<?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 deals with multidisciplinary objective functions."/><meta name = "description" content = "This section deals with multidisciplinary objective functions."/><meta name = "DC.format" content = "HTML5"/><meta name = "DC.identifier" content = "tso-c-usr-terms-multidiscObjFunc"/><meta name = "DC.language" content = "en"/><link rel = "stylesheet" type = "text/css" href = "../DSDocUI_XML34.css"/><title>Multidisciplinary Objectives (Minmax and Maxmin Formulations)</title>
<script type = "text/javascript" src = "../DSDocUI_Highlight34.js">
  	/* */
  	</script><script type = "text/javascript" src = "../MathJax/MathJax.js?config=DS-default,local/local">
  		/* */
  		</script></head><body onLoad = "highlightSearchTerms();" id = "tso-c-usr-terms-multidiscObjFunc">
<a name = "hj-top"> </a><table class = "table1" id = "table11"><tr><td><table class = "DocHeader"><tr><td class = "DocHeader1" colspan = "2"><h1>Multidisciplinary Objectives (Minmax and Maxmin Formulations)</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 deals with multidisciplinary objective functions. </span>

</p>
<p>This page discusses: </p><ul><li><a href = "#tso-c-usr-terms-multidiscObjFunc__tso-c-user-ObjFun-MinMaxObj" id = "toc_rg" title = "">Multidisciplinary Objective (Minmax /Maxmin Formulation)</a></li><li><a href = "#tso-c-usr-terms-multidiscObjFunc__tso-c-user-ObjFun-MinMaxObj-weights" id = "toc_rg" title = "">Multiple Objective Termns (Weighting Factors)</a></li></ul>
</p></td></tr></table></td></tr></table>




<div class = "body conbody">
<p>It is possible to minimize the maximum term or to maximize the minimum term
referenced in the objective function. In such cases, the value of the objective function is generated with
a maximum or a minimum function over a set of terms defined by Design Responses.</p>

<p>If the maximum objective term should be minimized, the definition
is as follows:</p>
  
<pre class = "codeblock">
<code class = "ph codeph">
OBJ_FUNC
 ID_NAME = ...
 DRESP   = ...
 DRESP   = ...
 ...
 TARGET  = MINMAX
END_
</code>
</pre>

<p>If the minimum objective term should be maximized, the definition
is as follows:</p>

<pre class = "codeblock">
<code class = "ph codeph">
OBJ_FUNC
 ID_NAME = ...
 DRESP   = ...
 DRESP   = ...
 ...
 TARGET  = MAXMIN
END_
</code>
</pre>
  
<p>In both cases, the <code class = "ph codeph">DRESP</code>
definitions are referring to the desired design responses for the objective
function using the ID name of the defined responses. The defined responses
that should be minimized or maximized must be valid design responses.</p>

<div class = "section" id = "tso-c-usr-terms-multidiscObjFunc__tso-c-user-ObjFun-MinMaxObj"><h2 class = "title sectiontitle">Multidisciplinary Objective (Minmax /Maxmin Formulation)</h2>

