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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 the Internal Forces Example</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 = "shortdesc">
The present example shows that the topology optimization by <span class = "ph">SIMULIA Tosca Structure</span> 
can also use the internal forces as the design response. 
<p>This page discusses: </p><ul><li><a href = "#tso-c-example-topo-sensTopoIntForces__cs-model" id = "toc_rg" title = "">About the Model</a></li><li><a href = "#tso-c-example-topo-sensTopoIntForces__cs-TheFirstApproach" id = "toc_rg" title = "">First Approach</a></li><li><a href = "#tso-c-example-topo-sensTopoIntForces__cs-TheSecondApproach" id = "toc_rg" title = "">Second Approach</a></li><li><a href = "#tso-c-example-topo-sensTopoIntForces__cs-summary" id = "toc_rg" title = "">Procedure Summary:</a></li></ul>
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<div class = "section" id = "tso-c-example-topo-sensTopoIntForces__cs-model"><h2 class = "title sectiontitle">About the Model</h2>

<p>A model of a beam structure loaded with a single offset load and
fully clamped at the sides. The beam
structure should be optimized for stiffness but then at the same
time each of the sides should only carry half of the applied force
P. That each of the clamped set of boundaries on the side should be
carrying P/2 can be ensured using two different approaches. In the
following, both approaches will be applied.</p>
<p>In both approaches, all the elements are defined as design elements
and the top layer of elements in the beam model is defined
as frozen.</p>
<p>Initial model of a beam structure loaded with a single offset load
and fully clamped at the sides. The beam structure should be
optimized for stiffness, but then at the same time each of the sides
should only carry half of the applied force P.</p>
<p><br/><img class = "image" src = "../TsoExampleImages/sensTopoInternForceModel.png"/><br/></p>
</div>


<div class = "section" id = "tso-c-example-topo-sensTopoIntForces__cs-TheFirstApproach"><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">First Approach</h2>

<p>In the first approach, a constraint is defined for the sum of
internal forces through a cut in the y-direction of the beam
structure. To sum up the internal forces
in the y-direction, an element group (EL_INTERNAL_GROUP) and a node
group (ND_INTERNAL_GROUP) is defined.
<br/><img class = "image" src = "../TsoExampleImages/sensTopoInternForceApp1.png"/><br/></p>
</div>


<div class = "section" id = "tso-c-example-topo-sensTopoIntForces__cs-TheSecondApproach"><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">Second Approach</h2>

<p>In the second approach, a constraint is defined for the sum of
reaction forces in the y-direction for all the nodes on the left side
of the beam structure. To sum up the reaction forces in the
y-direction, a node group (ND_REACTION_GROUP) is defined.
<br/><img class = "image" src = "../TsoExampleImages/sensTopoInternForceApp2.png"/><br/></p>
</div>


<div class = "section" id = "tso-c-example-topo-sensTopoIntForces__cs-summary"><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">Procedure Summary:</h2>

<p>
<table class = "table"><caption/><colgroup><col style = "width:13.071895424836603%"/><col style = "width:86.9281045751634%"/></colgroup><tbody class = "tbody">
<tr class = "row">
<td class = "entry">Model:</td>
<td class = "entry">internal_forces.ext</td>
</tr>
<tr class = "row">
<td class = "entry">Design Area:</td>
<td class = "entry">All elements</td>
</tr>
<tr class = "row">
<td class = "entry">Design Variable Constraint:</td>
<td class = "entry">Fix elements of group TOP_FROZEN</td>
</tr>
<tr class = "row">
<td class = "entry">Objective:</td>
<td class = "entry">Maximize stiffness (minimize compliance)</td>
</tr>
<tr class = "row"><td class = "entry">Constraint Approach 1:</td>
<td class = "entry">The sum of the internal forces in y-direction in the section cut is
                      at least 0.0015 (greater or equal constraint)</td>
</tr>
<tr class = "row">
<td class = "entry">Constraint Approach 2:</td>
<td class = "entry">The sum of the reaction forces in y-direction on the left side
                      should not exceed 0.0015 (less or equal constraint)</td>
</tr>
<tr class = "row">
<td class = "entry">Constraint:</td>
<td class = "entry">Relative volume of 15 % (less or equal constraint)</td>
</tr>
<tr class = "row">
<td class = "entry">Settings:</td>
<td class = "entry">DENSITY_UPDATE is set to CONSERVATIVE and a 0.1 DENSITY_- MOVE
                      value is specified for stabilizing the optimization</td>
</tr>
</tbody></table></p>
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