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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 Design Variables (DV_SHAPE)</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">Design variables for shape optimization are defined when assigning
a node group to the design area. </span>

</p>
<p>This page discusses: </p><ul><li><a href = "#tso-c-usr-shape-desArea-desVar__tso-c-usr-shape-desArea-desVar-displVec" id = "toc_rg" title = "">Determination of Optimization Displacement Vectors</a></li><li><a href = "#tso-c-usr-shape-desArea-desVar__tso-c-usr-shape-desArea-desVar-shapeSensElems-AbqSens" id = "toc_rg" title = "">Supported Elements Attached to Shape Sensitivity Design Nodes using SENS_CALC_MODE = SOLVER with 
<span class = "ph">Abaqus</span>.</a></li><li><a href = "#tso-c-usr-shape-desArea-desVar__tso-c-usr-shape-desArea-desVar-shapeSensElems" id = "toc_rg" title = "">Supported Elements Attached to Shape Sensitivity Design Nodes using SENS_CALC_MODE = TOSCA.</a></li></ul>
</p></td></tr></table></td><td class = "DocHeader2"><table class = "DocTopicsSeeAlso" id = "table13"><tr><td class = "TopicsTitle">See Also</td></tr><tr><td><a title = "Design variables for shape optimization are defined when assigning a node group to the design area." href = "tso-t-usr-shape-desArea-desVar.htm#tso-t-usr-shape-desArea-desVar">Defining Design Variables</a></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 = "Definition of the design nodes for shape optimization." href = "../TsoCmdMap/tso-r-cmd-dvShape.htm#tso-r-cmd-dvShape">DV_SHAPE</a></td></tr></table></td></tr></table>




<div class = "body conbody">
<p><table class = "Remark" id = "table132"><tr><td class = "Remark"><span class = "run-in.important">Important:
				</span><span class = "notecontent">
<p>Only surface nodes are allowed as design nodes.</p>
<ul class = "ul">
<li class = "li">The design nodes must define one or more continuous areas, i.e.,
the individual design areas must consist of at least three design nodes.
Single design nodes without neighboring design nodes are not permitted.</li>
<li class = "li">Only corner nodes (from finite elements) are supported as design
nodes. Midside nodes might be included in the design node group but the
optimization displacements of the midside nodes of second order elements
is interpolated from the optimization displacement of the adjacent
corner nodes, which maintains a curvature of the initial design during
optimization.</li>
</ul>
</span></td></tr></table>
</p>
<p>Strictly speaking, design variables are the signed amounts of optimization
displacement applied to the design nodes. In
unrestricted tasks, the direction of the optimization displacement vector
corresponds to the outer surface unit normal on the node and the amount
of displacement is determined by the optimization procedure. Restrictions
influence the amount and direction of the optimization displacement vector.</p>
<p>Basically there are three cases that might occur: 
<ul class = "ul">
<li class = "li"><span class = "ph uicontrol">Growth</span> means that
a design node is moved outwards (positive amount of displacement).</li>
<li class = "li"><span class = "ph uicontrol">Shrinkage</span>
means that a design node is moved inwards (negative amount of displacement).</li>
<li class = "li"><span class = "ph uicontrol">Neutral</span> means that a design node is moved neither outwards nor inwards
(zero displacement).</li></ul></p>
<p><table class = "Remark" id = "table132"><tr><td class = "Remark"><span class = "run-in.important">Important:
				</span><span class = "notecontent">
<p>The optimization displacement vector contains the optimized
changes in positions of the nodes and not the displacements of the nodes
obtained from the FE analysis. </p>
<p>When unrestricted design nodes lie in component areas in which they
have only a little mechanical effect on the system as a whole, an undesirable
“shrink effect” might occur. Therefore, design areas should not be
selected before the mechanical component behavior is known. It is recommended
to analyze the mechanical behavior of the component in a preliminary
FE calculation before specifying the design area.</p>
</span></td></tr></table>
</p>

<div class = "section" id = "tso-c-usr-shape-desArea-desVar__tso-c-usr-shape-desArea-desVar-displVec"><h2 class = "title sectiontitle">Determination of Optimization Displacement Vectors</h2>

<ul class = "ul" id = "tso-c-usr-shape-desArea-desVar__ul_8AD9A241C0634BCE8070FB6F3B06B512">
<li class = "li">The optimization displacement vector on the design node is determined
by superimposing all external element normal vectors on the boundaries
of neighboring elements. In two-dimensional models the normals are formed
relative to element edges and in three-dimensional to element surfaces.
The only element edges or element surfaces that are taken into consideration
are those spanning design nodes. Isolated
design nodes (neighboring nodes on the surface are not design nodes)
are not permitted and must be removed from the design node group. The
optimization displacement direction is a uniform vector.

