<?xml version='1.0' encoding='UTF-8' ?>
<!DOCTYPE html
  SYSTEM "about:legacy-compat">
<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 = "This section showcases the algorithm on a relatively large model of a car door."/><meta name = "description" content = "This section showcases the algorithm on a relatively large model of a car door."/><meta name = "DC.format" content = "HTML5"/><meta name = "DC.identifier" content = "tso-c-example-sizing-discrete-Example_1"/><meta name = "DC.language" content = "en"/><link rel = "stylesheet" type = "text/css" href = "../DSDocUI_XML34.css"/><title>Front Door of a Car—Reducing Weight</title>
<script type = "text/javascript" src = "../DSDocUI_Highlight34.js">
  	/* */
  	</script></head><body onLoad = "highlightSearchTerms();" id = "tso-c-example-sizing-discrete-Example_1">
<a name = "hj-top"> </a><table class = "table1" id = "table11"><tr><td><table class = "DocHeader"><tr><td class = "DocHeader1" colspan = "2"><h1> Front Door of a Car—Reducing Weight </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 showcases the algorithm on a relatively large  model of a car door.
</span>

</p>
<p>This page discusses: </p><ul><li><a href = "#tso-c-example-sizing-discrete-Example_1__cs-TheFEModel" id = "toc_rg" title = "">FE Model </a></li><li><a href = "#tso-c-example-sizing-discrete-Example_1__cs-TheOptimizationProblem" id = "toc_rg" title = "">Optimization Problem</a></li><li><a href = "#tso-c-example-sizing-discrete-Example_1__cs-OptimizationResults" 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-example-sizing-discrete-Example_1__cs-TheFEModel"><h2 class = "title sectiontitle">FE Model </h2>

 <p> The model is for the analysis of the sagging behavior of a car door. The Loads applied are, a
        moment load on the two hinges, which are constrained using boundary conditions and a
        concentrated load on the side opposite to the hinges (near the locking mechanism). The
        hinges and the locking area are excluded from the optimization domain. Clustering has been
        used to create mechanically sensible results. The result was requested from the following
        discrete range:</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-example-sizing-discrete-Example_1__cs-TheFEModel__entry__1" colspan = "2">Available Thicknesses</th></tr></thead><tbody class = "tbody"><tr class = "row"><td class = "entry" headers = "tso-c-example-sizing-discrete-Example_1__cs-TheFEModel__entry__1"> 0.152 </td><td class = "entry" headers = "tso-c-example-sizing-discrete-Example_1__cs-TheFEModel__entry__1"> 0.531 </td></tr><tr class = "row"><td class = "entry" headers = "tso-c-example-sizing-discrete-Example_1__cs-TheFEModel__entry__1"> 0.163 </td><td class = "entry" headers = "tso-c-example-sizing-discrete-Example_1__cs-TheFEModel__entry__1"> 0.607 </td></tr><tr class = "row"><td class = "entry" headers = "tso-c-example-sizing-discrete-Example_1__cs-TheFEModel__entry__1"> 0.17 </td><td class = "entry" headers = "tso-c-example-sizing-discrete-Example_1__cs-TheFEModel__entry__1"> 0.683 </td></tr><tr class = "row"><td class = "entry" headers = "tso-c-example-sizing-discrete-Example_1__cs-TheFEModel__entry__1"> 0.191 </td><td class = "entry" headers = "tso-c-example-sizing-discrete-Example_1__cs-TheFEModel__entry__1"> 0.759 </td></tr><tr class = "row"><td class = "entry" headers = "tso-c-example-sizing-discrete-Example_1__cs-TheFEModel__entry__1"> 0.208 </td><td class = "entry" headers = "tso-c-example-sizing-discrete-Example_1__cs-TheFEModel__entry__1"> 0.836 </td></tr><tr class = "row"><td class = "entry" headers = "tso-c-example-sizing-discrete-Example_1__cs-TheFEModel__entry__1"> 0.229 </td><td class = "entry" headers = "tso-c-example-sizing-discrete-Example_1__cs-TheFEModel__entry__1"> 0.912 </td></tr><tr class = "row"><td class = "entry" headers = "tso-c-example-sizing-discrete-Example_1__cs-TheFEModel__entry__1"> 0.246 </td><td class = "entry" headers = "tso-c-example-sizing-discrete-Example_1__cs-TheFEModel__entry__1"> 1.062 </td></tr><tr class = "row"><td class = "entry" headers = "tso-c-example-sizing-discrete-Example_1__cs-TheFEModel__entry__1"> 0.267 </td><td class = "entry" headers = "tso-c-example-sizing-discrete-Example_1__cs-TheFEModel__entry__1"> 1.214 </td></tr><tr class = "row"><td class = "entry" headers = "tso-c-example-sizing-discrete-Example_1__cs-TheFEModel__entry__1"> 0.305 </td><td class = "entry" headers = "tso-c-example-sizing-discrete-Example_1__cs-TheFEModel__entry__1"> 1.367 </td></tr><tr class = "row"><td class = "entry" headers = "tso-c-example-sizing-discrete-Example_1__cs-TheFEModel__entry__1"> 0.343 </td><td class = "entry" headers = "tso-c-example-sizing-discrete-Example_1__cs-TheFEModel__entry__1"> 1.519 </td></tr><tr class = "row"><td class = "entry" headers = "tso-c-example-sizing-discrete-Example_1__cs-TheFEModel__entry__1"> 0.378 </td><td class = "entry" headers = "tso-c-example-sizing-discrete-Example_1__cs-TheFEModel__entry__1"> 1.709 </td></tr><tr class = "row"><td class = "entry" headers = "tso-c-example-sizing-discrete-Example_1__cs-TheFEModel__entry__1"> 0.417 </td><td class = "entry" headers = "tso-c-example-sizing-discrete-Example_1__cs-TheFEModel__entry__1"> 1.897 </td></tr><tr class = "row"><td class = "entry" headers = "tso-c-example-sizing-discrete-Example_1__cs-TheFEModel__entry__1"> 0.455 </td><td class = "entry" headers = "tso-c-example-sizing-discrete-Example_1__cs-TheFEModel__entry__1"> 2.278 </td></tr></tbody></table><table class = "table"><caption/><colgroup><col/></colgroup><thead class = "thead"><tr class = "row"><th class = "entry" id = "tso-c-example-sizing-discrete-Example_1__cs-TheFEModel__entry__28">The FE model of the car door with boundary conditions and loads.</th></tr></thead><tbody class = "tbody">
<tr class = "row">
<td class = "entry" headers = "tso-c-example-sizing-discrete-Example_1__cs-TheFEModel__entry__28">
<br/><img class = "image" src = "../TsoExampleImages/Car_Door_Model.png" width = "265"/><br/>
</td>
</tr>
</tbody></table> 
</div>


