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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>Combined Responses in Sensitivity-Based Optimization</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 chapter lists the allowed combination of <code class = "ph codeph">DRESP</code>
type, <code class = "ph codeph">GROUP_OPER</code> and <code class = "ph codeph">VAR_OPER</code> parameter.
</span>

</p>
<p>This page discusses: </p><ul><li><a href = "#tso-c-usr-terms-combTermDrespSens__tso-c-usr-terms-combTermDrespSens-displ" id = "toc_rg" title = "">Displacements</a></li><li><a href = "#tso-c-usr-terms-combTermDrespSens__tso-c-usr-terms-combTermDrespSens-reacForce" id = "toc_rg" title = "">Reaction Forces</a></li><li><a href = "#tso-c-usr-terms-combTermDrespSens__tso-sb-usr-terms-combTermDrespSens-intForce" id = "toc_rg" title = "">Internal Forces</a></li><li><a href = "#tso-c-usr-terms-combTermDrespSens__tso-sb-usr-terms-combTermDrespSens-modalEigenfreq" id = "toc_rg" title = "">Modal Eigenfrequencies</a></li><li><a href = "#tso-c-usr-terms-combTermDrespSens__tso-sb-usr-terms-combTermDrespSens-freqSpecResp" id = "toc_rg" title = "">Frequency Spectrum Responses</a></li><li><a href = "#tso-c-usr-terms-combTermDrespSens__tso-c-usr-terms-combTermDrespSens-temp" id = "toc_rg" title = ""><span class = "ph">Temperature</span></a></li></ul>
</p></td></tr></table></td></tr></table>




<div class = "body conbody">

<div class = "section" id = "tso-c-usr-terms-combTermDrespSens__tso-c-usr-terms-combTermDrespSens-displ"><h2 class = "title sectiontitle">Displacements</h2>

<table class = "table" id = "tso-c-usr-terms-combTermDrespSens__xx751371"><caption/><colgroup><col/><col/><col/></colgroup><thead class = "thead">
<tr class = "row">
<th class = "entry" id = "tso-c-usr-terms-combTermDrespSens__xx751371__entry__1">
<p>TYPE</p>
<p>The allowable types for displacements and rotations</p>
</th>
<th class = "entry" id = "tso-c-usr-terms-combTermDrespSens__xx751371__entry__2">
<p>GROUP_OPER</p>
<p>The allowable definition types
for displacements and rotations</p>
</th>
<th class = "entry" id = "tso-c-usr-terms-combTermDrespSens__xx751371__entry__3">
<p>VAR_OPER</p>
<p>The allowable operators for displacements and rotations</p>
</th>
</tr>
</thead><tbody class = "tbody">
<tr class = "row">
<td class = "entry" headers = "tso-c-usr-terms-combTermDrespSens__xx751371__entry__1">
<p>DISP_X</p>
<p>DISP_Y</p>
<p>DISP_Z</p>
<p>ROT_X</p>
<p>ROT_Y </p>
<p>ROT_Z </p>
</td>
<td class = "entry" headers = "tso-c-usr-terms-combTermDrespSens__xx751371__entry__2">
<p>MAX</p>
<p>MIN</p>
<p>SUM</p>
</td>
<td class = "entry" headers = "tso-c-usr-terms-combTermDrespSens__xx751371__entry__3">
<p>SUB</p>
<p>SUB_ABS</p>
<p>COMBINE</p>
<p>ADD_ABS</p>
</td>
</tr>
<tr class = "row">
<td class = "entry" headers = "tso-c-usr-terms-combTermDrespSens__xx751371__entry__1">
<p>DISP_ABS</p>
</td>
<td class = "entry" headers = "tso-c-usr-terms-combTermDrespSens__xx751371__entry__2">
<p>MAX</p>
</td>
