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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>Overview of Reaction Force</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 describes the theory of reaction forces.</span>

</p>
<ul><li><a href = "#tso-c-usr-terms-reactForceOvw__tso-c-usr-terms-reactForceOvw-anaType" id = "toc_rg" title = "">Analysis Types: Static Linear or Nonlinear Analysis</a></li></ul>
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<div class = "body conbody">
<table class = "table" id = "tso-c-usr-terms-reactForceOvw__xx927492"><caption/><colgroup><col/><col/></colgroup><thead class = "thead">
<tr class = "row">
<th class = "entry" id = "tso-c-usr-terms-reactForceOvw__xx927492__entry__1"><p>Parameter Name</p></th>
<th class = "entry" id = "tso-c-usr-terms-reactForceOvw__xx927492__entry__2"><p>Formula</p></th>
</tr>
</thead><tbody class = "tbody">
<tr class = "row">
<td class = "entry" headers = "tso-c-usr-terms-reactForceOvw__xx927492__entry__1"><p>REACTION_FORCE_ABS</p></td>
<td class = "entry" headers = "tso-c-usr-terms-reactForceOvw__xx927492__entry__2"><span class = "ph inlineequation"><math class = "- topic/foreign "><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">F</mi><mo class = "- topic/foreign ">=</mo><mo class = "- topic/foreign ">|</mo><mo class = "- topic/foreign ">∑</mo><msub class = "- topic/foreign "><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">K</mi></mrow><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">e</mi></mrow></msub><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></mrow></math></span></td>
</tr>
<tr class = "row">
<td class = "entry" headers = "tso-c-usr-terms-reactForceOvw__xx927492__entry__1"><p>REACTION_FORCE_X, REACTION_FORCE_Y, REACTION_FORCE_Z</p></td>
<td class = "entry" headers = "tso-c-usr-terms-reactForceOvw__xx927492__entry__2"><span class = "ph inlineequation"><math class = "- topic/foreign "><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">F</mi><mo class = "- topic/foreign ">=</mo><mo class = "- topic/foreign ">∑</mo><msub class = "- topic/foreign "><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">K</mi></mrow><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">e</mi></mrow></msub><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></mrow></math></span></td>
</tr>
<tr class = "row">
<td class = "entry" headers = "tso-c-usr-terms-reactForceOvw__xx927492__entry__1"><p>REACTION_FORCE_X_ABS, REACTION_FORCE_Y_ABS, REACTION_FORCE_Z_ABS</p></td>
<td class = "entry" headers = "tso-c-usr-terms-reactForceOvw__xx927492__entry__2"><span class = "ph inlineequation"><math class = "- topic/foreign "><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">F</mi><mo class = "- topic/foreign ">=</mo><mo class = "- topic/foreign ">|</mo><mo class = "- topic/foreign ">∑</mo><msub class = "- topic/foreign "><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">K</mi></mrow><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">e</mi></mrow></msub><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></mrow></math></span></td>
</tr>
<tr class = "row">
<td class = "entry" headers = "tso-c-usr-terms-reactForceOvw__xx927492__entry__1"><p>REACTION_MOMENT_ABS</p></td>
<td class = "entry" headers = "tso-c-usr-terms-reactForceOvw__xx927492__entry__2"><span class = "ph inlineequation"><math class = "- topic/foreign "><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">F</mi><mo class = "- topic/foreign ">=</mo><mo class = "- topic/foreign ">|</mo><mo class = "- topic/foreign ">∑</mo><msub class = "- topic/foreign "><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">K</mi></mrow><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">e</mi></mrow></msub><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></mrow></math></span></td>
</tr>
<tr class = "row">
<td class = "entry" headers = "tso-c-usr-terms-reactForceOvw__xx927492__entry__1"><p>REACTION_MOMENT_X, REACTION_MOMENT_Y, REACTION_MOMENT_Z</p></td>
<td class = "entry" headers = "tso-c-usr-terms-reactForceOvw__xx927492__entry__2"><span class = "ph inlineequation"><math class = "- topic/foreign "><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">F</mi><mo class = "- topic/foreign ">=</mo><mo class = "- topic/foreign ">∑</mo><msub class = "- topic/foreign "><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">K</mi></mrow><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">e</mi></mrow></msub><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></mrow></math></span></td>
</tr>
<tr class = "row">
<td class = "entry" headers = "tso-c-usr-terms-reactForceOvw__xx927492__entry__1"><p>REACTION_MOMENT_X_ABS, REACTION_MOMENT_Y_ABS, REACTION_MOMENT_Z_ABS</p></td>
<td class = "entry" headers = "tso-c-usr-terms-reactForceOvw__xx927492__entry__2"><span class = "ph inlineequation"><math class = "- topic/foreign "><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">F</mi><mo class = "- topic/foreign ">=</mo><mo class = "- topic/foreign ">∑</mo><msub class = "- topic/foreign "><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">K</mi></mrow><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">e</mi></mrow></msub><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></mrow></math></span></td>
</tr>
</tbody></table>

