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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 Internal Force</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 = "header"><p class = "abstract">
<span class = "shortdesc">This section describes the theory of internal forces.</span>

</p>
<ul><li><a href = "#tso-c-usr-terms-intForceOvw__tso-c-usr-terms-intForceOvw-anaType" id = "toc_rg" title = "">Analysis Types: Static Linear or Nonlinear Analysis</a></li></ul>
</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 = "This chapter explains group operations for internal force(s)." href = "tso-c-usr-terms-combTermsGroupOperIntForces.htm#tso-c-usr-terms-combTermsGroupOperIntForces">Group Operations for Internal Forces</a></td></tr></table></td></tr></table>




<div class = "body conbody">
<table class = "table" id = "tso-c-usr-terms-intForceOvw__xx932482"><caption/><colgroup><col/><col/></colgroup><thead class = "thead">
<tr class = "row">
<th class = "entry" id = "tso-c-usr-terms-intForceOvw__xx932482__entry__1"><p>Parameter Name</p></th>
<th class = "entry" id = "tso-c-usr-terms-intForceOvw__xx932482__entry__2"><p>Formula</p></th>
</tr>
</thead><tbody class = "tbody">
<tr class = "row">
<td class = "entry" headers = "tso-c-usr-terms-intForceOvw__xx932482__entry__1"><p>INTERNAL_FORCE_ABS</p></td>
<td class = "entry" headers = "tso-c-usr-terms-intForceOvw__xx932482__entry__2"><span class = "ph inlineequation"><math class = "- topic/foreign "><mrow class = "- topic/foreign "><mstyle mathvariant = "normal" class = "- topic/foreign "><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">F</mi></mrow></mstyle><mo class = "- topic/foreign ">=</mo><mrow class = "- topic/foreign "/><mrow class = "- topic/foreign "><mstyle displaystyle = "false" class = "- topic/foreign "><mrow class = "- topic/foreign "><munder class = "- topic/foreign "><mo class = "- topic/foreign ">∑</mo><mrow class = "- topic/foreign "/></munder><mrow class = "- topic/foreign "><mo class = "- topic/foreign ">|</mo><mstyle mathvariant = "normal" class = "- topic/foreign "><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></mstyle><mo class = "- topic/foreign ">|</mo></mrow></mrow></mstyle></mrow></mrow></math></span></td>
</tr>
<tr class = "row">
<td class = "entry" headers = "tso-c-usr-terms-intForceOvw__xx932482__entry__1"><p>INTERNAL_FORCE_X, INTERNAL_FORCE_Y, INTERNAL_FORCE_Z</p></td>
<td class = "entry" headers = "tso-c-usr-terms-intForceOvw__xx932482__entry__2"><span class = "ph inlineequation"><math class = "- topic/foreign "><mrow class = "- topic/foreign "><mstyle mathvariant = "normal" class = "- topic/foreign "><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">F</mi></mrow></mstyle><mo class = "- topic/foreign ">=</mo><mrow class = "- topic/foreign "/><mrow class = "- topic/foreign "><mstyle displaystyle = "false" class = "- topic/foreign "><mrow class = "- topic/foreign "><munder class = "- topic/foreign "><mrow class = "- topic/foreign "><mo class = "- topic/foreign ">∑</mo></mrow><mrow class = "- topic/foreign "/></munder><mrow class = "- topic/foreign "><mstyle mathvariant = "normal" class = "- topic/foreign "><mrow class = "- topic/foreign "><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></mstyle></mrow></mrow></mstyle></mrow></mrow></math></span></td>
</tr>
<tr class = "row">
<td class = "entry" headers = "tso-c-usr-terms-intForceOvw__xx932482__entry__1"><p>INTERNAL_FORCE_X_ABS, INTERNAL_FORCE_Y_ABS, INTERNAL_FORCE_Z_ABS</p></td>
