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      <title>RBE3</title>
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      <div class="title_refTopic" id="xps10_pagetitle">RBE3 </div>
      <hr noshade="true">
      <h4 class="refClassification">Interpolation Constraint Element </h4>
      <p class="para_refTopic">Defines the motion at a reference grid point as the weighted average of the motions at a set of other grid points. </p>
      <div class="title_refCategory">Format: </div>
      <div class="refCategoryContent">
         <table border="1" width="100%" align="center">
            <colgroup span="1">
               <col span="1" width="9.98*">
               <col span="1" width="9.98*">
               <col span="1" width="9.40*">
               <col span="1" width="10.75*">
               <col span="1" width="9.98*">
               <col span="1" width="9.98*">
               <col span="1" width="9.98*">
               <col span="1" width="9.98*">
               <col span="1" width="9.98*">
               <col span="1" width="9.98*">
            </colgroup>
            <thead>
               <tr>
                  <th align="center" colspan="1" rowspan="1">
                     <p class="para_th">1 </p>
                  </th>
                  <th align="center" colspan="1" rowspan="1">
                     <p class="para_th">2 </p>
                  </th>
                  <th align="center" colspan="1" rowspan="1">
                     <p class="para_th">3 </p>
                  </th>
                  <th align="center" colspan="1" rowspan="1">
                     <p class="para_th">4 </p>
                  </th>
                  <th align="center" colspan="1" rowspan="1">
                     <p class="para_th">5 </p>
                  </th>
                  <th align="center" colspan="1" rowspan="1">
                     <p class="para_th">6 </p>
                  </th>
                  <th align="center" colspan="1" rowspan="1">
                     <p class="para_th">7 </p>
                  </th>
                  <th align="center" colspan="1" rowspan="1">
                     <p class="para_th">8 </p>
                  </th>
                  <th align="center" colspan="1" rowspan="1">
                     <p class="para_th">9 </p>
                  </th>
                  <th align="center" colspan="1" rowspan="1">
                     <p class="para_th">10 </p>
                  </th>
               </tr>
            </thead>
            <tbody>
               <tr>
                  <td align="left" colspan="1" rowspan="1" valign="top">
                     <p class="para_td">RBE3 </p>
                  </td>
                  <td align="center" colspan="1" rowspan="1">
                     <p class="para_td">EID </p>
                  </td>
                  <td align="center" bgcolor="gray" colspan="1" rowspan="1">
                     <p class="para_td">&nbsp; </p>
                  </td>
                  <td align="center" colspan="1" rowspan="1">
                     <p class="para_td">REFGRID </p>
                  </td>
                  <td align="center" colspan="1" rowspan="1">
                     <p class="para_td">REFC </p>
                  </td>
                  <td align="center" colspan="1" rowspan="1">
                     <p class="para_td">WT1 </p>
                  </td>
                  <td align="center" colspan="1" rowspan="1">
                     <p class="para_td">C1 </p>
                  </td>
                  <td align="center" colspan="1" rowspan="1">
                     <p class="para_td">G1,1 </p>
                  </td>
                  <td align="center" colspan="1" rowspan="1">
                     <p class="para_td">G1,2 </p>
                  </td>
                  <td align="center" colspan="1" rowspan="1">
                     <p class="para_td">&nbsp; </p>
                  </td>
               </tr>
               <tr>
                  <td align="left" colspan="1" rowspan="1" valign="top">
                     <p class="para_td">&nbsp; </p>
                  </td>
                  <td align="center" colspan="1" rowspan="1">
                     <p class="para_td">G1,3 </p>
                  </td>
                  <td align="center" colspan="1" rowspan="1">
                     <p class="para_td">WT2 </p>
                  </td>
                  <td align="center" colspan="1" rowspan="1">
                     <p class="para_td">C2 </p>
                  </td>
                  <td align="center" colspan="1" rowspan="1">
                     <p class="para_td">G2,1 </p>
                  </td>
                  <td align="center" colspan="1" rowspan="1">
                     <p class="para_td">G2,2 </p>
                  </td>
                  <td align="center" colspan="1" rowspan="1">
                     <p class="para_td">-etc.- </p>
                  </td>
                  <td align="center" colspan="1" rowspan="1">
                     <p class="para_td">WT3 </p>
                  </td>