<p>The following tables describe how the terms of design responses are handled
in the Min-Max / Max-Min formulation:</p>
<table class = "table" id = "tso-c-usr-terms-multidiscObjFunc__ag578554"><caption/><colgroup><col/><col/><col/></colgroup><thead class = "thead">
<tr class = "row">
<th class = "entry" id = "tso-c-usr-terms-multidiscObjFunc__ag578554__entry__1"><p> Compliance terms in Min-Max/Max-Min</p></th>
<th class = "entry" id = "tso-c-usr-terms-multidiscObjFunc__ag578554__entry__2"><p>Material volume terms in Min-Max/Max-Min</p></th>
<th class = "entry" id = "tso-c-usr-terms-multidiscObjFunc__ag578554__entry__3"><p>Eigenfrequency terms in Min-Max</p></th>
</tr>
</thead><tbody class = "tbody">
<tr class = "row">
<td class = "entry" headers = "tso-c-usr-terms-multidiscObjFunc__ag578554__entry__1"><p><span class = "ph inlineequation"><math class = "- topic/foreign "><mrow class = "- topic/foreign "><mo class = "- topic/foreign ">|</mo><mi class = "- topic/foreign ">α</mi><mo class = "- topic/foreign ">(</mo><msub class = "- topic/foreign "><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">C</mi></mrow><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">k</mi></mrow></msub><mo class = "- topic/foreign ">−</mo><msub class = "- topic/foreign "><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">C</mi></mrow><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">k</mi></mrow></msub><mo class = "- topic/foreign ">*</mo><mo class = "- topic/foreign ">)</mo><mo class = "- topic/foreign ">|</mo></mrow></math></span></p></td>
<td class = "entry" headers = "tso-c-usr-terms-multidiscObjFunc__ag578554__entry__2"><p><span class = "ph inlineequation"><math class = "- topic/foreign "><mrow class = "- topic/foreign "><mo class = "- topic/foreign ">|</mo><mi class = "- topic/foreign ">α</mi><mo class = "- topic/foreign ">(</mo><mi class = "- topic/foreign ">V</mi><mo class = "- topic/foreign ">−</mo><mi class = "- topic/foreign ">V</mi><mo class = "- topic/foreign ">*</mo><mo class = "- topic/foreign ">)</mo><mo class = "- topic/foreign ">|</mo></mrow></math></span></p></td>
<td class = "entry" headers = "tso-c-usr-terms-multidiscObjFunc__ag578554__entry__3"><p><span class = "ph inlineequation"><math class = "- topic/foreign "><mrow class = "- topic/foreign "><mo class = "- topic/foreign ">|</mo><mi class = "- topic/foreign ">α</mi><mfrac class = "- topic/foreign "><mrow class = "- topic/foreign "><mn class = "- topic/foreign ">1</mn></mrow><mrow class = "- topic/foreign "><msub class = "- topic/foreign "><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">f</mi></mrow><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">k</mi></mrow></msub><mo class = "- topic/foreign ">−</mo><msub class = "- topic/foreign "><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">f</mi></mrow><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">k</mi></mrow></msub><mo class = "- topic/foreign ">*</mo></mrow></mfrac><mo class = "- topic/foreign ">|</mo></mrow></math></span></p><p>Not for Max-Min formulation.</p></td>
</tr>
</tbody></table>