<td class = "entry" headers = "tso-c-usr-terms-combTermDrespSens__xx751371__entry__3">
<p>SUB</p>
<p>SUB_ABS*</p>
</td>
</tr>
<tr class = "row">
<td class = "entry" headers = "tso-c-usr-terms-combTermDrespSens__xx751371__entry__1">
<p>ROT_ABS</p>
</td>
<td class = "entry" headers = "tso-c-usr-terms-combTermDrespSens__xx751371__entry__2">
<p>MAX</p>
</td>
<td class = "entry" headers = "tso-c-usr-terms-combTermDrespSens__xx751371__entry__3">
<p>SUB_ABS*</p>
</td>
</tr>
<tr class = "row">
<td class = "entry" headers = "tso-c-usr-terms-combTermDrespSens__xx751371__entry__1">
<p>DISP_X_ABS </p>
<p>DISP_Y_ABS </p>
<p>DISP_Z_ABS</p>
<p>ROT_X_ABS </p>
<p>ROT_Y_ABS </p>
<p>ROT_Z_ABS </p>
</td>
<td class = "entry" headers = "tso-c-usr-terms-combTermDrespSens__xx751371__entry__2">
<p>MAX</p>
<p>MIN</p>
</td>
<td class = "entry" headers = "tso-c-usr-terms-combTermDrespSens__xx751371__entry__3">
<p>---</p>
</td>
</tr>
<tr class = "row">
<td class = "entry" headers = "tso-c-usr-terms-combTermDrespSens__xx751371__entry__1 tso-c-usr-terms-combTermDrespSens__xx751371__entry__2 tso-c-usr-terms-combTermDrespSens__xx751371__entry__3" colspan = "3">
<p>
* For these, <code class = "ph codeph">VAR_A</code>
and <code class = "ph codeph">VAR_B</code> must have the same <code class = "ph codeph">DRESP</code>
type. For example, the <code class = "ph codeph">DRESP</code> type for <code class = "ph codeph">VAR_A</code>
and <code class = "ph codeph">VAR_B</code> is <code class = "ph codeph">TYPE = DISP_ABS</code> yielding:</p>
<p>
<span class = "ph inlineequation"><math altimg-valign = "14" altimg-height = "39" altimg-width = "393" class = "- topic/foreign "><mrow class = "- topic/foreign "><mo class = "- topic/foreign ">|</mo><mo class = "- topic/foreign ">▵</mo><mi class = "- topic/foreign ">u</mi><mo class = "- topic/foreign ">|</mo><mo class = "- topic/foreign ">=</mo><msqrt class = "- topic/foreign "><mrow class = "- topic/foreign "><msup 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 ">x</mi><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 ">x</mi><mn class = "- topic/foreign ">2</mn></mrow></msub><mo class = "- topic/foreign ">)</mo></mrow><mrow class = "- topic/foreign "><mn class = "- topic/foreign ">2</mn></mrow></msup><mo class = "- topic/foreign ">+</mo><msup 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 ">y</mi><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 ">y</mi><mn class = "- topic/foreign ">2</mn></mrow></msub><mo class = "- topic/foreign ">)</mo></mrow><mrow class = "- topic/foreign "><mn class = "- topic/foreign ">2</mn></mrow></msup><mo class = "- topic/foreign ">+</mo><msup 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 ">z</mi><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 ">z</mi><mn class = "- topic/foreign ">2</mn></mrow></msub><mo class = "- topic/foreign ">)</mo></mrow><mrow class = "- topic/foreign "><mn class = "- topic/foreign ">2</mn></mrow></msup></mrow></msqrt></mrow></math></span>
</p>
</td>
</tr>
</tbody></table>

