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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>Introduction 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 = "header"><p class = "abstract">
<span class = "shortdesc">In this section, a small example is provided.</span>

</p>
<p>This page discusses: </p><ul><li><a href = "#tso-c-usr-sizing-discrete-interpret__tso-c-usr-sizing-Discrete-model_interpret" id = "toc_rg" title = "">FE Model</a></li><li><a href = "#tso-c-usr-sizing-discrete-interpret__tso-c-usr-sizing-discrete-task_interpret" id = "toc_rg" title = "">Optimization Problem</a></li><li><a href = "#tso-c-usr-sizing-discrete-interpret__tso-c-usr-sizing-discrete-task_result" id = "toc_rg" title = "">Optimization Results</a></li></ul>
</p></td></tr></table></td></tr></table>



<div class = "body conbody">

<div class = "section" id = "tso-c-usr-sizing-discrete-interpret__tso-c-usr-sizing-Discrete-model_interpret"><h2 class = "title sectiontitle">FE Model</h2>

<p>The model is a curved shell fixed at one edge and loaded in the X and Y 
   directions on the opposite edge. To obtain mechanically sensible results 
   from the optimization, the elements are clustered into 11 groups. Thickness 
   of each group will correspond to one design variable.</p>
  
<table class = "table"><caption/><colgroup><col style = "width:50%"/><col style = "width:50%"/></colgroup><thead class = "thead">
<tr class = "row">
<th class = "entry" id = "tso-c-usr-sizing-discrete-interpret__tso-c-usr-sizing-Discrete-model_interpret__entry__1"> FE Model </th>
<th class = "entry" id = "tso-c-usr-sizing-discrete-interpret__tso-c-usr-sizing-Discrete-model_interpret__entry__2"> Clustering </th>
</tr>
</thead><tbody class = "tbody">
<tr class = "row">
<td class = "entry" headers = "tso-c-usr-sizing-discrete-interpret__tso-c-usr-sizing-Discrete-model_interpret__entry__1"><br/><img class = "image" src = "../TsoUserImages/Curved_Shell_edge_load_model.png" width = "265"/><br/>          </td>
<td class = "entry" headers = "tso-c-usr-sizing-discrete-interpret__tso-c-usr-sizing-Discrete-model_interpret__entry__2"><br/><img class = "image" src = "../TsoUserImages/Curved_Shell_edge_load_clustering.png" width = "265"/><br/>          </td>
</tr>
</tbody></table>  
</div>


<div class = "section" id = "tso-c-usr-sizing-discrete-interpret__tso-c-usr-sizing-discrete-task_interpret"><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">Optimization Problem</h2>

<p>We consider a basic compliance minimization problem with a volume constraint. 
   The <code class = "ph codeph">*.par</code> file is shown below.</p>
<pre class = "codeblock">
<code class = "ph codeph">
DVCON_SIZING
  ID_NAME         = DVCON_SIZING_set_discr
  EL_GROUP        = ALL_ELEMENTS
  CHECK_TYPE      = DISCRETE
  DISCR_LIST_FILE = Sheet_sizing.csv
  DISCR_CYCLE     = 10
  DISCR_INTERVAL  = 4
  DISCR_FRACTION  = 0.2
  DISCR_CHANGE    = 10
END_

DVCON_SIZING
  ID_NAME     = DVCON_SIZING_bounds
  EL_GROUP    = ALL_ELEMENTS
  CHECK_TYPE  = THICKNESS_BOUNDS
  MAGNITUDE   = ABS
  LOWER_BOUND = 0.1
  UPPER_BOUND = 2.0
END_

  . . .

OPT_PARAM
  STOP_CRITERION_ITER = 30
END_
</code>
</pre>
</div>


<div class = "section" id = "tso-c-usr-sizing-discrete-interpret__tso-c-usr-sizing-discrete-task_result"><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">Optimization Results</h2>

<p>The following table contains the discrete thickness values which 
   were available for the considered optimization. </p>