<table class = "table" id = "tso-c-usr-terms-multidiscObjFunc__ag578576"><caption/><colgroup><col/><col/></colgroup><thead class = "thead">
<tr class = "row">
<th class = "entry" id = "tso-c-usr-terms-multidiscObjFunc__ag578576__entry__1"><p>Displacement terms in Min-Max/Max-Min</p></th>
<th class = "entry" id = "tso-c-usr-terms-multidiscObjFunc__ag578576__entry__2"><p>Reaction force terms in Min-Max/Max-Min</p></th>
</tr>
</thead><tbody class = "tbody">
<tr class = "row">
<td class = "entry" headers = "tso-c-usr-terms-multidiscObjFunc__ag578576__entry__1">
<p><span class = "ph inlineequation"><math class = "- topic/foreign "><mrow class = "- topic/foreign "><mo class = "- topic/foreign ">|</mo><mi class = "- topic/foreign ">α</mi><mo class = "- topic/foreign ">(</mo><msub class = "- topic/foreign "><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">u</mi></mrow><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">i</mi></mrow></msub><mo class = "- topic/foreign ">−</mo><msub class = "- topic/foreign "><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">u</mi></mrow><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">i</mi></mrow></msub><mo class = "- topic/foreign ">*</mo><mo class = "- topic/foreign ">)</mo><mo class = "- topic/foreign ">|</mo></mrow></math></span></p>
<p><span class = "ph inlineequation"><math class = "- topic/foreign "><mrow class = "- topic/foreign "><mo class = "- topic/foreign ">|</mo><mi class = "- topic/foreign ">α</mi><mo class = "- topic/foreign ">(</mo><msub class = "- topic/foreign "><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">θ</mi></mrow><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">i</mi></mrow></msub><mo class = "- topic/foreign ">−</mo><msub class = "- topic/foreign "><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">θ</mi></mrow><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">i</mi></mrow></msub><mo class = "- topic/foreign ">*</mo><mo class = "- topic/foreign ">)</mo><mo class = "- topic/foreign ">|</mo></mrow></math></span></p>
<p><span class = "ph inlineequation"><math class = "- topic/foreign "><mrow class = "- topic/foreign "><mo class = "- topic/foreign ">|</mo><mi class = "- topic/foreign ">α</mi><mo class = "- topic/foreign ">(</mo><msqrt class = "- topic/foreign "><mrow class = "- topic/foreign "><msubsup class = "- topic/foreign "><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">u</mi></mrow><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">i</mi></mrow><mrow class = "- topic/foreign "><mn class = "- topic/foreign ">2</mn></mrow></msubsup></mrow></msqrt><mo class = "- topic/foreign ">−</mo><msub class = "- topic/foreign "><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">u</mi></mrow><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">i</mi></mrow></msub><mo class = "- topic/foreign ">*</mo><mo class = "- topic/foreign ">)</mo><mo class = "- topic/foreign ">|</mo></mrow></math></span></p>
<p><span class = "ph inlineequation"><math class = "- topic/foreign "><mrow class = "- topic/foreign "><mo class = "- topic/foreign ">|</mo><mi class = "- topic/foreign ">α</mi><mo class = "- topic/foreign ">(</mo><msqrt class = "- topic/foreign "><mrow class = "- topic/foreign "><msubsup class = "- topic/foreign "><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">u</mi></mrow><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">x</mi></mrow><mrow class = "- topic/foreign "><mn class = "- topic/foreign ">2</mn></mrow></msubsup><mo class = "- topic/foreign ">+</mo><msubsup class = "- topic/foreign "><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">u</mi></mrow><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">y</mi></mrow><mrow class = "- topic/foreign "><mn class = "- topic/foreign ">2</mn></mrow></msubsup><mo class = "- topic/foreign ">+</mo><msubsup class = "- topic/foreign "><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">u</mi></mrow><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">z</mi></mrow><mrow class = "- topic/foreign "><mn class = "- topic/foreign ">2</mn></mrow></msubsup></mrow></msqrt><mo class = "- topic/foreign ">−</mo><mi class = "- topic/foreign ">u</mi><mo class = "- topic/foreign ">*</mo><mo class = "- topic/foreign ">)</mo><mo class = "- topic/foreign ">|</mo></mrow></math></span></p>