<p>Where e are the elements connected to the nodes i on supported DOFs.</p>
<div class = "section" id = "tso-c-usr-terms-reactForceOvw__tso-c-usr-terms-reactForceOvw-anaType"><h2 class = "title sectiontitle">Analysis Types: Static Linear or Nonlinear Analysis</h2>

<table class = "table" id = "tso-c-usr-terms-reactForceOvw__table_E11BB6BA8A504392B5DF84F2C0BA9397"><caption/><colgroup><col style = "width:100%"/></colgroup><tbody class = "tbody">
<tr class = "row"><td class = "entry"><span class = "ph inlineequation"><math class = "- topic/foreign "><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">K</mi><mi class = "- topic/foreign ">u</mi><mo class = "- topic/foreign ">=</mo><mi class = "- topic/foreign ">F</mi></mrow></math></span></td>
</tr>
</tbody></table>
<p> where K might be linear or nonlinear.</p>
<p>For reaction forces, the following table shows the allowed combinations between the strategy and
                the items <code class = "ph codeph">OBJ_FUNC</code> and <code class = "ph codeph">CONSTRAINT</code> with C for
                controller and S for sensitivity-based optimization.</p>
<table class = "table" id = "tso-c-usr-terms-reactForceOvw__xx927534"><caption/><colgroup><col/><col/><col/><col/><col/></colgroup><thead class = "thead">
<tr class = "row">
<th class = "entry" id = "tso-c-usr-terms-reactForceOvw__xx927534__entry__1"/>
<th class = "entry" id = "tso-c-usr-terms-reactForceOvw__xx927534__entry__2"><p>TOPO</p></th>
<th class = "entry" id = "tso-c-usr-terms-reactForceOvw__xx927534__entry__3"><p>SHAPE</p></th>
<th class = "entry" id = "tso-c-usr-terms-reactForceOvw__xx927534__entry__4"><p>BEAD</p></th>
<th class = "entry" id = "tso-c-usr-terms-reactForceOvw__xx927534__entry__5"><p>SIZING</p></th>
</tr>
</thead><tbody class = "tbody">
<tr class = "row">
<td class = "entry" headers = "tso-c-usr-terms-reactForceOvw__xx927534__entry__1"><p>OBJ_FUNC</p></td>
<td class = "entry" headers = "tso-c-usr-terms-reactForceOvw__xx927534__entry__2"><p>S</p></td>
<td class = "entry" headers = "tso-c-usr-terms-reactForceOvw__xx927534__entry__3"><p>S</p></td>
<td class = "entry" headers = "tso-c-usr-terms-reactForceOvw__xx927534__entry__4"><p>S</p></td>
<td class = "entry" headers = "tso-c-usr-terms-reactForceOvw__xx927534__entry__5"><p>S</p></td>
</tr>
<tr class = "row">
<td class = "entry" headers = "tso-c-usr-terms-reactForceOvw__xx927534__entry__1"><p>CONSTRAINT</p></td>
<td class = "entry" headers = "tso-c-usr-terms-reactForceOvw__xx927534__entry__2"><p>S</p></td>
<td class = "entry" headers = "tso-c-usr-terms-reactForceOvw__xx927534__entry__3"><p>S</p></td>
<td class = "entry" headers = "tso-c-usr-terms-reactForceOvw__xx927534__entry__4"><p>S</p></td>
<td class = "entry" headers = "tso-c-usr-terms-reactForceOvw__xx927534__entry__5"><p>S</p></td>
</tr>
</tbody></table>
<p><ul class = "ul">
<li class = "li">Differences between reaction forces can be defined using group operations.</li>
<li class = "li">Examples for combinations of reaction forces can be found in <a class = "xref" href = "tso-c-usr-terms-combTermsGroupOperReacForceMoment.htm" title = "This chapter explains group operations for reaction force(s) and moment(s) through the example of reaction forces.">Group Operations for Reaction Forces/Moments</a>.</li>
</ul></p>  

<table class = "Remark" id = "table132"><tr><td class = "Remark"><span class = "run-in.important">Important:
				</span><span class = "notecontent"><p><ul class = "ul" id = "tso-c-usr-terms-reactForceOvw__ol_758EBB65AC8247018F7F21BDD4B7DB28">
<li class = "li">The reaction forces and the reaction moments can only be defined as a <code class = "ph codeph">DRESP</code>
                            (design response) in the sensitivity-based optimization approaches.</li><li class = "li">A reference coordinate system (<code class = "ph codeph">CS_REF</code>) cannot be used
for the reaction force responses defined using <code class = "ph codeph">REACTION_FORCE_ABS</code>
and <code class = "ph codeph">REACTION_MOMENT_ABS</code>.</li>
<li class = "li">The reaction force, reaction moment, internal force and/or internal
moment in a given DOF of a node applied in the optimization formulation
must have stiffness in the DOF direction similar to the DOF direction
of the reaction force or internal force used in the optimization formulation.
Meaning that at least one of the elements surrounding the node must
have stiffness in the DOF direction similar to the reaction force or
internal force direction applied in the optimization formulation.  Hence,
this criterion is also physical meaningful since a structure having no
stiffness in a given direction will always have zero reaction force in
this direction. </li>


</ul></p></span></td></tr></table>

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