<span class = "ph uicontrol">Remarks</span>
<ol class = "ol" id = "tso-c-usr-terms-combTermDrespSens__ol_0F566F3758AD4A44A90B801756692A92">
<li class = "li">
For <code class = "ph codeph">TYPE=DISP_ABS </code>with <code class = "ph codeph">VAR_OPER=SUB </code>both
<code class = "ph codeph">VAR_A</code> and <code class = "ph codeph">VAR_B</code> are <code class = "ph codeph">TYPE=DISP_ABS</code>.
For this case the displacement of <code class = "ph codeph">DRESP</code> is calculated
as following:
<table class = "table" id = "tso-c-usr-terms-combTermDrespSens__table_C0A1619CF1934290AB5B77091E3E1BD4"><caption/><colgroup><col style = "width:100%"/></colgroup><tbody class = "tbody">
<tr class = "row">
<td class = "entry">
<p>
<span class = "ph inlineequation"><math altimg-valign = "5" altimg-height = "19" altimg-width = "197" class = "- topic/foreign "><mrow class = "- topic/foreign "><mtext class = "- topic/foreign ">DRESP=</mtext><mo class = "- topic/foreign ">Δ</mo><mi class = "- topic/foreign ">u</mi><mo class = "- topic/foreign ">=</mo><msub class = "- topic/foreign "><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">l</mi></mrow><mrow class = "- topic/foreign "><mtext class = "- topic/foreign ">def</mtext></mrow></msub><mo class = "- topic/foreign ">−</mo><msub class = "- topic/foreign "><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">l</mi></mrow><mrow class = "- topic/foreign "><mtext class = "- topic/foreign ">ini</mtext></mrow></msub></mrow></math></span>
</p>
<p>
with
<span class = "ph inlineequation"><math altimg-valign = "10" altimg-height = "35" altimg-width = "528" class = "- topic/foreign "><mrow class = "- topic/foreign "><msub class = "- topic/foreign "><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">l</mi></mrow><mrow class = "- topic/foreign "><mtext class = "- topic/foreign ">def</mtext></mrow></msub><mo class = "- topic/foreign ">=</mo><msqrt class = "- topic/foreign "><mrow class = "- topic/foreign "><msup class = "- topic/foreign "><mrow class = "- topic/foreign "><mo class = "- topic/foreign ">(</mo><mo class = "- topic/foreign ">Δ</mo><msub class = "- topic/foreign "><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">x</mi></mrow><mrow class = "- topic/foreign "><mtext class = "- topic/foreign ">pos</mtext></mrow></msub><mo class = "- topic/foreign ">+</mo><mo class = "- topic/foreign ">Δ</mo><msub 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></msub><mo class = "- topic/foreign ">)</mo></mrow><mrow class = "- topic/foreign "><mn class = "- topic/foreign ">2</mn></mrow></msup><mo class = "- topic/foreign ">+</mo><msup class = "- topic/foreign "><mrow class = "- topic/foreign "><mo class = "- topic/foreign ">(</mo><mo class = "- topic/foreign ">Δ</mo><msub class = "- topic/foreign "><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">y</mi></mrow><mrow class = "- topic/foreign "><mtext class = "- topic/foreign ">pos</mtext></mrow></msub><mo class = "- topic/foreign ">+</mo><mo class = "- topic/foreign ">Δ</mo><msub 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></msub><mo class = "- topic/foreign ">)</mo></mrow><mrow class = "- topic/foreign "><mn class = "- topic/foreign ">2</mn></mrow></msup><mo class = "- topic/foreign ">+</mo><msup class = "- topic/foreign "><mrow class = "- topic/foreign "><mo class = "- topic/foreign ">(</mo><mo class = "- topic/foreign ">Δ</mo><msub class = "- topic/foreign "><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">z</mi></mrow><mrow class = "- topic/foreign "><mtext class = "- topic/foreign ">pos</mtext></mrow></msub><mo class = "- topic/foreign ">+</mo><mo class = "- topic/foreign ">Δ</mo><msub 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></msub><mo class = "- topic/foreign ">)</mo></mrow><mrow class = "- topic/foreign "><mn class = "- topic/foreign ">2</mn></mrow></msup></mrow></msqrt></mrow></math></span>
as deformed length</p>
<p>
and