<p><span class = "ph inlineequation"><math class = "- topic/foreign "><mrow class = "- topic/foreign "><mo class = "- topic/foreign ">|</mo><mi class = "- topic/foreign ">α</mi><mo class = "- topic/foreign ">(</mo><mo class = "- topic/foreign ">(</mo><msub class = "- topic/foreign "><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">u</mi></mrow><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">i</mi><mo class = "- topic/foreign ">,</mo><mn class = "- topic/foreign ">1</mn></mrow></msub><mo class = "- topic/foreign ">−</mo><msub class = "- topic/foreign "><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">u</mi></mrow><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">i</mi><mo class = "- topic/foreign ">,</mo><mn class = "- topic/foreign ">2</mn></mrow></msub><mo class = "- topic/foreign ">)</mo><mo class = "- topic/foreign ">−</mo><msub class = "- topic/foreign "><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">u</mi></mrow><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">i</mi></mrow></msub><mo class = "- topic/foreign ">*</mo><mo class = "- topic/foreign ">)</mo><mo class = "- topic/foreign ">|</mo></mrow></math></span></p>
<p><span class = "ph inlineequation"><math class = "- topic/foreign "><mrow class = "- topic/foreign "><mo class = "- topic/foreign ">|</mo><mi class = "- topic/foreign ">α</mi><mo class = "- topic/foreign ">(</mo><msqrt class = "- topic/foreign "><mrow class = "- topic/foreign "><mo class = "- topic/foreign ">(</mo><msub class = "- topic/foreign "><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">u</mi></mrow><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">i</mi><mo class = "- topic/foreign ">,</mo><mn class = "- topic/foreign ">1</mn></mrow></msub><mo class = "- topic/foreign ">−</mo><msub class = "- topic/foreign "><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">u</mi></mrow><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">i</mi><mo class = "- topic/foreign ">,</mo><mn class = "- topic/foreign ">2</mn></mrow></msub><mo class = "- topic/foreign ">)</mo><mstyle class = "- topic/foreign "><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">²</mi></mrow></mstyle></mrow></msqrt><mo class = "- topic/foreign ">−</mo><msub class = "- topic/foreign "><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">u</mi></mrow><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">i</mi></mrow></msub><mo class = "- topic/foreign ">*</mo><mo class = "- topic/foreign ">)</mo><mo class = "- topic/foreign ">|</mo></mrow></math></span></p></td>
<td class = "entry" headers = "tso-c-usr-terms-multidiscObjFunc__ag578576__entry__2">
<p><span class = "ph inlineequation"><math class = "- topic/foreign "><mrow class = "- topic/foreign "><mo class = "- topic/foreign ">|</mo><mi class = "- topic/foreign ">α</mi><mo class = "- topic/foreign ">(</mo><msub class = "- topic/foreign "><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">R</mi></mrow><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">i</mi></mrow></msub><mo class = "- topic/foreign ">−</mo><msub class = "- topic/foreign "><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">R</mi></mrow><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">i</mi></mrow></msub><mo class = "- topic/foreign ">*</mo><mo class = "- topic/foreign ">)</mo><mo class = "- topic/foreign ">|</mo></mrow></math></span></p>
<p><span class = "ph inlineequation"><math class = "- topic/foreign "><mrow class = "- topic/foreign "><mo class = "- topic/foreign ">|</mo><mi class = "- topic/foreign ">α</mi><mo class = "- topic/foreign ">(</mo><msub class = "- topic/foreign "><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">M</mi></mrow><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">i</mi></mrow></msub><mo class = "- topic/foreign ">−</mo><msub class = "- topic/foreign "><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">M</mi></mrow><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">i</mi></mrow></msub><mo class = "- topic/foreign ">*</mo><mo class = "- topic/foreign ">)</mo><mo class = "- topic/foreign ">|</mo></mrow></math></span></p>
