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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>Group Operations for Displacements</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 explains group operations for displacements.</span>

</p>
<p>This page discusses: </p><ul><li><a href = "#tso-c-usr-terms-combTermsGroupOperDispl__tso-c-usr-terms-combTermsGroupOperDispl-objFunc" id = "toc_rg" title = ""> Use in Objective Function</a></li><li><a href = "#tso-c-usr-terms-combTermsGroupOperDispl__tso-c-usr-terms-combTermsGroupOperDispl-constr" id = "toc_rg" title = "">Use in Constraints</a></li></ul>
</p></td></tr></table></td></tr></table>




<div class = "body conbody">
<p>The picture below shows a structure loaded at the nodes 15, 16 and
17. The y-displacement of these three nodes should be minimized or applied
in a set of constraints using <code class = "ph codeph">GROUP_OPER=MAX</code> or <code class = "ph codeph">GROUP_OPER=SUM</code>.
</p>
<table class = "table" id = "tso-c-usr-terms-combTermsGroupOperDispl__xx947848"><caption/><colgroup><col/></colgroup><tbody class = "tbody">
<tr class = "row">
<td class = "entry"><br/><img class = "image" id = "tso-c-usr-terms-combTermsGroupOperDispl__image_80132828CDDE4B0EB025BCCD2C94D48E" src = "../TsoUserImages/terms_node_force_dislpacement.png" width = "289" height = "197"/><br/></td>
</tr>
</tbody></table>

<div class = "section" id = "tso-c-usr-terms-combTermsGroupOperDispl__tso-c-usr-terms-combTermsGroupOperDispl-objFunc"><h2 class = "title sectiontitle"> Use in Objective Function</h2>