<span class = "ph inlineequation"><math altimg-valign = "10" altimg-height = "35" altimg-width = "341" class = "- topic/foreign "><mrow class = "- topic/foreign "><msub class = "- topic/foreign "><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">l</mi></mrow><mrow class = "- topic/foreign "><mtext class = "- topic/foreign ">ini</mtext></mrow></msub><mo class = "- topic/foreign ">=</mo><msqrt class = "- topic/foreign "><mrow class = "- topic/foreign "><msup class = "- topic/foreign "><mrow class = "- topic/foreign "><mo class = "- topic/foreign ">(</mo><mo class = "- topic/foreign ">Δ</mo><msub class = "- topic/foreign "><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">x</mi></mrow><mrow class = "- topic/foreign "><mtext class = "- topic/foreign ">pos</mtext></mrow></msub><mo class = "- topic/foreign ">)</mo></mrow><mrow class = "- topic/foreign "><mn class = "- topic/foreign ">2</mn></mrow></msup><mo class = "- topic/foreign ">+</mo><msup class = "- topic/foreign "><mrow class = "- topic/foreign "><mo class = "- topic/foreign ">(</mo><mo class = "- topic/foreign ">Δ</mo><msub class = "- topic/foreign "><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">y</mi></mrow><mrow class = "- topic/foreign "><mtext class = "- topic/foreign ">pos</mtext></mrow></msub><mo class = "- topic/foreign ">)</mo></mrow><mrow class = "- topic/foreign "><mn class = "- topic/foreign ">2</mn></mrow></msup><mo class = "- topic/foreign ">+</mo><msup class = "- topic/foreign "><mrow class = "- topic/foreign "><mo class = "- topic/foreign ">(</mo><mo class = "- topic/foreign ">Δ</mo><msub class = "- topic/foreign "><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">z</mi></mrow><mrow class = "- topic/foreign "><mtext class = "- topic/foreign ">pos</mtext></mrow></msub><mo class = "- topic/foreign ">)</mo></mrow><mrow class = "- topic/foreign "><mn class = "- topic/foreign ">2</mn></mrow></msup></mrow></msqrt></mrow></math></span>
as initial length.</p>
<p>
Thereby 
<span class = "ph inlineequation"><math altimg-valign = "8" altimg-height = "22" altimg-width = "223" class = "- topic/foreign "><mrow class = "- topic/foreign "><mo class = "- topic/foreign ">Δ</mo><msub class = "- topic/foreign "><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">n</mi></mrow><mrow class = "- topic/foreign "><mtext class = "- topic/foreign ">pos</mtext></mrow></msub><mo class = "- topic/foreign ">=</mo><mo class = "- topic/foreign ">Δ</mo><msub class = "- topic/foreign "><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">n</mi></mrow><mrow class = "- topic/foreign "><mtext class = "- topic/foreign ">pos</mtext><mn class = "- topic/foreign ">1</mn></mrow></msub><mo class = "- topic/foreign ">−</mo><mo class = "- topic/foreign ">Δ</mo><msub class = "- topic/foreign "><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">n</mi></mrow><mrow class = "- topic/foreign "><mtext class = "- topic/foreign ">pos</mtext><mn class = "- topic/foreign ">2</mn></mrow></msub></mrow></math></span>, 
for n = x,y,z and
<span class = "ph inlineequation"><math altimg-valign = "4" altimg-height = "18" altimg-width = "176" class = "- topic/foreign "><mrow class = "- topic/foreign "><mo class = "- topic/foreign ">Δ</mo><msub class = "- topic/foreign "><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">u</mi></mrow><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">n</mi></mrow></msub><mo class = "- topic/foreign ">=</mo><mo class = "- topic/foreign ">Δ</mo><msub class = "- topic/foreign "><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">u</mi></mrow><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">n</mi><mn class = "- topic/foreign ">1</mn></mrow></msub><mo class = "- topic/foreign ">−</mo><mo class = "- topic/foreign ">Δ</mo><msub class = "- topic/foreign "><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">u</mi></mrow><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">n</mi><mn class = "- topic/foreign ">2</mn></mrow></msub></mrow></math></span>, 
for n = x,y,z, where pos1 and pos2
are the coordinates of the nodes and u the displacements. The DRESP can
also be negative and gives the stretch between two nodes (that is, the difference
between the two notes in deformed and undeformed configuration). </p>
</td>
</tr>
</tbody></table>
</li>