<p><span class = "ph inlineequation"><math class = "- topic/foreign "><mrow class = "- topic/foreign "><mo class = "- topic/foreign ">|</mo><mi class = "- topic/foreign ">α</mi><mo class = "- topic/foreign ">(</mo><msqrt class = "- topic/foreign "><mrow class = "- topic/foreign "><msubsup class = "- topic/foreign "><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">R</mi></mrow><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">i</mi></mrow><mrow class = "- topic/foreign "><mn class = "- topic/foreign ">2</mn></mrow></msubsup></mrow></msqrt><mo class = "- topic/foreign ">−</mo><msub class = "- topic/foreign "><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">R</mi></mrow><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">i</mi></mrow></msub><mo class = "- topic/foreign ">*</mo><mo class = "- topic/foreign ">)</mo><mo class = "- topic/foreign ">|</mo></mrow></math></span></p>
<p><span class = "ph inlineequation"><math class = "- topic/foreign "><mrow class = "- topic/foreign "><mo class = "- topic/foreign ">|</mo><mi class = "- topic/foreign ">α</mi><mo class = "- topic/foreign ">(</mo><msqrt class = "- topic/foreign "><mrow class = "- topic/foreign "><msubsup class = "- topic/foreign "><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">R</mi></mrow><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">x</mi></mrow><mrow class = "- topic/foreign "><mn class = "- topic/foreign ">2</mn></mrow></msubsup><mo class = "- topic/foreign ">+</mo><msubsup class = "- topic/foreign "><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">R</mi></mrow><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">y</mi></mrow><mrow class = "- topic/foreign "><mn class = "- topic/foreign ">2</mn></mrow></msubsup><mo class = "- topic/foreign ">+</mo><msubsup class = "- topic/foreign "><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">R</mi></mrow><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">z</mi></mrow><mrow class = "- topic/foreign "><mn class = "- topic/foreign ">2</mn></mrow></msubsup></mrow></msqrt><mo class = "- topic/foreign ">−</mo><mi class = "- topic/foreign ">R</mi><mo class = "- topic/foreign ">*</mo><mo class = "- topic/foreign ">)</mo><mo class = "- topic/foreign ">|</mo></mrow></math></span></p>
<p><span class = "ph inlineequation"><math class = "- topic/foreign "><mrow class = "- topic/foreign "><mo class = "- topic/foreign ">|</mo><mi class = "- topic/foreign ">α</mi><mo class = "- topic/foreign ">(</mo><mo class = "- topic/foreign ">(</mo><msub class = "- topic/foreign "><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">R</mi></mrow><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">i</mi><mo class = "- topic/foreign ">,</mo><mn class = "- topic/foreign ">1</mn></mrow></msub><mo class = "- topic/foreign ">−</mo><msub class = "- topic/foreign "><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">R</mi></mrow><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">i</mi><mo class = "- topic/foreign ">,</mo><mn class = "- topic/foreign ">2</mn></mrow></msub><mo class = "- topic/foreign ">)</mo><mo class = "- topic/foreign ">−</mo><msub class = "- topic/foreign "><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">R</mi></mrow><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">i</mi></mrow></msub><mo class = "- topic/foreign ">*</mo><mo class = "- topic/foreign ">)</mo><mo class = "- topic/foreign ">|</mo></mrow></math></span></p>
<p><span class = "ph inlineequation"><math class = "- topic/foreign "><mrow class = "- topic/foreign "><mo class = "- topic/foreign ">|</mo><mi class = "- topic/foreign ">α</mi><mo class = "- topic/foreign ">(</mo><msqrt class = "- topic/foreign "><mrow class = "- topic/foreign "><mo class = "- topic/foreign ">(</mo><msub class = "- topic/foreign "><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">R</mi></mrow><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">i</mi><mo class = "- topic/foreign ">,</mo><mn class = "- topic/foreign ">1</mn></mrow></msub><mo class = "- topic/foreign ">−</mo><msub class = "- topic/foreign "><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">R</mi></mrow><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">i</mi><mo class = "- topic/foreign ">,</mo><mn class = "- topic/foreign ">2</mn></mrow></msub><mo class = "- topic/foreign ">)</mo><mstyle class = "- topic/foreign "><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">²</mi></mrow></mstyle></mrow></msqrt><mo class = "- topic/foreign ">−</mo><msub class = "- topic/foreign "><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">R</mi></mrow><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">i</mi></mrow></msub><mo class = "- topic/foreign ">*</mo><mo class = "- topic/foreign ">)</mo><mo class = "- topic/foreign ">|</mo></mrow></math></span></p></td>
</tr>
</tbody></table>