<p>Initially, a node group is defined containing the nodes 15, 16 and 17 (see figure above)
yielding:</p>
<pre class = "codeblock">
<code class = "ph codeph">
GROUP_DEF
 ID_NAME = DISP_NODES
 TYPE    = NODE
 FORMAT  = LIST
LIST_BEGIN
 15, 16, 17
END_
<span class = "ph uicontrol">GROUP_OPER = MAX</span>
</code></pre>
<p>Based on the node group a design response for the displacements in y-directions are defined
in a <code class = "ph codeph">DRESP</code> using <code class = "ph codeph">GROUP_OPER=MAX</code> yielding:</p>
<pre class = "codeblock">
<code class = "ph codeph">
DRESP
 ID_NAME    = DRESP_DISP_MAX
 DEF_TYPE   = SYSTEM
 TYPE       = DISP_Y
 LC_SET     = STATIC,1,
 ND_GROUP   =<var class = "keyword varname varname"> DISP_NODES</var>
 GROUP_OPER = MAX
END_
</code></pre>
<p>Internally, <span class = "ph">SIMULIA Tosca Structure</span> generates three <code class = "ph codeph">DRESP</code>s. One <code class = "ph codeph">DRESP</code> for the displacement
of node 15, one <code class = "ph codeph">DRESP</code> for the displacement of node 16 and one
<code class = "ph codeph">DRESP</code> for the displacement of node 17. </p>
<p>If one then applies the <code class = "ph codeph">DRESP</code> in the objective yielding: </p>
<pre class = "codeblock">
<code class = "ph codeph">
OBJ_FUNC
 ID_NAME = MIN_DISP_MAX
 DRESP   = DRESP_DISP_MAX
 TARGET  = MIN
END_
</code></pre>
<p><span class = "ph">SIMULIA Tosca Structure</span> then sums up the three displacements like the following:</p><table class = "table" id = "tso-c-usr-terms-combTermsGroupOperDispl__table_81BBE30CD9AA4E76B6D884FAF5CA67C7"><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 "><mtext class = "- topic/foreign ">minimize</mtext><mo class = "- topic/foreign ">⁡</mo><mrow class = "- topic/foreign "><mo class = "- topic/foreign ">{</mo><msub class = "- topic/foreign "><mrow class = "- topic/foreign "><mi mathvariant = "normal" class = "- topic/foreign ">Φ</mi></mrow><mrow class = "- topic/foreign "><mn class = "- topic/foreign ">0</mn></mrow></msub><mo class = "- topic/foreign ">}</mo></mrow><mo class = "- topic/foreign ">=</mo><mtext class = "- topic/foreign ">minimize</mtext><mo class = "- topic/foreign ">⁡</mo><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 "><mn class = "- topic/foreign ">15</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 "><mn class = "- topic/foreign ">16</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 "><mn class = "- topic/foreign ">17</mn></mrow></msub><mo class = "- topic/foreign ">}</mo></mrow></mrow></math></span></td>
</tr>
</tbody></table>
<p><span class = "ph uicontrol">Remark:</span> If you want to minimize the maximum of the three
displacements you need to define an objective function with target <code class = "ph codeph">MIN_MAX</code>
operating on three design responses (one for each node). </p>
<table class = "table" id = "tso-c-usr-terms-combTermsGroupOperDispl__table_34FDFE17737F4A4DA3CFB897C184302B"><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 "><mtext class = "- topic/foreign ">minimize</mtext><mrow class = "- topic/foreign "><mo class = "- topic/foreign ">{</mo><msub class = "- topic/foreign "><mrow class = "- topic/foreign "><mi mathvariant = "normal" class = "- topic/foreign ">Φ</mi></mrow><mrow class = "- topic/foreign "><mn class = "- topic/foreign ">0</mn></mrow></msub><mo class = "- topic/foreign ">}</mo></mrow><mo class = "- topic/foreign ">=</mo><mi class = "- topic/foreign ">max</mi><mfenced open = "{" close = "}" separators = ";" class = "- topic/foreign "><mrow class = "- topic/foreign "><msub class = "- topic/foreign "><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">u</mi></mrow><mrow class = "- topic/foreign "><mn class = "- topic/foreign ">15</mn></mrow></msub></mrow><mrow class = "- topic/foreign "><msub class = "- topic/foreign "><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">u</mi></mrow><mrow class = "- topic/foreign "><mn class = "- topic/foreign ">16</mn></mrow></msub></mrow><mrow class = "- topic/foreign "><msub class = "- topic/foreign "><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">u</mi></mrow><mrow class = "- topic/foreign "><mn class = "- topic/foreign ">17</mn></mrow></msub></mrow></mfenced></mrow></math></span></td>
</tr>
</tbody></table>
<span class = "ph uicontrol">GROUP_OPER = SUM</span>
<p>Based on the node group a design response for the displacements in y-directions are defined
in a <code class = "ph codeph">DRESP</code> using <code class = "ph codeph">GROUP_OPER=SUM</code> yielding:</p>
<pre class = "codeblock">
<code class = "ph codeph">
DRESP
 ID_NAME    = DRESP_DISP_SUM
 DEF_TYPE   = SYSTEM
 TYPE       = DISP_Y
 LC_SET     = STATIC,1,
 ND_GROUP   =<var class = "keyword varname varname"> DISP_NODES</var>
 GROUP_OPER = SUM
END_
</code></pre>
<p>Internally, <span class = "ph">SIMULIA Tosca Structure</span> generates one <code class = "ph codeph">DRESP</code> consisting of the sum of the displacements of the
nodes 15, 16 and 17. </p>
<p>If one then applies the <code class = "ph codeph">DRESP</code> in the objective yielding: </p>
<pre class = "codeblock">
<code class = "ph codeph">
OBJ_FUNC
 ID_NAME = MIN_DISP_SUM
 DRESP   =<var class = "keyword varname varname"> DRESP_DISP_SUM</var>
 TARGET  = MIN
END_
</code></pre>
<p><span class = "ph">SIMULIA Tosca Structure</span> then sum up the three displacements like the following: <table class = "table" id = "tso-c-usr-terms-combTermsGroupOperDispl__table_E5A3A8F00E3C4B4C9B968FB3C2BD0B68"><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 "><mtext class = "- topic/foreign ">minimize</mtext><mo class = "- topic/foreign ">⁡</mo><mrow class = "- topic/foreign "><mo class = "- topic/foreign ">{</mo><msub class = "- topic/foreign "><mrow class = "- topic/foreign "><mi mathvariant = "normal" class = "- topic/foreign ">Φ</mi></mrow><mrow class = "- topic/foreign "><mn class = "- topic/foreign ">0</mn></mrow></msub><mo class = "- topic/foreign ">}</mo></mrow><mo class = "- topic/foreign ">=</mo><mtext class = "- topic/foreign ">minimize</mtext><mo class = "- topic/foreign ">⁡</mo><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 "><mn class = "- topic/foreign ">15</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 "><mn class = "- topic/foreign ">16</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 "><mn class = "- topic/foreign ">17</mn></mrow></msub><mo class = "- topic/foreign ">}</mo></mrow></mrow></math></span></td>
</tr>
</tbody></table></p>
<span class = "ph uicontrol">Alternative Definition of Objective Function</span>
<p>Alternatively, one could also define three <code class = "ph codeph">DRESP</code>s for each node like the
following: </p>
<pre class = "codeblock">
<code class = "ph codeph">
DRESP
 ID_NAME    = DRESP_DISP_1
 DEF_TYPE   = SYSTEM
 TYPE       = DISP_Y
<span class = "ph uicontrol"> NODE       = 15</span>
 LC_SET     = STATIC,1
 GROUP_OPER = MAX  or  SUM
END_