<td class = "entry" headers = "tso-c-usr-terms-intForceOvw__xx932482__entry__2"><span class = "ph inlineequation"><math class = "- topic/foreign "><mrow class = "- topic/foreign "><mstyle mathvariant = "normal" class = "- topic/foreign "><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">F</mi></mrow></mstyle><mo class = "- topic/foreign ">=</mo><mrow class = "- topic/foreign "/><mrow class = "- topic/foreign "><mstyle displaystyle = "false" class = "- topic/foreign "><mrow class = "- topic/foreign "><munder class = "- topic/foreign "><mo class = "- topic/foreign ">∑</mo><mrow class = "- topic/foreign "/></munder><mrow class = "- topic/foreign "><mo class = "- topic/foreign ">|</mo><mstyle mathvariant = "normal" class = "- topic/foreign "><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></mstyle><mo class = "- topic/foreign ">|</mo></mrow></mrow></mstyle></mrow></mrow></math></span></td>
</tr>
<tr class = "row">
<td class = "entry" headers = "tso-c-usr-terms-intForceOvw__xx932482__entry__1"><p>INTERNAL_MOMENT_ABS</p></td>
<td class = "entry" headers = "tso-c-usr-terms-intForceOvw__xx932482__entry__2"><span class = "ph inlineequation"><math class = "- topic/foreign "><mrow class = "- topic/foreign "><mstyle mathvariant = "normal" class = "- topic/foreign "><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">F</mi></mrow></mstyle><mo class = "- topic/foreign ">=</mo><mrow class = "- topic/foreign "/><mrow class = "- topic/foreign "><mstyle displaystyle = "false" class = "- topic/foreign "><mrow class = "- topic/foreign "><munder class = "- topic/foreign "><mo class = "- topic/foreign ">∑</mo><mrow class = "- topic/foreign "/></munder><mrow class = "- topic/foreign "><mo class = "- topic/foreign ">|</mo><mstyle mathvariant = "normal" class = "- topic/foreign "><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></mstyle><mo class = "- topic/foreign ">|</mo></mrow></mrow></mstyle></mrow></mrow></math></span></td>
</tr>
<tr class = "row">
<td class = "entry" headers = "tso-c-usr-terms-intForceOvw__xx932482__entry__1"><p>INTERNAL_MOMENT_X, INTERNAL_MOMENT_Y, INTERNAL_MOMENT_Z</p></td>
<td class = "entry" headers = "tso-c-usr-terms-intForceOvw__xx932482__entry__2"><span class = "ph inlineequation"><math class = "- topic/foreign "><mrow class = "- topic/foreign "><mstyle mathvariant = "normal" class = "- topic/foreign "><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">F</mi></mrow></mstyle><mo class = "- topic/foreign ">=</mo><mrow class = "- topic/foreign "/><mrow class = "- topic/foreign "><mstyle displaystyle = "false" class = "- topic/foreign "><mrow class = "- topic/foreign "><munder class = "- topic/foreign "><mrow class = "- topic/foreign "><mo class = "- topic/foreign ">∑</mo></mrow><mrow class = "- topic/foreign "/></munder><mrow class = "- topic/foreign "><mstyle mathvariant = "normal" class = "- topic/foreign "><mrow class = "- topic/foreign "><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></mstyle></mrow></mrow></mstyle></mrow></mrow></math></span></td>
</tr>
<tr class = "row">
<td class = "entry" headers = "tso-c-usr-terms-intForceOvw__xx932482__entry__1"><p>INTERNAL_MOMENT_X_ABS, INTERNAL_MOMENT_Y_ABS, INTERNAL_MOMENT_Z_ABS</p></td>
<td class = "entry" headers = "tso-c-usr-terms-intForceOvw__xx932482__entry__2"><span class = "ph inlineequation"><math class = "- topic/foreign "><mrow class = "- topic/foreign "><mstyle mathvariant = "normal" class = "- topic/foreign "><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">F</mi></mrow></mstyle><mo class = "- topic/foreign ">=</mo><mrow class = "- topic/foreign "/><mrow class = "- topic/foreign "><mstyle displaystyle = "false" class = "- topic/foreign "><mrow class = "- topic/foreign "><munder class = "- topic/foreign "><mo class = "- topic/foreign ">∑</mo><mrow class = "- topic/foreign "/></munder><mrow class = "- topic/foreign "><mo class = "- topic/foreign ">|</mo><mstyle mathvariant = "normal" class = "- topic/foreign "><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></mstyle><mo class = "- topic/foreign ">|</mo></mrow></mrow></mstyle></mrow></mrow></math></span></td>
</tr>
</tbody></table>