<table class = "table" id = "tso-c-usr-terms-multidiscObjFunc__ag578631"><caption/><colgroup><col/><col/><col/></colgroup><thead class = "thead">
<tr class = "row">
<th class = "entry" id = "tso-c-usr-terms-multidiscObjFunc__ag578631__entry__1"><p>Von Mises stress terms in Min-Max/Max-Min</p></th>
<th class = "entry" id = "tso-c-usr-terms-multidiscObjFunc__ag578631__entry__2"><p>Center gravity terms in Min-Max/Max-Min</p></th>
<th class = "entry" id = "tso-c-usr-terms-multidiscObjFunc__ag578631__entry__3"><p>Moment of inertia terms in Min-Max/Max-Min</p></th>
</tr>
</thead><tbody class = "tbody">
<tr class = "row">
<td class = "entry" headers = "tso-c-usr-terms-multidiscObjFunc__ag578631__entry__1"><p><span class = "ph inlineequation"><math class = "- topic/foreign "><mrow class = "- topic/foreign "><mo class = "- topic/foreign ">+</mo><mi class = "- topic/foreign ">α</mi><mi class = "- topic/foreign ">M</mi><mi class = "- topic/foreign ">a</mi><mi class = "- topic/foreign ">x</mi><mo class = "- topic/foreign ">|</mo><mfrac class = "- topic/foreign "><mrow class = "- topic/foreign "><msub class = "- topic/foreign "><mrow class = "- topic/foreign "><mo class = "- topic/foreign ">(</mo><mi class = "- topic/foreign ">σ</mi></mrow><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">v</mi><msup class = "- topic/foreign "><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">M</mi><mi class = "- topic/foreign ">i</mi><mi class = "- topic/foreign ">s</mi><mi class = "- topic/foreign ">e</mi><mi class = "- topic/foreign ">s</mi></mrow><mrow class = "- topic/foreign "><mo class = "- topic/foreign ">)</mo><mi class = "- topic/foreign ">²</mi></mrow></msup></mrow></msub></mrow><mrow class = "- topic/foreign "><mo class = "- topic/foreign ">(</mo><mi class = "- topic/foreign ">f</mi><mo class = "- topic/foreign ">(</mo><msub class = "- topic/foreign "><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">ρ</mi></mrow><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">i</mi></mrow></msub><mo class = "- topic/foreign ">)</mo><msub class = "- topic/foreign "><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">σ</mi></mrow><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">r</mi><mi class = "- topic/foreign ">e</mi><mi class = "- topic/foreign ">f</mi></mrow></msub><mo class = "- topic/foreign ">)</mo><mi class = "- topic/foreign ">²</mi></mrow></mfrac><mo class = "- topic/foreign ">⋅</mo><msub class = "- topic/foreign "><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">σ</mi></mrow><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">r</mi><mi class = "- topic/foreign ">e</mi><mi class = "- topic/foreign ">f</mi></mrow></msub><mo class = "- topic/foreign ">|</mo></mrow></math></span></p><p>(Constant temperature loading is supported.)</p></td>
<td class = "entry" headers = "tso-c-usr-terms-multidiscObjFunc__ag578631__entry__2"><p><span class = "ph inlineequation"><math class = "- topic/foreign "><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">α</mi><mo class = "- topic/foreign ">|</mo><msub class = "- topic/foreign "><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">i</mi></mrow><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">c</mi></mrow></msub><mo class = "- topic/foreign ">−</mo><msub class = "- topic/foreign "><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">i</mi></mrow><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">c</mi></mrow></msub><mo class = "- topic/foreign ">*</mo><mo class = "- topic/foreign ">|</mo></mrow></math></span></p></td>
<td class = "entry" headers = "tso-c-usr-terms-multidiscObjFunc__ag578631__entry__3"><p><span class = "ph inlineequation"><math class = "- topic/foreign "><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">α</mi><mo class = "- topic/foreign ">|</mo><msub class = "- topic/foreign "><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">I</mi></mrow><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">i</mi><mi class = "- topic/foreign ">j</mi></mrow></msub><mo class = "- topic/foreign ">−</mo><msub class = "- topic/foreign "><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">I</mi></mrow><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">i</mi><mi class = "- topic/foreign ">j</mi></mrow></msub><mo class = "- topic/foreign ">*</mo><mo class = "- topic/foreign ">|</mo></mrow></math></span></p></td>
</tr>
</tbody></table>
<table class = "table" id = "tso-c-usr-terms-multidiscObjFunc__ag578631-1"><caption/><colgroup><col/><col/></colgroup><thead class = "thead">
<tr class = "row">
<th class = "entry" id = "tso-c-usr-terms-multidiscObjFunc__ag578631-1__entry__1"><p>Plastic strain terms in objective**</p></th>