                  <td align="center" colspan="1" rowspan="1">
                     <p class="para_td">C3 </p>
                  </td>
                  <td align="center" colspan="1" rowspan="1">
                     <p class="para_td">&nbsp; </p>
                  </td>
               </tr>
               <tr>
                  <td align="left" colspan="1" rowspan="1" valign="top">
                     <p class="para_td">&nbsp; </p>
                  </td>
                  <td align="center" colspan="1" rowspan="1">
                     <p class="para_td">G3,1 </p>
                  </td>
                  <td align="center" colspan="1" rowspan="1">
                     <p class="para_td">G3,2 </p>
                  </td>
                  <td align="center" colspan="1" rowspan="1">
                     <p class="para_td">-etc.- </p>
                  </td>
                  <td align="center" colspan="1" rowspan="1">
                     <p class="para_td">WT4 </p>
                  </td>
                  <td align="center" colspan="1" rowspan="1">
                     <p class="para_td">C4 </p>
                  </td>
                  <td align="center" colspan="1" rowspan="1">
                     <p class="para_td">G4,1 </p>
                  </td>
                  <td align="center" colspan="1" rowspan="1">
                     <p class="para_td">G4,2 </p>
                  </td>
                  <td align="center" colspan="1" rowspan="1">
                     <p class="para_td">-etc.- </p>
                  </td>
                  <td align="center" colspan="1" rowspan="1">
                     <p class="para_td">&nbsp; </p>
                  </td>
               </tr>
               <tr>
                  <td align="left" colspan="1" rowspan="1" valign="top">
                     <p class="para_td">&nbsp; </p>
                  </td>
                  <td align="center" colspan="1" rowspan="1">
                     <p class="para_td">&ldquo;UM&rdquo; </p>
                  </td>
                  <td align="center" colspan="1" rowspan="1">
                     <p class="para_td">GM1 </p>
                  </td>
                  <td align="center" colspan="1" rowspan="1">
                     <p class="para_td">CM1 </p>
                  </td>
                  <td align="center" colspan="1" rowspan="1">
                     <p class="para_td">GM2 </p>
                  </td>
                  <td align="center" colspan="1" rowspan="1">
                     <p class="para_td">CM2 </p>
                  </td>
                  <td align="center" colspan="1" rowspan="1">
                     <p class="para_td">GM3 </p>
                  </td>
                  <td align="center" colspan="1" rowspan="1">
                     <p class="para_td">CM3 </p>
                  </td>
                  <td align="center" bgcolor="gray" colspan="1" rowspan="1">
                     <p class="para_td">&nbsp; </p>
                  </td>
                  <td align="center" colspan="1" rowspan="1">
                     <p class="para_td">&nbsp; </p>
                  </td>
               </tr>
               <tr>
                  <td align="left" colspan="1" rowspan="1" valign="top">
                     <p class="para_td">&nbsp; </p>
                  </td>
                  <td align="center" bgcolor="gray" colspan="1" rowspan="1">
                     <p class="para_td">&nbsp; </p>
                  </td>
                  <td align="center" colspan="1" rowspan="1">
                     <p class="para_td">GM4 </p>
                  </td>
                  <td align="center" colspan="1" rowspan="1">
                     <p class="para_td">CM4 </p>
                  </td>
                  <td align="center" colspan="1" rowspan="1">
                     <p class="para_td">GM5 </p>
                  </td>
                  <td align="center" colspan="1" rowspan="1">
                     <p class="para_td">CM5 </p>
                  </td>
                  <td align="center" colspan="1" rowspan="1">
                     <p class="para_td">-etc.- </p>
                  </td>
                  <td align="center" colspan="1" rowspan="1">
                     <p class="para_td">&nbsp; </p>
                  </td>
                  <td align="center" bgcolor="gray" colspan="1" rowspan="1">
                     <p class="para_td">&nbsp; </p>
                  </td>
                  <td align="center" colspan="1" rowspan="1">
                     <p class="para_td">&nbsp; </p>
                  </td>
               </tr>
            </tbody>
         </table><br></div>
      <div class="title_refCategory">Example: </div>
      <div class="refCategoryContent">
         <table border="1" width="100%" align="center">
            <colgroup span="1">
               <col span="1" width="10.12*">
               <col span="1" width="10.12*">
               <col span="1" width="8.94*">
               <col span="1" width="10.12*">
               <col span="1" width="10.12*">
               <col span="1" width="10.12*">