<div class = "section" id = "tso-c-example-sizing-discrete-Example_1__cs-TheOptimizationProblem"><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 weight minimization problem with a stiffness constraint. The parameter 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_truncated.csv
    DISCR_CYCLE     = 10
    DISCR_INTERVAL  = 4
    DISCR_FRACTION  = 0.2
    DISCR_CHANGE    = 10
  END_
  
  . . .

  OPT_PARAM
    STOP_CRITERION_ITER = 28
  END_
  
  . . . 
  
</code>  
</pre>
</div>


<div class = "section" id = "tso-c-example-sizing-discrete-Example_1__cs-OptimizationResults"><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 figures below show the optimization results. A comparison between the optimization with continuous  and discrete variables is also done. </p>
  

  

<table class = "table"><caption/><colgroup><col/></colgroup><thead class = "thead"><tr class = "row"><th class = "entry" id = "tso-c-example-sizing-discrete-Example_1__cs-OptimizationResults__entry__1">History of objective and constraints from the sizing optimization for discrete variables.</th></tr></thead><tbody class = "tbody">
<tr class = "row">
<td class = "entry" headers = "tso-c-example-sizing-discrete-Example_1__cs-OptimizationResults__entry__1">
<br/><img class = "image" src = "../TsoExampleImages/Car_door_Graphs_discrete.png" height = "378" width = "567"/><br/>
</td>
</tr>
</tbody></table>
 

<table class = "table"><caption/><colgroup><col/></colgroup><thead class = "thead"><tr class = "row"><th class = "entry" id = "tso-c-example-sizing-discrete-Example_1__cs-OptimizationResults__entry__3"><p>History of objective and constraints from the sizing optimization for continuous variables.</p>
</th></tr></thead><tbody class = "tbody">
 <tr class = "row">
<td class = "entry" headers = "tso-c-example-sizing-discrete-Example_1__cs-OptimizationResults__entry__3">
<br/><img class = "image" src = "../TsoExampleImages/car_door_Standard_graph_discrete.png" height = "416"/><br/>
</td>
</tr>
</tbody></table>


<table class = "table"><caption/><colgroup><col/><col/></colgroup><thead class = "thead"><tr class = "row"><th class = "entry" id = "tso-c-example-sizing-discrete-Example_1__cs-OptimizationResults__entry__5" colspan = "2">Resulting thicknesses from the sizing optimization for discrete variables.</th></tr></thead><tbody class = "tbody"> 
<tr class = "row">
<td class = "entry" headers = "tso-c-example-sizing-discrete-Example_1__cs-OptimizationResults__entry__5">
<br/><img class = "image" src = "../TsoExampleImages/Car_door_legend_discrete.png" height = "302"/><br/>
</td>
<td class = "entry" headers = "tso-c-example-sizing-discrete-Example_1__cs-OptimizationResults__entry__5">
<br/><img class = "image" src = "../TsoExampleImages/Car_Door_discrete_result.png" height = "302"/><br/>
</td>
</tr>

</tbody></table>
  


<table class = "table"><caption/><colgroup><col/><col/></colgroup><thead class = "thead"><tr class = "row"><th class = "entry" id = "tso-c-example-sizing-discrete-Example_1__cs-OptimizationResults__entry__8" colspan = "2">Resulting thicknesses from the sizing optimization for continuous variables.</th></tr></thead><tbody class = "tbody">   
<tr class = "row"><td class = "entry" headers = "tso-c-example-sizing-discrete-Example_1__cs-OptimizationResults__entry__8">
<br/><img class = "image" src = "../TsoExampleImages/Car_door_legend_discrete.png" height = "302"/><br/>
</td>
  
<td class = "entry" headers = "tso-c-example-sizing-discrete-Example_1__cs-OptimizationResults__entry__8">
<br/><img class = "image" src = "../TsoExampleImages/Car_Door_Standard_result.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>  
  
</div>


</div>

</td></tr></table><script type = "text/javascript" src = "../DSDocUI_Bottom34.js">/* */</script></body>
</html>
