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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>Symmetry Restrictions for the Airbeam Model </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">This section shows how to define symmetry restrictions on the Airbeam example.</span>

</p>
<p>This task shows you how to:
					</p><ul><li><a href = "#tso-c-example-aboutAirbeamSym-cs-model" id = "toc_rg" title = "">About the Model</a></li><li><a href = "#t-setupSym" id = "toc_rg" title = "">Defining Symmetry Restriction</a></li></ul>
</p></td></tr></table></td></tr></table>




<article class = "topic task nested1" aria-labelledby = "ariaid-title2" id = "tso-c-example-aboutAirbeamSym-cs-model">
<h2 class = "title topictitle2">About the Model</h2>

<div class = "body taskbody">
  <p class = "result">
<p>
  To define symmetry restrictions, you first define the coordinate system and then the symmetry restrictions.
  Several definitions of symmetry restrictions are given in the example file in
  the installation manual but only the plane symmetry definition is activated. All
  other types of symmetries can be activated by changing the parameter file,
  but only one symmetry condition can be activated at the same time.
</p>
  <p>
  The model is identical to the Airbeam example. To define a symmetry plane, a symmetry point, or a
  cyclic symmetry, you always need to include a reference coordinate system.
  In this example, the origin of the coordinate system is in the middle of the design
  area ("center_cs").
  <br/><img class = "image" src = "../TsoExampleImages/airbeamSymModel.png"/><br/>
  </p>
</p>
</div>

</article>

<article class = "topic task nested1" aria-labelledby = "ariaid-title3" id = "t-setupSym">
<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 topictitle2">Defining Symmetry Restriction</h2>

<div class = "body taskbody">
<section><ol class = "ol steps"><li class = "li step stepexpand">
Define the coordinate system with the CS_DEF command:
<div class = "itemgroup stepresult">
<pre class = "codeblock">
!COORDINATE SYSTEM IN THE CENTRE OF THE BEAM
CS_DEF
  ID_NAME               = center_cs
  CS_TYPE               = RECTANGULAR
  DEF_TYPE              = LOCAL
  CS_REF                = CS_0
  ORIGIN_123            = 43.5,14.5,0
  ROTATION_321          = 0,0,0
END
</pre>
<div class = "note"><span class = "run-in.note">Note:
			</span><span class = "notecontent">If the coordinate system is already defined in the model, it can be imported.</span></div>

</div>
</li><li class = "li step stepexpand">
          Define a plane symmetry restriction with the LINK_TOPO command:
          <div class = "itemgroup stepresult">
            <pre class = "codeblock">
!define the link condition
LINK_TOPO
  ID_NAME               = link_topo1
  TYPE                  = LINK_SYM
  CS                    = main_cs
  GROUP_MAIN          = main
  CS_CHILD              = cs_child1
  MAIN                = MAX
END_

!DEFINE PLANE SYMMETRY
!SYMMETRY PLANE: X-Z PLANE OF CENTER_CS
LINK_TOPO
  ID_NAME               = link_topo2
  TYPE                  = PLANE_SYM, AXIS_2
  CS                    = center_cs
END_

!Define the point symmetry
LINK_TOPO
  ID_NAME               = link_topo3
  TYPE                  = POINT_SYM
  CS                    = center_cs
END_

!define the rotation symmetry
!Angle = 60 -&gt; 6 Segments
LINK_TOPO
  ID_NAME               = link_topo4
  TYPE                  = ROTATION_SYM, AXIS_3
  CS                    = center_cs
  ANGLE                 = 60.
  IGNORE_FROZEN         = true
END_

!define the cyclic symmetry
!segment width: 21
!direction: x-Axis of center_cs
LINK_TOPO
  ID_NAME               = link_topo5
  TYPE                  = CYCLIC_SYM, AXIS_1
  CS                    = center_cs
  TRANSLATION           = 21.
  IGNORE_FROZEN         = TRUE
END_
</pre>
            <p>This definition specifies the type of symmetry (point, plane, cyclic,...), the
              reference to the applied coordinate system and the type of coupling. The main
              element group and the child-coordinate system are referenced.</p>
          </div>
        </li><li class = "li step stepexpand">
Define a Design Variable Constraint (DVCON_TOPO) that references the LINK_TOPO command:
<div class = "itemgroup stepresult">
<pre class = "codeblock">
DVCON_TOPO
  ID_NAME               = dvcon_link
  EL_GROUP              = ALL_ELEMENTS
  CHECK_TYPE            = LINK_TOPO
  CHECK_LINK            = link_topo1
END_

DVCON_TOPO
  ID_NAME               = dvcon_plane
  EL_GROUP              = ALL_ELEMENTS
  CHECK_TYPE            = LINK_TOPO
  CHECK_LINK            = link_topo2
END_

DVCON_TOPO
  ID_NAME               = dvcon_point
  EL_GROUP              = ALL_ELEMENTS
  CHECK_TYPE            = LINK_TOPO
  CHECK_LINK            = link_topo3
END_

DVCON_TOPO
  ID_NAME               = dvcon_rotation
  EL_GROUP              = ALL_ELEMENTS
  CHECK_TYPE            = LINK_TOPO
  CHECK_LINK            = link_topo4
END_

DVCON_TOPO
  ID_NAME               = dvcon_cyclic
  EL_GROUP              = ALL_ELEMENTS
  CHECK_TYPE            = LINK_TOPO
  CHECK_LINK            = link_topo5
END_
</pre>
</div>
</li><li class = "li step stepexpand">
To activate the restriction, reference the DVCON_TOPO command in the OPTIMIZE command.
<div class = "itemgroup stepresult">
<pre class = "codeblock">
OPTIMIZE
  ID_NAME               = topology_optimization
  DV                    = design_variables
  OBJ_FUNC              = maximize_stiffness
  DVCON                 = dvcon_frozen
  CONSTRAINT            = volume_constraint
  ! Link Topo Constraint
  DVCON                 = dvcon_link
  ! Plane Symmetry
  DVCON                 = dvcon_plane
  ! Point Symmetry
  DVCON                 = dvcon_point
  ! Rotation Symmetry
  DVCON                 = dvcon_rotation
  ! Cyclic Symmetry
  DVCON                 = dvcon_cyclic
END_
</pre>
</div>
</li></ol></section>
<p class = "result">
<p>The optimization result without symmetry (left) and with plane symmetry (right) is shown in the following figure.</p>
<table class = "table"><caption/><colgroup><col/></colgroup><tbody class = "tbody">
<tr class = "row">
<td class = "entry"><br/><img class = "image" src = "../TsoExampleImages/topo_beam_symmetry_1.png" width = "550"/><br/></td>
</tr>
</tbody></table>
<p>The optimization result of point symmetry (left) and rotational symmetry (right) is demonstrated as next.</p>
<table class = "table"><caption/><colgroup><col/></colgroup><tbody class = "tbody">
<tr class = "row">
<td class = "entry"><br/><img class = "image" src = "../TsoExampleImages/topo_beam_symmetry_2.png" width = "550"/><br/></td>
</tr>
</tbody></table>
<p>The last figures demonstrate the cyclic symmetry (left) and a link condition (right).</p>
<table class = "table"><caption/><colgroup><col/></colgroup><tbody class = "tbody">
<tr class = "row">
<td class = "entry"><br/><img class = "image" src = "../TsoExampleImages/topo_beam_symmetry_3.png" width = "550"/><br/></td>
</tr>
</tbody></table>
</p>
</div>

</article>
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