li>
<li class = "li">
The recommended procedure is to define the assigned restrictions
immediately after defining the design area (see <code class = "ph codeph">DV_SHAPE</code>
command) and the mesh smoothing area (see <code class = "ph codeph">MESH_SMOOTH</code>
parameter). The system-defined <code class = "ph codeph">MESH_SMOOTH</code> node group
can then be reused to define the restrictions.</li>
</ul></p></span></td></tr></table>

</div>

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