<th class = "entry" id = "tso-c-usr-terms-multidiscObjFunc__ag578631-1__entry__2"><p>Thermal terms in objective**</p></th>
</tr>
</thead><tbody class = "tbody">
<tr class = "row">
<td class = "entry" headers = "tso-c-usr-terms-multidiscObjFunc__ag578631-1__entry__1"><p><span class = "ph inlineequation"><math class = "- topic/foreign "><mrow class = "- topic/foreign "><mo class = "- topic/foreign ">|</mo><mi class = "- topic/foreign ">α</mi><mo class = "- topic/foreign ">(</mo><msqrt class = "- topic/foreign "><mrow class = "- topic/foreign "><mfrac class = "- topic/foreign "><mrow class = "- topic/foreign "><mn class = "- topic/foreign ">2</mn></mrow><mrow class = "- topic/foreign "><mn class = "- topic/foreign ">3</mn></mrow></mfrac><mrow class = "- topic/foreign "><msup class = "- topic/foreign "><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">ε</mi></mrow><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">pl</mi></mrow></msup><mo class = "- topic/foreign ">:</mo><msup class = "- topic/foreign "><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">ε</mi></mrow><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">pl</mi></mrow></msup></mrow></mrow></msqrt><mo class = "- topic/foreign ">-</mo><mrow class = "- topic/foreign "><msup class = "- topic/foreign "><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">ε</mi></mrow><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">pl</mi></mrow></msup><mo class = "- topic/foreign ">*</mo></mrow><mo class = "- topic/foreign ">)</mo><mo class = "- topic/foreign ">|</mo></mrow></math></span></p></td>
<td class = "entry" headers = "tso-c-usr-terms-multidiscObjFunc__ag578631-1__entry__2">
<p><span class = "ph inlineequation"><math class = "- topic/foreign "><mrow class = "- topic/foreign "><mo class = "- topic/foreign ">|</mo><mi class = "- topic/foreign ">α</mi><mo class = "- topic/foreign ">(</mo><msub class = "- topic/foreign "><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">c</mi></mrow><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">T</mi></mrow></msub></mrow><mo class = "- topic/foreign ">-</mo><mrow class = "- topic/foreign "><msub class = "- topic/foreign "><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">c</mi></mrow><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">T</mi></mrow></msub><mo class = "- topic/foreign ">*</mo></mrow><mo class = "- topic/foreign ">)</mo><mo class = "- topic/foreign ">|</mo></math></span></p>
<p><span class = "ph inlineequation"><math class = "- topic/foreign "><mrow class = "- topic/foreign "><mo class = "- topic/foreign ">|</mo><mi class = "- topic/foreign ">α</mi><mo class = "- topic/foreign ">(</mo><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">T</mi></mrow></mrow><mo class = "- topic/foreign ">-</mo><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">T</mi></mrow><mo class = "- topic/foreign ">*</mo><mo class = "- topic/foreign ">)</mo><mo class = "- topic/foreign ">|</mo></math></span></p>
<p><span class = "ph inlineequation"><math class = "- topic/foreign "><mrow class = "- topic/foreign "><mo class = "- topic/foreign ">|</mo><mi class = "- topic/foreign ">α</mi><mo class = "- topic/foreign ">(</mo><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">q</mi></mrow></mrow><mo class = "- topic/foreign ">-</mo><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">q</mi><mo class = "- topic/foreign ">*</mo></mrow><mo class = "- topic/foreign ">)</mo><mo class = "- topic/foreign ">|</mo></math></span></p>
<p><span class = "ph inlineequation"><math class = "- topic/foreign "><mrow class = "- topic/foreign "><mo class = "- topic/foreign ">|</mo><mi class = "- topic/foreign ">α</mi><mo class = "- topic/foreign ">(</mo><mrow class = "- topic/foreign "><munder class = "- topic/foreign "><mo class = "- topic/foreign ">∑</mo><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">e</mi></mrow></munder></mrow><mrow class = "- topic/foreign "><munder class = "- topic/foreign "><mo class = "- topic/foreign ">∑</mo><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">n</mi></mrow></munder></mrow><mrow class = "- topic/foreign "><msub class = "- topic/foreign "><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">Q</mi></mrow><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">e,n</mi></mrow></msub></mrow><mrow class = "- topic/foreign "><mo class = "- topic/foreign ">-</mo><mi class = "- topic/foreign ">q</mi></mrow><mo class = "- topic/foreign ">-</mo><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">q</mi><mo class = "- topic/foreign ">*</mo></mrow><mo class = "- topic/foreign ">)</mo><mo class = "- topic/foreign ">|</mo></mrow></math></span></p></td>
</tr>
</tbody></table>
  