<p>For the elements e attached to the nodes i.</p>
<div class = "section" id = "tso-c-usr-terms-intForceOvw__tso-c-usr-terms-intForceOvw-anaType"><h2 class = "title sectiontitle">Analysis Types: Static Linear or Nonlinear Analysis</h2>

<table class = "table" id = "tso-c-usr-terms-intForceOvw__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 internal 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-intForceOvw__xx932539"><caption/><colgroup><col/><col/><col/><col/><col/></colgroup><thead class = "thead">
<tr class = "row">
<th class = "entry" id = "tso-c-usr-terms-intForceOvw__xx932539__entry__1"/>
<th class = "entry" id = "tso-c-usr-terms-intForceOvw__xx932539__entry__2"><p>TOPO</p></th>
<th class = "entry" id = "tso-c-usr-terms-intForceOvw__xx932539__entry__3"><p>SHAPE</p></th>
<th class = "entry" id = "tso-c-usr-terms-intForceOvw__xx932539__entry__4"><p>BEAD</p></th>
<th class = "entry" id = "tso-c-usr-terms-intForceOvw__xx932539__entry__5"><p>SIZING</p></th>
</tr>
</thead><tbody class = "tbody">
<tr class = "row">
<td class = "entry" headers = "tso-c-usr-terms-intForceOvw__xx932539__entry__1"><p>OBJ_FUNC</p></td>
<td class = "entry" headers = "tso-c-usr-terms-intForceOvw__xx932539__entry__2"><p>S</p></td>
<td class = "entry" headers = "tso-c-usr-terms-intForceOvw__xx932539__entry__3"><p>S</p></td>
<td class = "entry" headers = "tso-c-usr-terms-intForceOvw__xx932539__entry__4"><p>S</p></td>
<td class = "entry" headers = "tso-c-usr-terms-intForceOvw__xx932539__entry__5"><p>S</p></td>
</tr>
<tr class = "row">
<td class = "entry" headers = "tso-c-usr-terms-intForceOvw__xx932539__entry__1"><p>CONSTRAINT</p></td>
<td class = "entry" headers = "tso-c-usr-terms-intForceOvw__xx932539__entry__2"><p>S</p></td>
<td class = "entry" headers = "tso-c-usr-terms-intForceOvw__xx932539__entry__3"><p>S</p></td>
<td class = "entry" headers = "tso-c-usr-terms-intForceOvw__xx932539__entry__4"><p>S</p></td>
<td class = "entry" headers = "tso-c-usr-terms-intForceOvw__xx932539__entry__5"><p>S</p></td>
</tr>
</tbody></table>

<p>The internal forces and the internal moments can be defined as a <code class = "ph codeph">DRESP</code>
(design response) in the sensitivity-based optimization approaches.
</p>
<p>The internal forces as <code class = "ph codeph">DRESP</code>s are supported for <span class = "ph">Abaqus</span>, <span class = "ph">ANSYS®</span> and <span class = "ph">MSC Nastran®</span>. The following figure shows the definition of internal forces through nodes and elements. On
    the left the internal axial forces of a bar or beam is defined by using only one node and one
    element. On the right side, the internal axial forces of a continuum element are defined by
    summing up the forces in axial direction using a node and an element group. </p>
<table class = "table" id = "tso-c-usr-terms-intForceOvw__xx660959"><caption/><colgroup><col/></colgroup><tbody class = "tbody">
<tr class = "row">
<td class = "entry"><br/><img class = "image" id = "tso-c-usr-terms-intForceOvw__image_BB408584DC0B44F7856747303730523D" src = "../TsoUserImages/terms_reac_explain.png" width = "568" height = "241"/><br/></td>
</tr>
</tbody></table>

<p> As previously shown, the internal forces are defined by nodes and
elements. Meaning that the design response is defined in the following
way:</p>
<pre class = "codeblock">
<code class = "ph codeph">
DRESP
 ID_NAME = .....
 DEF_TYPE = SYSTEM
<span class = "ph uicontrol"> TYPE</span> = .....
 CS_DEF = .....
<span class = "ph uicontrol"> GROUP_OPER</span> = MAX  or  SUM
 ND_GROUP = .....or use the NODE-definition
 NODE = .....or use the ND_GROUP-definition
 EL_GROUP = .....or use the ELEM-definition
 ELEM = .....or use the ELEM_GROUP-definition
 LC_SET = .....
END_
</code></pre>
<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-intForceOvw__ol_44F588E58D9742A4B15FDD8B38955011">
<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>
<li class = "li">Internal forces are only supported for elements having
       node numbers. If the element is not defined by nodes (for example, some weld element), the
       internal forces of this element cannot be applied in the optimization.</li>
<li class = "li">Both node(s) and element(s) always must be defined for internal
forces.</li>
<li class = "li">In addition, see the tables of supported element types
       for a list of elements that can be used for internal forces. </li>
<li class = "li">A reference coordinate system (<code class = "ph codeph">CS_REF</code>) cannot be
used for the internal force responses defined using <code class = "ph codeph">INTERNAL_FORCE_ABS</code>
and <code class = "ph codeph">INTERNAL_MOMENT_ABS</code>.</li>
<li class = "li">Internal forces are supported for <span class = "ph">Abaqus</span>,
<span class = "ph">ANSYS®</span>
and <span class = "ph">MSC Nastran®</span>.</li>

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

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