<p>
<span class = "ph uicontrol">Example:</span></p>
<p>In a two-dimensional model each design node has two neighboring
nodes on the boundary of the component. If both of these neighboring
nodes are design nodes, see the figure above on the left, two normal
vectors are formed, one each for the respective element edges, and superimposed.
If only one of the neighboring nodes is a design node, see the
figure above on the right, there is only one normal vector. This is identical
with the normal vector of the design node.</p>
<p><br/><img border = "1" class = "image" id = "tso-c-usr-shape-desArea-desVar__image_BB47F3928D984887A522BDF0B045E4E8" src = "../TsoUserImages/shape_normal_vector.png" width = "355" height = "182"/><br/></p></li>

<li class = "li"> If the displacement direction of a node is restricted
                    by a design variable constraint (<code class = "ph codeph">DVCON_SHAPE</code>), the direction of
                    the optimization displacement vectors is correspondingly adjusted. </li>
<li class = "li">The optimization displacement vector is derived from scaling the
optimization displacement direction with the signed amount of displacement
calculated by the optimization procedure.</li>
<li class = "li">The length of the optimization displacement vector might also be influenced
by design variable constraints (<code class = "ph codeph">DVCON_SHAPE</code>).</li>
</ul>

<div class = "note"><span class = "run-in.note">Note:
			</span><span class = "notecontent">
<p>
<ul class = "ul" id = "tso-c-usr-shape-desArea-desVar__ul_32B77ED0BE834EA38F8FB6D4EA7298B0">
<li class = "li">The optimization displacement vector determined by the optimizer is
adjusted to the changed conditions in each design cycle (for example, shape of
the structure, effective restrictions, mesh quality, etc.). The optimization
displacement vectors are therefore not constant; they are subject to
certain changes in each cycle. </li>
<li class = "li">With the <code class = "ph codeph">VECTOR</code> parameter in the
                            optimization settings (command <code class = "ph codeph">OPT_PARAM</code>), it is
                            possible to control when the optimization displacement vectors are
                            calculated.</li>
</ul>
</p>
</span></div>

</div>


<div class = "section" id = "tso-c-usr-shape-desArea-desVar__tso-c-usr-shape-desArea-desVar-shapeSensElems-AbqSens"><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">Supported Elements Attached to Shape Sensitivity Design Nodes using SENS_CALC_MODE = SOLVER with 
<span class = "ph">Abaqus</span>.</h2>

<p>
<table class = "table"><caption/><colgroup><col/><col/></colgroup><tbody class = "tbody">
<tr class = "row">
<td class = "entry"><p>Valid element types for sensitivity-based </p>
                      <p>nodal optimization with <span class = "ph">Abaqus</span> sensitivities.</p></td>
<td class = "entry"><p><span class = "ph">Abaqus</span> element type</p></td>
</tr>


<tr class = "row">
<td class = "entry"><p>PLANE_QUAD_4</p></td>
<td class = "entry"><p>CPE4</p>
                      
                      
                      
                      <p>CPE4R</p>
                      
                      </td>
</tr>
<tr class = "row">
<td class = "entry"><p>PLANE_QUAD_4</p></td>
<td class = "entry"><p>CPEG4</p>
                      <p>CPEG4R</p></td>
</tr>
<tr class = "row">
<td class = "entry"><p>PLANE_QUAD_4</p></td>
<td class = "entry"><p>CPS4</p>
                      
                      <p>CPS4R</p></td>
</tr>
<tr class = "row">
<td class = "entry"><p>PLANE_QUAD_8</p></td>
<td class = "entry">
                      
                      <p>CPEG8</p>
                      <p>CPEG8R</p></td>
</tr>
<tr class = "row">
<td class = "entry"><p>PLANE_QUAD_8</p></td>
<td class = "entry"><p>CPS8</p>
                      
                      <p>CPS8R</p>
                      </td>
</tr>


<tr class = "row">
<td class = "entry"><p>PLANE_QUAD_8</p></td>
<td class = "entry"><p>CPE8</p>
                      
                      
                      
                      <p>CPE8R</p>
                      </td>
</tr>
<tr class = "row">
<td class = "entry"><p>PLANE_TRIANG_3</p></td>
<td class = "entry">
                      <p>CGAX3</p>
                      <p>CGAX3H</p>
                      <p>CPE3</p>
                      
                      <p>CPS3</p>
                      </td>
</tr>

<tr class = "row">
<td class = "entry"><p>PLANE_TRIANG_6</p></td>
<td class = "entry"><p>CPEG6</p>
                      </td>
</tr>
<tr class = "row">
<td class = "entry"><p>PLANE_TRIANG_6</p></td>
<td class = "entry"><p>CPS6</p>
                      </td>
</tr>