               <col span="1" width="10.12*">
               <col span="1" width="10.12*">
               <col span="1" width="10.12*">
               <col span="1" width="10.12*">
            </colgroup>
            <tbody>
               <tr>
                  <td align="left" colspan="1" rowspan="1" valign="top">
                     <p class="para_td">RBE3 </p>
                  </td>
                  <td align="center" colspan="1" rowspan="1">
                     <p class="para_td">14 </p>
                  </td>
                  <td align="center" colspan="1" rowspan="1">
                     <p class="para_td">&nbsp; </p>
                  </td>
                  <td align="center" colspan="1" rowspan="1">
                     <p class="para_td">100 </p>
                  </td>
                  <td align="center" colspan="1" rowspan="1">
                     <p class="para_td">1234 </p>
                  </td>
                  <td align="center" colspan="1" rowspan="1">
                     <p class="para_td">1.0 </p>
                  </td>
                  <td align="center" colspan="1" rowspan="1">
                     <p class="para_td">123 </p>
                  </td>
                  <td align="center" colspan="1" rowspan="1">
                     <p class="para_td">1 </p>
                  </td>
                  <td align="center" colspan="1" rowspan="1">
                     <p class="para_td">3 </p>
                  </td>
                  <td align="center" colspan="1" rowspan="1">
                     <p class="para_td">&nbsp; </p>
                  </td>
               </tr>
               <tr>
                  <td align="left" colspan="1" rowspan="1" valign="top">
                     <p class="para_td">&nbsp; </p>
                  </td>
                  <td align="center" colspan="1" rowspan="1">
                     <p class="para_td">5 </p>
                  </td>
                  <td align="center" colspan="1" rowspan="1">
                     <p class="para_td">4.7 </p>
                  </td>
                  <td align="center" colspan="1" rowspan="1">
                     <p class="para_td">1 </p>
                  </td>
                  <td align="center" colspan="1" rowspan="1">
                     <p class="para_td">2 </p>
                  </td>
                  <td align="center" colspan="1" rowspan="1">
                     <p class="para_td">4 </p>
                  </td>
                  <td align="center" colspan="1" rowspan="1">
                     <p class="para_td">6 </p>
                  </td>
                  <td align="center" colspan="1" rowspan="1">
                     <p class="para_td">5.2 </p>
                  </td>
                  <td align="center" colspan="1" rowspan="1">
                     <p class="para_td">2 </p>
                  </td>
                  <td align="center" colspan="1" rowspan="1">
                     <p class="para_td">&nbsp; </p>
                  </td>
               </tr>
               <tr>
                  <td align="left" colspan="1" rowspan="1" valign="top">
                     <p class="para_td">&nbsp; </p>
                  </td>
                  <td align="center" colspan="1" rowspan="1">
                     <p class="para_td">7 </p>
                  </td>
                  <td align="center" colspan="1" rowspan="1">
                     <p class="para_td">8 </p>
                  </td>
                  <td align="center" colspan="1" rowspan="1">
                     <p class="para_td">9 </p>
                  </td>
                  <td align="center" colspan="1" rowspan="1">
                     <p class="para_td">5.1 </p>
                  </td>
                  <td align="center" colspan="1" rowspan="1">
                     <p class="para_td">1 </p>
                  </td>
                  <td align="center" colspan="1" rowspan="1">
                     <p class="para_td">15 </p>
                  </td>
                  <td align="center" colspan="1" rowspan="1">
                     <p class="para_td">16 </p>
                  </td>
                  <td align="center" colspan="1" rowspan="1">
                     <p class="para_td">&nbsp; </p>
                  </td>
                  <td align="center" colspan="1" rowspan="1">
                     <p class="para_td">&nbsp; </p>
                  </td>
               </tr>
               <tr>
                  <td align="left" colspan="1" rowspan="1" valign="top">
                     <p class="para_td">&nbsp; </p>
                  </td>
                  <td align="center" colspan="1" rowspan="1">
                     <p class="para_td">UM </p>
                  </td>
                  <td align="center" colspan="1" rowspan="1">
                     <p class="para_td">100 </p>
                  </td>
                  <td align="center" colspan="1" rowspan="1">
                     <p class="para_td">14 </p>
                  </td>
                  <td align="center" colspan="1" rowspan="1">