<table class = "table"><caption/><colgroup><col style = "width:100%"/></colgroup><thead class = "thead">
<tr class = "row">
<th class = "entry" id = "tso-c-usr-sizing-discrete-interpret__tso-c-usr-sizing-discrete-task_result__entry__1">  Available thicknesses: </th>
</tr>
</thead><tbody class = "tbody">
<tr class = "row">
<td class = "entry" headers = "tso-c-usr-sizing-discrete-interpret__tso-c-usr-sizing-discrete-task_result__entry__1">0.152;0.163;0.170;0.191;0.208;0.229;0.246;0.267;0.305;0.343;0.378;0.417</td>
</tr>
<tr class = "row">
<td class = "entry" headers = "tso-c-usr-sizing-discrete-interpret__tso-c-usr-sizing-discrete-task_result__entry__1">0.455;0.531;0.607;0.683;0.759;0.836;0.912;1.062;1.214;1.367;1.519;1.709</td>
</tr>
<tr class = "row">
<td class = "entry" headers = "tso-c-usr-sizing-discrete-interpret__tso-c-usr-sizing-discrete-task_result__entry__1">1.897;2.278;2.657;3.038;3.416;3.797;4.176;4.554;4.935;5.314;5.695;6.073</td>
</tr>
</tbody></table>  
  
<p>The figure below shows the optimization history of objective and constraints. The constraining cycles and the initial cycles have been marked out.</p> 
<table class = "table"><caption/><colgroup><col/></colgroup><tbody class = "tbody">
<tr class = "row">
<td class = "entry"><br/><img class = "image" src = "../TsoUserImages/Intro_Example_Graphs.png" height = "378"/><br/></td>
</tr>
</tbody></table>

<table class = "table"><caption/><colgroup><col style = "width:100%"/></colgroup><thead class = "thead">
<tr class = "row">
<th class = "entry" id = "tso-c-usr-sizing-discrete-interpret__tso-c-usr-sizing-discrete-task_result__entry__6">  Optimized discrete thicknesses: </th>
</tr>
</thead><tbody class = "tbody">
<tr class = "row">
<td class = "entry" headers = "tso-c-usr-sizing-discrete-interpret__tso-c-usr-sizing-discrete-task_result__entry__6">0.3780;0.6070;0.7590;0.9120;1.0620;1.2140;1.5190;1.5190;1.7090;1.7090;1.8970</td>
</tr>
</tbody></table>

<table class = "table"><caption/><colgroup><col/></colgroup><thead class = "thead"><tr class = "row">
<th class = "entry rowsep-1" id = "tso-c-usr-sizing-discrete-interpret__tso-c-usr-sizing-discrete-task_result__entry__8">Resulting thicknesses using sizing optimization with discrete design variables</th>
</tr>
</thead><tbody class = "tbody">
 
<tr class = "row">
<td class = "entry rowsep-1" headers = "tso-c-usr-sizing-discrete-interpret__tso-c-usr-sizing-discrete-task_result__entry__8">
<br/><img class = "image" src = "../TsoUserImages/Curved_Shell_edge_load_discrete.png" height = "302"/><br/>
</td>
</tr>
</tbody></table>

<table class = "table"><caption/><colgroup><col style = "width:100%"/></colgroup><thead class = "thead">
<tr class = "row">
<th class = "entry" id = "tso-c-usr-sizing-discrete-interpret__tso-c-usr-sizing-discrete-task_result__entry__10">  Optimized  continuous thicknesses: </th>
</tr>
</thead><tbody class = "tbody">
<tr class = "row">
<td class = "entry" headers = "tso-c-usr-sizing-discrete-interpret__tso-c-usr-sizing-discrete-task_result__entry__10">0.3795;  0.5878;0.7792;0.9563;1.1177;1.2414;1.4012;1.5763;1.6843;1.7651;1.8386</td>
</tr>
</tbody></table>  
  
<table class = "table"><caption/><colgroup><col/></colgroup><thead class = "thead"><tr class = "row">
<th class = "entry rowsep-1" id = "tso-c-usr-sizing-discrete-interpret__tso-c-usr-sizing-discrete-task_result__entry__12">Resulting thicknesses using sizing optimization with continuous design variables</th>
</tr>
</thead><tbody class = "tbody">
   
  
<tr class = "row">
<td class = "entry rowsep-1" headers = "tso-c-usr-sizing-discrete-interpret__tso-c-usr-sizing-discrete-task_result__entry__12">
<br/><img class = "image" src = "../TsoUserImages/Curved_Shell_edge_load_standard.png" height = "302"/><br/>
</td>
</tr>
</tbody></table>
<p>The difference in the objective functions for the standard and discrete 
   optimization is less than 2% and the constraints are fulfilled within an 
   error of 0.001 in this example.</p>  

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