<li class = "li">
<code class = "ph codeph">GROUP_OPER</code> is default <code class = "ph codeph">GROUP_OPER = MAX</code>.</li>
<li class = "li">
A node group (<code class = "ph codeph">ND_GROUP</code>) must be applied in the
<code class = "ph codeph">DRESP</code> when more than one node is required.</li>
<li class = "li">
Maximal 5000 <code class = "ph codeph">DRESP</code>s can be defined. Therefore, the
maximal number of nodes for <code class = "ph codeph">GROUP_OPER = MAX</code> is 5000
or less as in this case one design response is created for each group
member.</li>
<li class = "li">
If possible, define design responses for displacements for single
nodes (allows better control). Often 1 representative node is sufficient
for the task.</li>
<li class = "li">
The maximal number of nodes for <code class = "ph codeph">GROUP_OPER = SUM</code>
us unlimited.</li>
<li class = "li">
Design responses combined using <code class = "ph codeph">VAR_OPER</code> should
refer to the same group.</li>
</ol>
</div>

<div class = "section" id = "tso-c-usr-terms-combTermDrespSens__tso-c-usr-terms-combTermDrespSens-reacForce"><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">Reaction Forces</h2>

<table class = "table" id = "tso-c-usr-terms-combTermDrespSens__xx677200"><caption/><colgroup><col/><col/><col/></colgroup><thead class = "thead">
<tr class = "row">
<th class = "entry" id = "tso-c-usr-terms-combTermDrespSens__xx677200__entry__1">
<p>TYPE</p>
<p>The allowable types for </p>
<p>reaction forces</p>
</th>
<th class = "entry" id = "tso-c-usr-terms-combTermDrespSens__xx677200__entry__2">
<p>GROUP_OPER</p>
<p>The allowable definition types for reaction forces</p>
</th>
<th class = "entry" id = "tso-c-usr-terms-combTermDrespSens__xx677200__entry__3">
<p>VAR_OPER</p>
<p>The allowable operators for reaction forces</p>
</th>
</tr>
</thead><tbody class = "tbody">
<tr class = "row">
<td class = "entry" headers = "tso-c-usr-terms-combTermDrespSens__xx677200__entry__1">
<p>REACTION_FORCE_X</p>
<p>REACTION_FORCE_Y</p>
<p>REACTION_FORCE_Z</p>
<p>REACTION_MOMENT_X</p>
<p>REACTION_MOMENT_Y</p>
<p>REACTION_MOMENT_Z</p>
</td>
<td class = "entry" headers = "tso-c-usr-terms-combTermDrespSens__xx677200__entry__2">
<p>MAX</p>
<p>MIN</p>
<p>SUM</p>
</td>
<td class = "entry" headers = "tso-c-usr-terms-combTermDrespSens__xx677200__entry__3">
<p>SUB</p>
<p>SUB_ABS</p>
<p>COMBINE</p>
<p>ADD_ABS</p>
</td>
</tr>
<tr class = "row">
<td class = "entry" headers = "tso-c-usr-terms-combTermDrespSens__xx677200__entry__1">
<p>REACTION_FORCE_ABS</p>
<p>REACTION_MOMENT_ABS</p>
</td>
<td class = "entry" headers = "tso-c-usr-terms-combTermDrespSens__xx677200__entry__2">
<p>MAX</p>
</td>
<td class = "entry" headers = "tso-c-usr-terms-combTermDrespSens__xx677200__entry__3">
<p>SUB_ABS*</p>
</td>
</tr>
<tr class = "row">
<td class = "entry" headers = "tso-c-usr-terms-combTermDrespSens__xx677200__entry__1">
<p>REACTION_FORCE_X_ABS</p>
<p>REACTION_FORCE_Y_ABS</p>
<p>REACTION_FORCE_Z_ABS</p>
<p>REACTION_MOMENT_X_ABS</p>
<p>REACTION_MOMENT_Y_ABS</p>
<p>REACTION_MOMENT_Z_ABS</p>
</td>
<td class = "entry" headers = "tso-c-usr-terms-combTermDrespSens__xx677200__entry__2">
<p>MAX</p>
<p>MIN</p>
</td>
<td class = "entry" headers = "tso-c-usr-terms-combTermDrespSens__xx677200__entry__3">
<p>---</p>
</td>
</tr>
<tr class = "row">
<td class = "entry" headers = "tso-c-usr-terms-combTermDrespSens__xx677200__entry__1 tso-c-usr-terms-combTermDrespSens__xx677200__entry__2 tso-c-usr-terms-combTermDrespSens__xx677200__entry__3" colspan = "3">
<p>* For these, <code class = "ph codeph">VAR_A</code>
and <code class = "ph codeph">VAR_B</code> must have the same <code class = "ph codeph">DRESP</code> type.</p>
<p>For example, the <code class = "ph codeph">DRESP</code> type for <code class = "ph codeph">VAR_A</code>
and <code class = "ph codeph">VAR_B</code> is</p>
<p><code class = "ph codeph">TYPE = REACTION_FORCE_ABS</code> yielding</p>
<p><span class = "ph inlineequation"><math altimg-valign = "9" altimg-height = "33" altimg-width = "413" class = "- topic/foreign "><mrow class = "- topic/foreign "><mo class = "- topic/foreign ">Δ</mo><mi class = "- topic/foreign ">R</mi><mo class = "- topic/foreign ">=</mo><msqrt class = "- topic/foreign "><mrow class = "- topic/foreign "><msup class = "- topic/foreign "><mrow 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 ">x</mi><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 ">x</mi><mn class = "- topic/foreign ">2</mn></mrow></msub><mo class = "- topic/foreign ">)</mo></mrow></mrow><mrow class = "- topic/foreign "><mn class = "- topic/foreign ">2</mn></mrow></msup><mo class = "- topic/foreign ">+</mo><msup class = "- topic/foreign "><mrow 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 ">y</mi><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 ">y</mi><mn class = "- topic/foreign ">2</mn></mrow></msub><mo class = "- topic/foreign ">)</mo></mrow></mrow><mrow class = "- topic/foreign "><mn class = "- topic/foreign ">2</mn></mrow></msup><mo class = "- topic/foreign ">+</mo><msup class = "- topic/foreign "><mrow 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 ">z</mi><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 ">z</mi><mn class = "- topic/foreign ">2</mn></mrow></msub><mo class = "- topic/foreign ">)</mo></mrow></mrow><mrow class = "- topic/foreign "><mn class = "- topic/foreign ">2</mn></mrow></msup></mrow></msqrt></mrow></math></span>
</p>
</td>
</tr>
</tbody></table>

</div>

<div class = "section" id = "tso-c-usr-terms-combTermDrespSens__tso-sb-usr-terms-combTermDrespSens-intForce"><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">Internal Forces</h2>