                     <p class="para_td">5 </p>
                  </td>
                  <td align="center" colspan="1" rowspan="1">
                     <p class="para_td">3 </p>
                  </td>
                  <td align="center" colspan="1" rowspan="1">
                     <p class="para_td">7 </p>
                  </td>
                  <td align="center" colspan="1" rowspan="1">
                     <p class="para_td">2 </p>
                  </td>
                  <td align="center" colspan="1" rowspan="1">
                     <p class="para_td">&nbsp; </p>
                  </td>
                  <td align="center" colspan="1" rowspan="1">
                     <p class="para_td">&nbsp; </p>
                  </td>
               </tr>
            </tbody>
         </table><br></div>
      <div class="title_refCategory">Fields:</div>
      <div class="refCategoryContent">
         <table cellpadding="9" width="100%" align="center">
            <colgroup span="1">
               <col span="1" width="16*">
               <col span="1" width="84*">
            </colgroup>
            <thead>
               <tr>
                  <th align="left" colspan="1" rowspan="1">
                     <p class="para_th"><b class="uiTerm">Field </b></p>
                  </th>
                  <th align="left" colspan="1" rowspan="1">
                     <p class="para_th"><b class="uiTerm">Contents </b></p>
                  </th>
               </tr>
            </thead>
            <tbody>
               <tr>
                  <td align="left" colspan="1" rowspan="1" valign="top">
                     <p class="para_td">EID </p>
                  </td>
                  <td align="left" colspan="1" rowspan="1" valign="top">
                     <p class="para_td">Element identification number.  Unique with respect to other rigid elements.  (Integer &gt; 0) </p>
                  </td>
               </tr>
               <tr>
                  <td align="left" colspan="1" rowspan="1" valign="top">
                     <p class="para_td">REFGRID </p>
                  </td>
                  <td align="left" colspan="1" rowspan="1" valign="top">
                     <p class="para_td">Reference grid point identification number.  (Integer &gt; 0) </p>
                  </td>
               </tr>
               <tr>
                  <td align="left" colspan="1" rowspan="1" valign="top">
                     <p class="para_td">REFC </p>
                  </td>
                  <td align="left" colspan="1" rowspan="1" valign="top">
                     <p class="para_td">Component numbers at the reference grid point.  (Any of the Integers 1 through 6 with no embedded blanks.) </p>
                  </td>
               </tr>
               <tr>
                  <td align="left" colspan="1" rowspan="1" valign="top">
                     <p class="para_td">WTi </p>
                  </td>
                  <td align="left" colspan="1" rowspan="1" valign="top">
                     <p class="para_td">Weighting factor for components of motion on the following entry at grid points Gi,j.  (Real) </p>
                  </td>
               </tr>
               <tr>
                  <td align="left" colspan="1" rowspan="1" valign="top">
                     <p class="para_td">Ci </p>
                  </td>
                  <td align="left" colspan="1" rowspan="1" valign="top">
                     <p class="para_td">Component numbers with weighting factor WTi at grid points Gi,j.  (Any of the Integers 1 through 6 with no embedded blanks.) </p>
                  </td>
               </tr>
               <tr>
                  <td align="left" colspan="1" rowspan="1" valign="top">
                     <p class="para_td">Gi,j </p>
                  </td>
                  <td align="left" colspan="1" rowspan="1" valign="top">
                     <p class="para_td">Grid points with components Ci that have weighting factor WTi in the averaging equations.  (Integer &gt; 0) </p>
                  </td>
               </tr>
               <tr>
                  <td align="left" colspan="1" rowspan="1" valign="top">
                     <p class="para_td">&ldquo;UM&rdquo; </p>
                  </td>
                  <td align="left" colspan="1" rowspan="1" valign="top">
                     <p class="para_td">Indicates the start of the degrees-of-freedom belonging to the m-set.  The default action is to assign only the components in REFC to the m-set.  (Character) </p>
                  </td>
               </tr>
               <tr>
                  <td align="left" colspan="1" rowspan="1" valign="top">
                     <p class="para_td">GMi </p>
                  </td>
                  <td align="left" colspan="1" rowspan="1" valign="top">
                     <p class="para_td">Identification numbers of grid points with degrees-of-freedom in the m-set.  (Integer &gt; 0) </p>
                  </td>
               </tr>
               <tr>
                  <td align="left" colspan="1" rowspan="1" valign="top">
