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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> Car Model–Volume Reduction</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 an industrial scale model of a car.</span>

</p>
<p>This page discusses: </p><ul><li><a href = "#tso-c-example-sizing-discrete-Example_2__cs-TheFEModel" id = "toc_rg" title = "">FE Model</a></li><li><a href = "#tso-c-example-sizing-discrete-Example_2__cs-TheOptimizationProblem" id = "toc_rg" title = "">Optimization Problem</a></li><li><a href = "#tso-c-example-sizing-discrete-Example_2__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_2__cs-TheFEModel"><h2 class = "title sectiontitle">FE Model</h2>

<p>The model is a complete car represented with all the details of the chassis. There are three
        separate <span class = "ph">load cases</span>, where load is applied on the whole frame as follows: a bending load, a
        torsional load and an axial load. The displacement boundary conditions are applied at the
        wheels. The result was requested from the following discrete range: </p>
 
   
<table class = "table"><caption/><colgroup><col style = "width:25%"/><col style = "width:25%"/><col style = "width:25%"/><col style = "width:25%"/></colgroup><thead class = "thead"><tr class = "row"><th class = "entry" id = "tso-c-example-sizing-discrete-Example_2__cs-TheFEModel__entry__1" colspan = "2">Available Thicknesses</th><th class = "entry" id = "tso-c-example-sizing-discrete-Example_2__cs-TheFEModel__entry__2" colspan = "2"/></tr></thead><tbody class = "tbody"><tr class = "row"><td class = "entry" headers = "tso-c-example-sizing-discrete-Example_2__cs-TheFEModel__entry__1"> 0.152 </td><td class = "entry" headers = "tso-c-example-sizing-discrete-Example_2__cs-TheFEModel__entry__1"> 0.417 </td><td class = "entry" headers = "tso-c-example-sizing-discrete-Example_2__cs-TheFEModel__entry__2"> 1.367 </td><td class = "entry" headers = "tso-c-example-sizing-discrete-Example_2__cs-TheFEModel__entry__2"> 4.935 </td></tr><tr class = "row"><td class = "entry" headers = "tso-c-example-sizing-discrete-Example_2__cs-TheFEModel__entry__1"> 0.163 </td><td class = "entry" headers = "tso-c-example-sizing-discrete-Example_2__cs-TheFEModel__entry__1"> 0.455 </td><td class = "entry" headers = "tso-c-example-sizing-discrete-Example_2__cs-TheFEModel__entry__2"> 1.519 </td><td class = "entry" headers = "tso-c-example-sizing-discrete-Example_2__cs-TheFEModel__entry__2"> 5.314 </td></tr><tr class = "row"><td class = "entry" headers = "tso-c-example-sizing-discrete-Example_2__cs-TheFEModel__entry__1"> 0.17 </td><td class = "entry" headers = "tso-c-example-sizing-discrete-Example_2__cs-TheFEModel__entry__1"> 0.531 </td><td class = "entry" headers = "tso-c-example-sizing-discrete-Example_2__cs-TheFEModel__entry__2"> 1.709 </td><td class = "entry" headers = "tso-c-example-sizing-discrete-Example_2__cs-TheFEModel__entry__2"> 5.695 </td></tr><tr class = "row"><td class = "entry" headers = "tso-c-example-sizing-discrete-Example_2__cs-TheFEModel__entry__1"> 0.191 </td><td class = "entry" headers = "tso-c-example-sizing-discrete-Example_2__cs-TheFEModel__entry__1"> 0.607 </td><td class = "entry" headers = "tso-c-example-sizing-discrete-Example_2__cs-TheFEModel__entry__2"> 1.897 </td><td class = "entry" headers = "tso-c-example-sizing-discrete-Example_2__cs-TheFEModel__entry__2"> 6.073 </td></tr><tr class = "row"><td class = "entry" headers = "tso-c-example-sizing-discrete-Example_2__cs-TheFEModel__entry__1"> 0.208 </td><td class = "entry" headers = "tso-c-example-sizing-discrete-Example_2__cs-TheFEModel__entry__1"> 0.683 </td><td class = "entry" headers = "tso-c-example-sizing-discrete-Example_2__cs-TheFEModel__entry__2"> 2.278 </td><td class = "entry" headers = "tso-c-example-sizing-discrete-Example_2__cs-TheFEModel__entry__2"/></tr><tr class = "row"><td class = "entry" headers = "tso-c-example-sizing-discrete-Example_2__cs-TheFEModel__entry__1"> 0.229 </td><td class = "entry" headers = "tso-c-example-sizing-discrete-Example_2__cs-TheFEModel__entry__1"> 0.759 </td><td class = "entry" headers = "tso-c-example-sizing-discrete-Example_2__cs-TheFEModel__entry__2"> 2.657 </td><td class = "entry" headers = "tso-c-example-sizing-discrete-Example_2__cs-TheFEModel__entry__2"/></tr><tr class = "row"><td class = "entry" headers = "tso-c-example-sizing-discrete-Example_2__cs-TheFEModel__entry__1"> 0.246 </td><td class = "entry" headers = "tso-c-example-sizing-discrete-Example_2__cs-TheFEModel__entry__1"> 0.836 </td><td class = "entry" headers = "tso-c-example-sizing-discrete-Example_2__cs-TheFEModel__entry__2"> 3.038 </td><td class = "entry" headers = "tso-c-example-sizing-discrete-Example_2__cs-TheFEModel__entry__2"/></tr><tr class = "row"><td class = "entry" headers = "tso-c-example-sizing-discrete-Example_2__cs-TheFEModel__entry__1"> 0.267 </td><td class = "entry" headers = "tso-c-example-sizing-discrete-Example_2__cs-TheFEModel__entry__1"> 0.912 </td><td class = "entry" headers = "tso-c-example-sizing-discrete-Example_2__cs-TheFEModel__entry__2"> 3.416 </td><td class = "entry" headers = "tso-c-example-sizing-discrete-Example_2__cs-TheFEModel__entry__2"/></tr><tr class = "row"><td class = "entry" headers = "tso-c-example-sizing-discrete-Example_2__cs-TheFEModel__entry__1"> 0.305 </td><td class = "entry" headers = "tso-c-example-sizing-discrete-Example_2__cs-TheFEModel__entry__1"> 1.062 </td><td class = "entry" headers = "tso-c-example-sizing-discrete-Example_2__cs-TheFEModel__entry__2"> 3.797 </td><td class = "entry" headers = "tso-c-example-sizing-discrete-Example_2__cs-TheFEModel__entry__2"/></tr><tr class = "row"><td class = "entry" headers = "tso-c-example-sizing-discrete-Example_2__cs-TheFEModel__entry__1"> 0.343 </td><td class = "entry" headers = "tso-c-example-sizing-discrete-Example_2__cs-TheFEModel__entry__1"> 1.214 </td><td class = "entry" headers = "tso-c-example-sizing-discrete-Example_2__cs-TheFEModel__entry__2"> 4.176 </td><td class = "entry" headers = "tso-c-example-sizing-discrete-Example_2__cs-TheFEModel__entry__2"/></tr><tr class = "row"><td class = "entry" headers = "tso-c-example-sizing-discrete-Example_2__cs-TheFEModel__entry__1">0.378 </td><td class = "entry" headers = "tso-c-example-sizing-discrete-Example_2__cs-TheFEModel__entry__1">1.367</td><td class = "entry" headers = "tso-c-example-sizing-discrete-Example_2__cs-TheFEModel__entry__2"> 4.554 </td><td class = "entry" headers = "tso-c-example-sizing-discrete-Example_2__cs-TheFEModel__entry__2"/></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_2__cs-TheFEModel__entry__47">The FE model of the car  with boundary conditions.</th></tr></thead><tbody class = "tbody">
<tr class = "row">
<td class = "entry" headers = "tso-c-example-sizing-discrete-Example_2__cs-TheFEModel__entry__47">
  <br/><img class = "image" src = "../TsoExampleImages/size_typtasks_MinVol_modal_Obj2.png" height = "189"/><br/>
</td>
</tr>
<tr class = "row">
<td class = "entry" headers = "tso-c-example-sizing-discrete-Example_2__cs-TheFEModel__entry__47">
  <br/><img class = "image" src = "../TsoExampleImages/Car_model_original_discrete.png" height = "302"/><br/>
</td>
</tr>
</tbody></table> 
</div>