<table class = "table" id = "tso-c-usr-terms-combTermDrespSens__xx677254"><caption/><colgroup><col/><col/><col/></colgroup><thead class = "thead">
<tr class = "row">
<th class = "entry" id = "tso-c-usr-terms-combTermDrespSens__xx677254__entry__1">
<p>TYPE</p>
<p>The allowable types for </p>
<p>internal forces</p>
</th>
<th class = "entry" id = "tso-c-usr-terms-combTermDrespSens__xx677254__entry__2">
<p>GROUP_OPER</p>
<p>The allowable definition types for internal forces</p>
</th>
<th class = "entry" id = "tso-c-usr-terms-combTermDrespSens__xx677254__entry__3">
<p>VAR_OPER</p>
<p>The allowable operators for internal forces</p>
</th>
</tr>
</thead><tbody class = "tbody"> 
<tr class = "row">
<td class = "entry" headers = "tso-c-usr-terms-combTermDrespSens__xx677254__entry__1">
<p>INTERNAL_FORCE_X</p>
<p>INTERNAL_FORCE_Y</p>
<p>INTERNAL_FORCE_Z</p>
<p>INTERNAL_MOMENT_X</p>
<p>INTERNAL_MOMENT_Y</p>
<p>INTERNAL_MOMENT_Z</p>
</td>
<td class = "entry" headers = "tso-c-usr-terms-combTermDrespSens__xx677254__entry__2">
<p>MAX</p>
<p>MIN</p>
<p>SUM</p>
</td>
<td class = "entry" headers = "tso-c-usr-terms-combTermDrespSens__xx677254__entry__3">
<p>SUB</p>
<p>SUB_ABS</p>
<p>COMBINE</p>
<p>ADD_ABS</p>
</td>
</tr>
<tr class = "row">
<td class = "entry" headers = "tso-c-usr-terms-combTermDrespSens__xx677254__entry__1">
<p>INTERNAL_FORCE_ABS </p>
<p>INTERNAL_MOMENT_ABS</p>
</td>
<td class = "entry" headers = "tso-c-usr-terms-combTermDrespSens__xx677254__entry__2">
<p>MAX</p>
</td>
<td class = "entry" headers = "tso-c-usr-terms-combTermDrespSens__xx677254__entry__3">
<p>SUB_ABS*</p>
</td>
</tr>
<tr class = "row">
<td class = "entry" headers = "tso-c-usr-terms-combTermDrespSens__xx677254__entry__1">
<p>INTERNAL_FORCE_X_ABS </p>
<p>INTERNAL_FORCE_Y_ABS</p>
<p>INTERNAL_FORCE_Z_ABS</p>
<p>INTERNAL_MOMENT_X_ABS</p>
<p>INTERNAL_MOMENT_Y_ABS</p>
<p>INTERNAL_MOMENT_Z_ABS</p>
</td>
<td class = "entry" headers = "tso-c-usr-terms-combTermDrespSens__xx677254__entry__2">
<p>MAX</p>
<p>MIN</p>
</td>
<td class = "entry" headers = "tso-c-usr-terms-combTermDrespSens__xx677254__entry__3">
<p>---</p>
</td>
</tr>
<tr class = "row">
<td class = "entry" headers = "tso-c-usr-terms-combTermDrespSens__xx677254__entry__1 tso-c-usr-terms-combTermDrespSens__xx677254__entry__2 tso-c-usr-terms-combTermDrespSens__xx677254__entry__3" colspan = "3">
<p>* For these, <code class = "ph codeph">VAR_A</code>
and <code class = "ph codeph">VAR_B</code> must have the same <code class = "ph codeph">DRESP</code> type.</p>
<p>For example, The <code class = "ph codeph">DRESP</code> type for <code class = "ph codeph">VAR_A</code> and <code class = "ph codeph">VAR_B</code> is</p>
<p><code class = "ph codeph">TYPE = INTERNAL_FORCE_ABS</code> yielding</p>
<p>
<span class = "ph inlineequation"><math altimg-valign = "9" altimg-height = "33" altimg-width = "413" class = "- topic/foreign "><mrow class = "- topic/foreign "><mo class = "- topic/foreign ">Δ</mo><mi class = "- topic/foreign ">R</mi><mo class = "- topic/foreign ">=</mo><msqrt class = "- topic/foreign "><mrow class = "- topic/foreign "><msup class = "- topic/foreign "><mrow class = "- topic/foreign "><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 ">x</mi><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 ">F</mi></mrow><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">x</mi><mn class = "- topic/foreign ">2</mn></mrow></msub><mo class = "- topic/foreign ">)</mo></mrow><mrow class = "- topic/foreign "><mn class = "- topic/foreign ">2</mn></mrow></msup><mo class = "- topic/foreign ">+</mo><msup class = "- topic/foreign "><mrow class = "- topic/foreign "><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 ">y</mi><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 ">F</mi></mrow><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">y</mi><mn class = "- topic/foreign ">2</mn></mrow></msub><mo class = "- topic/foreign ">)</mo></mrow><mrow class = "- topic/foreign "><mn class = "- topic/foreign ">2</mn></mrow></msup><mo class = "- topic/foreign ">+</mo><msup class = "- topic/foreign "><mrow class = "- topic/foreign "><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 ">z</mi><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 ">F</mi></mrow><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">z</mi><mn class = "- topic/foreign ">2</mn></mrow></msub><mo class = "- topic/foreign ">)</mo></mrow><mrow class = "- topic/foreign "><mn class = "- topic/foreign ">2</mn></mrow></msup></mrow></msqrt></mrow></math></span>
</p>
</td>
</tr>
</tbody></table>