                     <p class="para_td">CMi </p>
                  </td>
                  <td align="left" colspan="1" rowspan="1" valign="top">
                     <p class="para_td">Component numbers of GMi to be assigned to the m-set.  (Any of the Integers 1 through 6 with no embedded blanks.) </p>
                  </td>
               </tr>
            </tbody>
         </table><br></div>
      <div class="title_refCategory">Remarks: </div>
      <div class="refCategoryContent">
         <ol type="1" start="1">
            <li><a name="ref28073"></a><p class="para_item">It is recommended that for most applications only the translation components 123 be used for Ci.  An exception is the case where the Gi,j are colinear.  A rotation component may then be added to one grid point to stabilize its associated rigid body mode for the element. </p>
            </li>
            <li>
               <p class="para_item">Blank spaces may be left at the end of a Gi,j sequence. </p>
            </li>
            <li>
               <p class="para_item">The default for &ldquo;UM&rdquo; should be used except in cases where the user wishes to include some or all REFC components in displacement sets exclusive from the m-set.  If the default is not used for &ldquo;UM&rdquo;: </p>
               <ul>
                  <li>
                     <p class="para_item">The total number of components in the m-set (i.e., the total number of dependent degrees-of-freedom defined by the element) must be equal to the number of components in REFC (four components in the example). </p>
                  </li>
                  <li>
                     <p class="para_item">The components specified after &ldquo;UM&rdquo; must be a subset of the components specified under REFC and (Gi,j, Ci). </p>
                  </li>
                  <li>
                     <p class="para_item">The coefficient matrix [R<sub class="subscript">m</sub>] described in<a class="links" href="javascript:void(0)" onclick="top.popUpPage('User/index.html?goto=User/14ref37867_14.html&vars=-aux,-home','linkInter','menubar=yes,status=yes,resizable=yes,toolbar=yes,scrollbars=yes,location=no,directories=no');return(false);">&ldquo;Multipoint Constraint Operations in SubDMAPs SEKR and SEMR2 and SEMRB&rdquo; </a>in the <em>NX Nastran User&rsquo;s Guide</em> must be nonsingular.  PARAM,CHECKOUT in SOLs 101 through 200 may be used to check for this condition. 
                     </p>
                  </li>
               </ul>
            </li>
            <li>
               <p class="para_item">Dependent degrees-of-freedom assigned by one rigid element may not also be assigned dependent by another rigid element or by a multipoint constraint. </p>
            </li>
            <li>
               <p class="para_item">Rigid elements, unlike MPCs, are not selected through the Case Control Section. </p>
            </li>
            <li>
               <p class="para_item">Forces of multipoint constraint may be recovered in all solution sequences, except SOL 129, with the MPCFORCE Case Control command. </p>
            </li>
            <li>
               <p class="para_item">Rigid elements are ignored in heat transfer problems. </p>
            </li>
            <li>
               <p class="para_item">The m-set coordinates specified on this entry may not be specified on other entries that define mutually exclusive sets.  See <a class="links" href="javascript:void(0)" onclick="top.openFile('QRG/10ref73695_1.html');return(false);">&ldquo;Degree-of-Freedom Sets&rdquo; </a> for a list of these entries. 
               </p>
            </li>
            <li>
               <p class="para_item">The formulation for the RBE3 element was changed in MSC.Nastran Version 70.7. This change allowed the element to give consistent answers that are not dependent upon the units of the model. Only models that connected rotation degrees of freedom for Ci were affected. Note that these models are ignoring the recommendation in Remark <a class="links" href="javascript:void(0)" onclick="top.openFile('QRG/19topic_23.html#ref28073');return(false);">33-1. </a> The formulation prior to MSC.Nastran Version 70.7 may be obtained by setting SYSTEM(310)=1. 
               </p>
            </li>
         </ol>
      </div>
      <div class="title_refCategory">Remarks related to SOLs 601 and 701: </div>
      <div class="refCategoryContent">
         <ol type="1" start="1">
            <li>
               <p class="para_item">All GMi and CMi are ignored. </p>
            </li>
            <li>
               <p class="para_item">No output of forces of multipoint constraint may be requested. </p>
            </li>
            <li>
               <p class="para_item">A dependent degree-of-freedom may not be also assigned as an independent degree-of-freedom by another rigid element or by a multipoint constraint. An error message will be issued in such a case. </p>
            </li>
         </ol>
      </div>
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