<?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 = "task"/><meta name = "description" content = "This example shows the difference between a MIN and MINMAX formulation for the Objective Function."/><meta name = "DC.relation" scheme = "URI" content = "tso-c-example-topo-checkOptResult.htm#tso-c-example-topo-checkOptResult"/><meta name = "DC.format" content = "HTML5"/><meta name = "DC.identifier" content = "tso-t-example-topo-sensTopoBonnet"/><meta name = "DC.language" content = "en"/><link rel = "stylesheet" type = "text/css" href = "../DSDocUI_XML34.css"/><title>Minimizing the Compliance of the Bonnet Model</title>
<script type = "text/javascript" src = "../DSDocUI_Highlight34.js">
  	/* */
  	</script></head><body onLoad = "highlightSearchTerms();" id = "tso-t-example-topo-sensTopoBonnet">
<a name = "hj-top"> </a><table class = "table1" id = "table11"><tr><td><table class = "DocHeader"><tr><td class = "DocHeader1" colspan = "2"><h1>Minimizing the Compliance of the Bonnet Model </h1></td></tr><tr><td class = "DocHeader4" colspan = "2"/></tr><tr><td class = "DocHeader3"><table class = "DocHeaderIntro" id = "table12"><tr><td class = "Intro1Only"><p class = "shortdesc">This example shows the difference between a MIN and MINMAX formulation for the Objective Function.
</p></td></tr></table></td><td class = "DocHeader2"><table class = "DocTopicsSeeAlso" id = "table13"><tr><td class = "TopicsTitle">See Also</td></tr><tr><td><a title = "To get an impression of the quality of the optimization, it is necessary to check the values of the constraints and the objective at the end of the optimization." href = "tso-c-example-topo-checkOptResult.htm#tso-c-example-topo-checkOptResult">About Checking the Quality of the Optimization Result</a></td></tr></table></td></tr></table>



<div class = "body taskbody">
<section><ol class = "ol steps"><li class = "li step stepexpand">
Define three Design Responses (DRESP) with the compliance of each <span class = "ph">load case</span>:
<div class = "itemgroup stepresult">
<pre class = "codeblock">
DRESP
  ID_NAME    = COMPL_1
  TYPE       = STRAIN_ENERGY
  DEF_TYPE   = SYS
  LC_SET     = STATIC,1,
  EL_GROUP   = ALL_ELEMENTS
  GROUP_OPER = SUM
END_
</pre>
<pre class = "codeblock">
DRESP
  ID_NAME    = COMPL_2
  TYPE       = STRAIN_ENERGY
  DEF_TYPE   = SYS
  LC_SET     = STATIC,2,
  EL_GROUP   = ALL_ELEMENTS
  GROUP_OPER = SUM
END_
</pre>
<pre class = "codeblock">
DRESP
  ID_NAME    = COMPL_3
  TYPE       = STRAIN_ENERGY
  DEF_TYPE   = SYS
  LC_SET     = STATIC,3,
  EL_GROUP   = ALL_ELEMENTS
  GROUP_OPER = SUM
END_
</pre>
</div>
</li><li class = "li step stepexpand">
Define the Objective Function (OBJ_FUNC) with a MIN formulation:
<div class = "itemgroup stepresult">
<pre class = "codeblock">
OBJ_FUNC
  ID_NAME = MIN_COMP
  DRESP   = COMPL_1, 1.0, 0.0
  DRESP   = COMPL_2, 1.0, 0.0
  DRESP   = COMPL_3, 1.0, 0.0
  TARGET  = MIN
END_
</pre>
<p>The formulation of the optimization problem is done in the classic way, which means that the
compliance of all three <span class = "ph">load cases</span>
is added and the sum of the compliance of the three load
cases is minimized. The result looks as follows:</p>
<p><br/><img class = "image" src = "../TsoExampleImages/sensTopoBonnetResultMin.png"/><br/></p>
</div>
</li><li class = "li step stepexpand">
Define the Objective Function (OBJ_FUNC) with a MINMAX formulation:
<div class = "itemgroup stepresult">
<pre class = "codeblock">
OBJ_FUNC
  ID_NAME = MIN_MAX_COMP
  DRESP   = COMPL_1, 1.0, 0.0
  DRESP   = COMPL_2, 1.0, 0.0
  DRESP   = COMPL_3, 1.0, 0.0
  TARGET  = MIN_MAX
END_
</pre>
<p>In this case, the sum of the compliance is not minimized. Instead the maximum
compliance of the three defined design responses is minimized. As
result the optimization system ends up with the following structure:</p>
<p><br/><img class = "image" src = "../TsoExampleImages/sensTopoBonnetResultMinMax.png"/><br/></p>
</div>
</li></ol></section>
</div>

<div class = "related-links"/>
</td></tr></table><script type = "text/javascript" src = "../DSDocUI_Bottom34.js">/* */</script></body>
</html>