</div>

<div class = "section" id = "tso-c-usr-terms-combTermDrespSens__tso-sb-usr-terms-combTermDrespSens-modalEigenfreq"><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">Modal Eigenfrequencies</h2>

<table class = "table" id = "tso-c-usr-terms-combTermDrespSens__xx677369"><caption/><colgroup><col/><col/><col/></colgroup><thead class = "thead">
<tr class = "row">
<th class = "entry" id = "tso-c-usr-terms-combTermDrespSens__xx677369__entry__1">
<p>TYPE</p>
</th>
<th class = "entry" id = "tso-c-usr-terms-combTermDrespSens__xx677369__entry__2">
<p>GROUP_OPER</p>
<p>The allowable definition types</p>
</th>
<th class = "entry" id = "tso-c-usr-terms-combTermDrespSens__xx677369__entry__3">
<p>VAR_OPER</p>
<p>The allowable operators</p>
</th>
</tr>
</thead><tbody class = "tbody">
<tr class = "row">
<td class = "entry" headers = "tso-c-usr-terms-combTermDrespSens__xx677369__entry__1">
<p>DYN_FREQ</p>
</td>
<td class = "entry" headers = "tso-c-usr-terms-combTermDrespSens__xx677369__entry__2">
<p>MAX</p>
<p>MIN</p>
</td>
<td class = "entry" headers = "tso-c-usr-terms-combTermDrespSens__xx677369__entry__3">
<p>SUB</p>
<p>SUB_ABS</p>
<p>COMBINE</p>
<p>KSO</p>
</td>
</tr>
</tbody></table>
<p>Note that with the operator <code class = "ph codeph">KSO</code> the Kreisselmeier-Steinhauser formulation can be constructed from single eigenfrequency DRESPs in context of sensitivity-based topology and sizing optimization. It is given by
<span class = "ph inlineequation"><math altimg-valign = "11" altimg-height = "33" altimg-width = "137" class = "- topic/foreign "><mfenced open = "" close = "" separators = " " class = "- topic/foreign "><mrow class = "- topic/foreign "><mo class = "- topic/foreign ">-</mo><mfrac class = "- topic/foreign "><mrow class = "- topic/foreign "><mn class = "- topic/foreign ">1</mn></mrow><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">k</mi></mrow></mfrac><mo class = "- topic/foreign ">ln</mo><mfenced open = "(" close = ")" separators = "" class = "- topic/foreign "><munder class = "- topic/foreign "><mo class = "- topic/foreign ">∑</mo><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">j</mi></mrow></munder><msup class = "- topic/foreign "><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">e</mi></mrow><mrow class = "- topic/foreign "><mo class = "- topic/foreign ">−</mo><mi class = "- topic/foreign ">k</mi><msub class = "- topic/foreign "><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">f</mi></mrow><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">j</mi></mrow></msub></mrow></msup></mfenced></mrow></mfenced></math></span>.
</p>

</div>

<div class = "section" id = "tso-c-usr-terms-combTermDrespSens__tso-sb-usr-terms-combTermDrespSens-freqSpecResp"><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">Frequency Spectrum Responses</h2>