DRESP
 ID_NAME    = DRESP_DISP_2
 DEF_TYPE   = SYSTEM
 TYPE       = DISP_Y
<span class = "ph uicontrol"> NODE       = 16</span>
 LC_SET     = STATIC,1
 GROUP_OPER = MAX  or  SUM
END_

DRESP
 ID_NAME    = DRESP_DISP_3
 DEF_TYPE   = SYSTEM
 TYPE       = DISP_Y
<span class = "ph uicontrol"> NODE       = 17</span>
 LC_SET     = STATIC,1
 GROUP_OPER = MAX  or  SUM
END_
</code></pre>
<p>And then add the three design response in the objective function:</p>
<pre class = "codeblock">
<code class = "ph codeph">
OBJ_FUNC
 ID_NAME = MIN_DISP_SUM
 DRESP   = DRESP_DISP_1
 DRESP   = DRESP_DISP_2
 DRESP   = DRESP_DISP_3
 TARGET  = MIN
END_
</code></pre>
<p>Meaning that the objective function minimizes the following:</p>
<table class = "table" id = "tso-c-usr-terms-combTermsGroupOperDispl__table_277CA0FF51E14D9A8CD93C8D11333438"><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 "><mtext class = "- topic/foreign ">minimize</mtext><mo class = "- topic/foreign ">⁡</mo><mrow class = "- topic/foreign "><mo class = "- topic/foreign ">{</mo><msub class = "- topic/foreign "><mrow class = "- topic/foreign "><mi mathvariant = "normal" class = "- topic/foreign ">Φ</mi></mrow><mrow class = "- topic/foreign "><mn class = "- topic/foreign ">0</mn></mrow></msub><mo class = "- topic/foreign ">}</mo></mrow><mo class = "- topic/foreign ">=</mo><mtext class = "- topic/foreign ">minimize</mtext><mo class = "- topic/foreign ">⁡</mo><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 "><mn class = "- topic/foreign ">15</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 "><mn class = "- topic/foreign ">16</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 "><mn class = "- topic/foreign ">17</mn></mrow></msub><mo class = "- topic/foreign ">}</mo></mrow></mrow></math></span></td>
</tr>
</tbody></table>
<p><span class = "ph uicontrol">Remark:</span> Consequently, it can be concluded that all three ways of
defining the optimization leads to the same objective function. In this case, it is strongly
recommended that you combine the displacements using <code class = "ph codeph">GROUP_OPER = SUM</code>,
which results in a better performance.</p>
</div>

<div class = "section" id = "tso-c-usr-terms-combTermsGroupOperDispl__tso-c-usr-terms-combTermsGroupOperDispl-constr"><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">Use in Constraints</h2>