</tbody></table>
</p>

<p>
<table class = "table"><caption/><colgroup><col/><col/></colgroup><tbody class = "tbody">

<tr class = "row">
<td class = "entry"><p>Valid element types for sensitivity-based </p>
                      <p>nodal optimization with <span class = "ph">Abaqus</span> sensitivities.</p></td>
<td class = "entry"><p><span class = "ph">Abaqus</span> element type</p></td>
</tr>
<tr class = "row">
<td class = "entry"><p>SHELL_QUAD_4</p></td>
<td class = "entry"><p>S4</p>
                      <p>S4R</p></td>
</tr>
<tr class = "row">
<td class = "entry"><p>SHELL_QUAD_8</p></td>
<td class = "entry"><p>M3D8</p>
                      <p>S8R</p></td>
</tr>
<tr class = "row">
<td class = "entry"><p>SHELL_TRIANG_3</p></td>
<td class = "entry"><p>S3</p>
                      <p>S3R</p>
                      </td>
</tr>

</tbody></table>
</p>

<p>
<table class = "table"><caption/><colgroup><col/><col/><col/><col/></colgroup><tbody class = "tbody">
<tr class = "row">
<td class = "entry"><p>Valid element types for sensitivity-based </p>
                      <p>nodal optimization with <span class = "ph">Abaqus</span> sensitivities.</p></td>
<td class = "entry"><p><span class = "ph">Abaqus</span> element type</p></td>
</tr>

<tr class = "row">
<td class = "entry"><p>SOLID_BRICK_8</p></td>
<td class = "entry"><p>C3D8</p>
                      
                      
                      
                      <p>C3D8R</p>
                      
                      </td>
</tr>
<tr class = "row">
<td class = "entry"><p>SOLID_BRICK_20</p></td>
<td class = "entry"><p>C3D20</p>
                      
                      
                      
                      <p>C3D20R</p>
                      
                      
                      </td>
</tr>
<tr class = "row">
<td class = "entry"><p>SOLID_TETRA_4</p></td>
<td class = "entry"><p>C3D4</p>
                      </td>
</tr>
<tr class = "row">
<td class = "entry"><p>SOLID_TETRA_10</p></td>
<td class = "entry"><p>C3D10</p>
                      
                      <p>C3D10HS</p>
                      
                      
                      
                      </td>
</tr>
<tr class = "row">
<td class = "entry"><p>SOLID_PENTA_6</p></td>
<td class = "entry"><p>C3D6</p>
                      
                      </td>
</tr>
<tr class = "row">
<td class = "entry"><p>SOLID_PENTA_15</p></td>
<td class = "entry"><p>C3D15</p>
                      </td>
</tr>
</tbody></table>
</p>
</div>


<div class = "section" id = "tso-c-usr-shape-desArea-desVar__tso-c-usr-shape-desArea-desVar-shapeSensElems"><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">Supported Elements Attached to Shape Sensitivity Design Nodes using SENS_CALC_MODE = TOSCA.</h2>

<p>
<table class = "table" id = "tso-c-usr-shape-desArea-desVar__aa193409"><caption/><colgroup><col/><col/><col/><col style = "width:100%"/></colgroup><tbody class = "tbody">
<tr class = "row">
<td class = "entry"><p>Valid element types for sensitivity-based shape optimization</p></td>
<td class = "entry"><p><span class = "ph">Abaqus</span> element type</p></td>
<td class = "entry"><p><span class = "ph">ANSYS®</span> element type</p></td>
<td class = "entry"><p><span class = "ph">MSC Nastran®</span> element type</p></td>
</tr>
<tr class = "row">
<td class = "entry" colspan = "4"><p><span class = "ph uicontrol">Solid elements</span></p></td>
</tr>
<tr class = "row">
<td class = "entry"><p>SOLID_TETRA_4</p></td>
<td class = "entry"><p>C3D4</p></td>
<td class = "entry"><p>SOLID285</p></td>
<td class = "entry"><p>CTETRA4</p></td>
</tr>
<tr class = "row">
<td class = "entry"><p>SOLID_TETRA_10</p></td>
<td class = "entry"><p>C3D10</p></td>
<td class = "entry"><p>SOLID148</p><p>SOLID187</p><p>SOLID92</p></td>
<td class = "entry"><p>CTETRA10</p></td>
</tr>
<tr class = "row">
<td class = "entry"><p>SOLID_BRICK_8</p></td>
<td class = "entry"><p>C3D8</p><p>C3D8R</p></td>
<td class = "entry"><p>SOLID185 </p><p>SOLID45</p></td>
<td class = "entry"><p>CHEXA8</p></td>
</tr>
</tbody></table>
</p>
</div>


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