<table class = "table" id = "tso-c-usr-terms-combTermDrespSens__xx677308"><caption/><colgroup><col/><col/><col/></colgroup><thead class = "thead">
<tr class = "row">
<th class = "entry" id = "tso-c-usr-terms-combTermDrespSens__xx677308__entry__1">
<p>TYPE</p>
<p>The allowable types for </p>
<p>frequency response</p>
</th>
<th class = "entry" id = "tso-c-usr-terms-combTermDrespSens__xx677308__entry__2">
<p>GROUP_OPER</p>
<p>The allowable definition types for frequency response</p>
</th>
<th class = "entry" id = "tso-c-usr-terms-combTermDrespSens__xx677308__entry__3">
<p>VAR_OPER</p>
<p>The allowable operators for frequency response</p>
</th>
</tr>
</thead><tbody class = "tbody">
<tr class = "row">
<td class = "entry" headers = "tso-c-usr-terms-combTermDrespSens__xx677308__entry__1">
<p>FS_DISP_X_ABS</p>
<p>FS_DISP_Y_ABS</p>
<p>FS_DISP_Z_ABS</p>
<p>FS_DISP_ABS</p>
</td>
<td class = "entry" headers = "tso-c-usr-terms-combTermDrespSens__xx677308__entry__2">
<p>MAX</p>
<p>MIN</p>
</td>
<td class = "entry" headers = "tso-c-usr-terms-combTermDrespSens__xx677308__entry__3">
<p>SUB_ABS*</p>
</td>
</tr>
<tr class = "row">
<td class = "entry" headers = "tso-c-usr-terms-combTermDrespSens__xx677308__entry__1">
<p>FS_PHASE_X</p>
<p>FS_PHASE_Y</p>
<p>FS_PHASE_Z</p>
<p>FS_VELOCITY_X</p>
<p>FS_VELOCITY_Y</p>
<p>FS_VELOCITY_Z</p>
<p>FS_ACCEL_X</p>
<p>FS_ACCEL_Y</p>
<p>FS_ACCEL_Z</p>
</td>
<td class = "entry" headers = "tso-c-usr-terms-combTermDrespSens__xx677308__entry__2">
<p>MAX</p>
<p>MIN</p>
</td>
<td class = "entry" headers = "tso-c-usr-terms-combTermDrespSens__xx677308__entry__3">
<p>---</p>
</td>
</tr>
<tr class = "row">
<td class = "entry" headers = "tso-c-usr-terms-combTermDrespSens__xx677308__entry__1 tso-c-usr-terms-combTermDrespSens__xx677308__entry__2 tso-c-usr-terms-combTermDrespSens__xx677308__entry__3" colspan = "3">
<p>* For these, <code class = "ph codeph">VAR_A</code>
and <code class = "ph codeph">VAR_B</code> must have the same <code class = "ph codeph">DRESP</code>
type.</p>
<p>For example, the <code class = "ph codeph">DRESP</code> type for <code class = "ph codeph">VAR_A</code>
and <code class = "ph codeph">VAR_B</code> is <code class = "ph codeph">TYPE = FS_DISP_X_ABS</code></p>
<p>yielding</p>
<p><span class = "ph inlineequation"><math altimg-valign = "9" altimg-height = "33" altimg-width = "339" class = "- topic/foreign "><mrow class = "- topic/foreign "><mo class = "- topic/foreign ">Δ</mo><msub class = "- topic/foreign "><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">A</mi></mrow><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">x</mi></mrow></msub><mo class = "- topic/foreign ">=</mo><msqrt class = "- topic/foreign "><mrow class = "- topic/foreign "><msup 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 ">R</mi><mo class = "- topic/foreign ">,</mo><mi class = "- topic/foreign ">x</mi><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 ">R</mi><mo class = "- topic/foreign ">,</mo><mi class = "- topic/foreign ">x</mi><mn class = "- topic/foreign ">2</mn></mrow></msub><mo class = "- topic/foreign ">)</mo></mrow><mrow class = "- topic/foreign "><mn class = "- topic/foreign ">2</mn></mrow></msup><mo class = "- topic/foreign ">+</mo><msup 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><mi class = "- topic/foreign ">y</mi><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><mi class = "- topic/foreign ">y</mi><mn class = "- topic/foreign ">2</mn></mrow></msub><mo class = "- topic/foreign ">)</mo></mrow><mrow class = "- topic/foreign "><mn class = "- topic/foreign ">2</mn></mrow></msup></mrow></msqrt></mrow></math></span>
</p>
</td>
</tr>
</tbody></table>

</div>

<div class = "section" id = "tso-c-usr-terms-combTermDrespSens__tso-c-usr-terms-combTermDrespSens-temp"><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"><span class = "ph">Temperature</span></h2>

<table class = "table" id = "tso-c-usr-terms-combTermDrespSens__xx932278"><caption/><colgroup><col/><col/><col/></colgroup><thead class = "thead">
<tr class = "row">
<th class = "entry" id = "tso-c-usr-terms-combTermDrespSens__xx932278__entry__1">
<p>TYPE</p>
<p>The allowable types for thermal analysis</p>
</th>
<th class = "entry" id = "tso-c-usr-terms-combTermDrespSens__xx932278__entry__2">
<p>GROUP_OPER</p>
<p>The allowable definition types for thermal analysis</p>
</th>
<th class = "entry" id = "tso-c-usr-terms-combTermDrespSens__xx932278__entry__3">
<p>VAR_OPER</p>
<p>The allowable operators for thermal analysis</p>
</th>
</tr>
</thead><tbody class = "tbody">
<tr class = "row">
<td class = "entry" headers = "tso-c-usr-terms-combTermDrespSens__xx932278__entry__1">
<p>TEMPERATURE</p>
<p>REACTION_HFLUX</p>
<p>INTERNAL_HFLUX</p>


</td>
<td class = "entry" headers = "tso-c-usr-terms-combTermDrespSens__xx932278__entry__2">
<p>MAX</p>
<p>SUM</p>
</td>
<td class = "entry" headers = "tso-c-usr-terms-combTermDrespSens__xx932278__entry__3">
<p>SUB</p>
<p>SUB_ABS</p>
<p>COMBINE</p>
</td>
</tr>
</tbody></table>

<p>
A maximum of 5000 Design response definitions (DRESP)
is allowed.</p>


</div>

</div>

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