<p>where the index <span class = "ph">i</span> and j are indicating one of the x-y-z-directions. The compliance,
eigenfrequencies, displacements, and reaction forces can be from different <span class = "ph">load cases</span>.</p>
<p>The <code class = "ph codeph">REFERENCE</code> values marked with "*" are
defined by the use in the <code class = "ph codeph">DRESP</code> command in <code class = "ph codeph">OBJ_FUNC</code>.
Normally, the reference values are zero. Hence, by default all reference
values are set to zero. The reference can be set individually for each
term in the objective function.</p>
</div>

<div class = "section" id = "tso-c-usr-terms-multidiscObjFunc__tso-c-user-ObjFun-MinMaxObj-weights"><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">Multiple Objective Termns (Weighting Factors)</h2>

<p>You define the weighting factors 
<span class = "ph inlineequation"><math class = "- topic/foreign "><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">α</mi></mrow></math></span> 
in the respective <code class = "ph codeph">DRESP</code> command item in <code class = "ph codeph">OBJ_FUNC</code>. The
weighting factors can be different for each individual term in the objective function. By
default, the weighting factors are all set to one, so that the individual objective terms are taken into
account with their actual value (e.g. stresses in the range of 100 MPa and frequencies in GHz).</p>
<p>The reference value and weight factor can be changed, for example, to 2.5 and 14.0 for response
id_dresp in the following way:</p>
<pre class = "codeblock">
<code class = "ph codeph">
OBJ_FUNC
 ...
 DRESP = id_dresp, 2.5, 14.0
 ...
END_
</code>
</pre>

<p><table class = "Remark" id = "table132"><tr><td class = "Remark"><span class = "run-in.important">Important:
				</span><span class = "notecontent"><ul class = "ul">
<li class = "li">The main difference between the scheme in <a class = "xref" href = "tso-c-usr-terms-minMaxObjFunc.htm#tso-c-usr-terms-minMaxObjFunc__tso-c-user-ObjFun-MaxOrMinObj">Minimization or Maximization of an Objective</a> and
the present scheme is the way the frequency terms are defined in the objective.</li>
<li class = "li">A minimization optimization task can be converted into a maximization
optimization task (or vice versa) by changing the sign of the weighting
factors in the definition of the objective function.</li>
<li class = "li">Design responses marked with <code class = "ph codeph">**</code> are allowed only using <span class = "ph">Abaqus</span>
sensitivities.</li>
</ul></span></td></tr></table>
</p>

</div>

</div>

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