<p>Initially, a node group is defined containing the nodes 15, 16 and 17 (see figure above)
yielding:</p>
<pre class = "codeblock">
<code class = "ph codeph">
GROUP_DEF
 ID_NAME = DISP_NODES
 TYPE    = NODE
 FORMAT  = LIST
 LIST_BEGIN
 15, 16, 17
END_
</code>
<span class = "ph uicontrol">GROUP_OPER = MAX</span>
</pre>
<p>Based on the node group a design response for the displacements in y-directions are defined
in a <code class = "ph codeph">DRESP</code> using <code class = "ph codeph">GROUP_OPER=MAX</code> yielding:</p>
<pre class = "codeblock">
<code class = "ph codeph">
DRESP
 ID_NAME    = DRESP_DISP_MAX
 DEF_TYPE   = SYSTEM
 TYPE       = DISP_Y
 LC_SET     = STATIC,1,
 ND_GROUP   =<var class = "keyword varname varname"> DISP_NODES</var>
 GROUP_OPER = MAX
END_
</code></pre>
<p>Internally, <span class = "ph">SIMULIA Tosca Structure</span> generates three <code class = "ph codeph">DRESP</code>s. One <code class = "ph codeph">DRESP</code> for the displacement
of node 15, one DRESP for the displacement of node 16 and one <code class = "ph codeph">DRESP</code> for the
displacement of node 17. </p>
<p>If you apply the <code class = "ph codeph">DRESP</code> in a constraint yielding: </p>
<pre class = "codeblock">
<code class = "ph codeph">
CONSTRAINT
 ID_NAME   = CONSTRAINT_MAX
 DRESP     =<var class = "keyword varname varname"> DRESP_DISP_MAX</var>
 MAGNITUDE = ABS
 LE_VALUE  = &lt;value&gt;
END_
</code>
</pre>
<p><span class = "ph">SIMULIA Tosca Structure</span> then generates three displacement constraints like the following:</p><table class = "table" id = "tso-c-usr-terms-combTermsGroupOperDispl__table_E0E9DD7B5D7B49D7B7237AD4AE138E13"><caption/><colgroup><col style = "width:100%"/></colgroup><tbody class = "tbody">
<tr class = "row">
<td class = "entry">
<p><span class = "ph inlineequation"><math class = "- topic/foreign "><mrow class = "- topic/foreign "><msub class = "- topic/foreign "><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">u</mi></mrow><mrow class = "- topic/foreign "><mn class = "- topic/foreign ">15</mn></mrow></msub><mo class = "- topic/foreign ">≤</mo><msup class = "- topic/foreign "><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">u</mi></mrow><mrow class = "- topic/foreign "><mo class = "- topic/foreign ">*</mo></mrow></msup><mspace indentalign = "left" linebreak = "newline" class = "- topic/foreign "/></mrow></math></span></p>
<p><span class = "ph inlineequation"><math class = "- topic/foreign "><mrow class = "- topic/foreign "><mspace indentalign = "left" linebreak = "newline" class = "- topic/foreign "/><msub class = "- topic/foreign "><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">u</mi></mrow><mrow class = "- topic/foreign "><mn class = "- topic/foreign ">16</mn></mrow></msub><mo class = "- topic/foreign ">≤</mo><msup class = "- topic/foreign "><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">u</mi></mrow><mrow class = "- topic/foreign "><mo class = "- topic/foreign ">*</mo></mrow></msup><mspace indentalign = "left" linebreak = "newline" class = "- topic/foreign "/></mrow></math></span></p>
<p><span class = "ph inlineequation"><math class = "- topic/foreign "><mrow class = "- topic/foreign "><mspace indentalign = "left" linebreak = "newline" class = "- topic/foreign "/><msub class = "- topic/foreign "><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">u</mi></mrow><mrow class = "- topic/foreign "><mn class = "- topic/foreign ">17</mn></mrow></msub><mo class = "- topic/foreign ">≤</mo><msup class = "- topic/foreign "><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">u</mi></mrow><mrow class = "- topic/foreign "><mo class = "- topic/foreign ">*</mo></mrow></msup></mrow></math></span></p>
</td>
</tr>
</tbody></table>
<p>
<span class = "ph uicontrol">GROUP_OPER = SUM</span></p>
<p>Based on the node group a design response for the displacements in y-directions are defined
in a <code class = "ph codeph">DRESP</code> using <code class = "ph codeph">GROUP_OPER=SUM</code> yielding:</p>
<pre class = "codeblock">
<code class = "ph codeph">
DRESP
 ID_NAME   = DRESP_DISP_SUM
 DEF_TYPE  = SYSTEM
 TYPE      = DISP_Y
 LC_SET    = STATIC,1,
 ND_GROUP  = DISP_NODES
 GROUP_MAX = SUM
END_
</code>
</pre>
<p>Internally, <span class = "ph">SIMULIA Tosca Structure</span> generates one <code class = "ph codeph">DRESP</code> consisting of the sum of the displacements of the
nodes 15, 16 and 17. </p>
<p>If you apply the <code class = "ph codeph">DRESP</code> in a constraint yielding: </p>
<pre class = "codeblock">
<code class = "ph codeph">
CONSTRAINT
 ID_NAME   = CONSTRAINT_MAX
 DRESP     = DRESP_DISP_MAX
 MAGNITUDE = ABS
 LE_VALUE  = &lt;value&gt;
END_
</code>
</pre>
<p><span class = "ph">SIMULIA Tosca Structure</span> then generates a single displacement constraint like the following:</p>
<table class = "table" id = "tso-c-usr-terms-combTermsGroupOperDispl__xx630258"><caption/><colgroup><col/></colgroup><tbody class = "tbody">
<tr class = "row">
<td class = "entry"><span class = "ph inlineequation"><math class = "- topic/foreign "><mrow class = "- topic/foreign "><msub class = "- topic/foreign "><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">u</mi></mrow><mrow class = "- topic/foreign "><mn class = "- topic/foreign ">15</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 "><mn class = "- topic/foreign ">16</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 "><mn class = "- topic/foreign ">17</mn></mrow></msub><mo class = "- topic/foreign ">≤</mo><mi class = "- topic/foreign ">u</mi><mo class = "- topic/foreign ">*</mo></mrow></math></span></td>
</tr>
</tbody></table>
<span class = "ph uicontrol">Alternative Definition of Constraints</span>
<p>Alternatively, one could also define three <code class = "ph codeph">DRESP</code>s for each node like the
following: </p>
<pre class = "codeblock">
<code class = "ph codeph">
DRESP
 ID_NAME    = DRESP_DISP_1
 DEF_TYPE   = SYSTEM
 TYPE       = DISP_Y
<span class = "ph uicontrol"> NODE       = 15</span>
 LC_SET     = STATIC,1
 GROUP_OPER = MAX  or  SUM
END_