<div class = "section" id = "tso-c-example-sizing-discrete-Example_2__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>The optimization problem is a basic volume minimization problem with three stiffness constraints. There are 198 clusters and over 2 million elements in this model.
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.csv
   DISCR_CYCLE      = 9
   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_2__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_2__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_2__cs-OptimizationResults__entry__1">
<br/><img class = "image" src = "../TsoExampleImages/Car_Full_Graphs.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_2__cs-OptimizationResults__entry__3">History of objective and constraints 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_2__cs-OptimizationResults__entry__3">
<br/><img class = "image" src = "../TsoExampleImages/Car_Full_Graphs_std.png" height = "416"/><br/>
</td>
</tr>
</tbody></table>



<table class = "table"><caption/><colgroup><col/><col/><col/></colgroup><thead class = "thead"><tr class = "row">
<th class = "entry" id = "tso-c-example-sizing-discrete-Example_2__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_2__cs-OptimizationResults__entry__5">
<br/><img class = "image" src = "../TsoExampleImages/Car_model_legend_discrete.png" height = "302"/><br/>
</td>  
<td class = "entry" headers = "tso-c-example-sizing-discrete-Example_2__cs-OptimizationResults__entry__5">
<br/><img class = "image" src = "../TsoExampleImages/Car_model_opt_discrete.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_2__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_2__cs-OptimizationResults__entry__8">
<br/><img class = "image" src = "../TsoExampleImages/Car_model_legend_discrete.png" height = "302"/><br/>
</td>  
<td class = "entry" headers = "tso-c-example-sizing-discrete-Example_2__cs-OptimizationResults__entry__8">
<br/><img class = "image" src = "../TsoExampleImages/Car_model_opt_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>  
  
</div>


</div>


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