DRESP
 ID_NAME    = DRESP_DISP_2
 DEF_TYPE   = SYSTEM
 TYPE       = DISP_Y
<span class = "ph uicontrol"> NODE       = 16</span>
 LC_SET     = STATIC,1
 GROUP_OPER = MAX  or  SUM
END_

DRESP
 ID_NAME    = DRESP_DISP_3
 DEF_TYPE   = SYSTEM
 TYPE       = DISP_Y
<span class = "ph uicontrol"> NODE       = 17</span>
 LC_SET     = STATIC,1
 GROUP_OPER = MAX  or  SUM
END_
</code>
</pre>
<p>And then add the three design response in three constraints:</p>
<pre class = "codeblock">
<code class = "ph codeph">
CONSTRAINT
 ID_NAME   = CONSTRAINT_1
 DRESP     = DRESP_DISP_1
 MAGNITUDE = ABS
 LE_VALUE  = &lt;value&gt;
END_

CONSTRAINT
 ID_NAME   = CONSTRAINT_2
 DRESP     = DRESP_DISP_2
 MAGNITUDE = ABS
 LE_VALUE  = &lt;value&gt;
END_

CONSTRAINT
 ID_NAME   = CONSTRAINT_3
 DRESP     = DRESP_DISP_3
 MAGNITUDE = ABS
 LE_VALUE  = &lt;value&gt;
END_
</code>
</pre>
<p><span class = "ph">SIMULIA Tosca Structure</span> then generates three displacement constraints like the following:</p><table class = "table" id = "tso-c-usr-terms-combTermsGroupOperDispl__table_FC38CEFB5F584DE4893164E960B508B6"><caption/><colgroup><col style = "width:100%"/></colgroup><tbody class = "tbody">
<tr class = "row">
<td class = "entry">
<p><span class = "ph inlineequation"><math class = "- topic/foreign "><mrow class = "- topic/foreign "><msub class = "- topic/foreign "><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">u</mi></mrow><mrow class = "- topic/foreign "><mn class = "- topic/foreign ">15</mn></mrow></msub><mo class = "- topic/foreign ">≤</mo><msup class = "- topic/foreign "><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">u</mi></mrow><mrow class = "- topic/foreign "><mo class = "- topic/foreign ">*</mo></mrow></msup><mspace indentalign = "left" linebreak = "newline" class = "- topic/foreign "/></mrow></math></span></p>
<p><span class = "ph inlineequation"><math class = "- topic/foreign "><mrow class = "- topic/foreign "><mspace indentalign = "left" linebreak = "newline" class = "- topic/foreign "/><msub class = "- topic/foreign "><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">u</mi></mrow><mrow class = "- topic/foreign "><mn class = "- topic/foreign ">16</mn></mrow></msub><mo class = "- topic/foreign ">≤</mo><msup class = "- topic/foreign "><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">u</mi></mrow><mrow class = "- topic/foreign "><mo class = "- topic/foreign ">*</mo></mrow></msup><mspace indentalign = "left" linebreak = "newline" class = "- topic/foreign "/></mrow></math></span></p>
<p><span class = "ph inlineequation"><math class = "- topic/foreign "><mrow class = "- topic/foreign "><mspace indentalign = "left" linebreak = "newline" class = "- topic/foreign "/><msub class = "- topic/foreign "><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">u</mi></mrow><mrow class = "- topic/foreign "><mn class = "- topic/foreign ">17</mn></mrow></msub><mo class = "- topic/foreign ">≤</mo><msup class = "- topic/foreign "><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">u</mi></mrow><mrow class = "- topic/foreign "><mo class = "- topic/foreign ">*</mo></mrow></msup></mrow></math></span></p>
</td>
</tr>
</tbody></table>
<p>Consequently, it can be concluded that there is fundamental difference in the constraints
if a node group (<code class = "ph codeph">ND_GROUP</code>) consisting of more than one node is applied and
the choice of <code class = "ph codeph">GROUP_OPER</code>. </p>
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