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      <title>SPLINE3</title>
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      <div class="title_refTopic" id="xps10_pagetitle">SPLINE3 </div>
      <hr noshade="true">
      <h4 class="refClassification">Aeroelastic Constraint Equation </h4>
      <p class="para_refTopic">Defines a constraint equation for aeroelastic problems.  Useful for control surface constraints. </p>
      <div class="title_refCategory">Format: </div>
      <div class="refCategoryContent">
         <table border="1" width="100%" align="center">
            <colgroup span="1">
               <col span="1" width="10*">
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            </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">SPLINE3 </p>
                  </td>
                  <td align="center" colspan="1" rowspan="1">
                     <p class="para_td">EID </p>
                  </td>
                  <td align="center" colspan="1" rowspan="1">
                     <p class="para_td">CAERO </p>
                  </td>
                  <td align="center" colspan="1" rowspan="1">
                     <p class="para_td">BOXID </p>
                  </td>
                  <td align="center" colspan="1" rowspan="1">
                     <p class="para_td">COMP </p>
                  </td>
                  <td align="center" colspan="1" rowspan="1">
                     <p class="para_td">G1 </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">A1 </p>
                  </td>
                  <td align="center" colspan="1" rowspan="1">
                     <p class="para_td">USAGE </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">G2 </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">A2 </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">-etc. </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>
                  <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*">
               <col span="1" width="10*">
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            <tbody>
               <tr>
                  <td align="left" colspan="1" rowspan="1" valign="top">
                     <p class="para_td">SPLINE3 </p>
                  </td>
                  <td align="center" colspan="1" rowspan="1">
                     <p class="para_td">7000 </p>
                  </td>
                  <td align="center" colspan="1" rowspan="1">
                     <p class="para_td">107 </p>
                  </td>
                  <td align="center" colspan="1" rowspan="1">
                     <p class="para_td">109 </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 </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">1.0 </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">43 </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">-1.0 </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>
                  <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>
                  <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">
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               <col span="1" width="84*">
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                  <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.  (Integer &gt; 0) </p>
                  </td>
               </tr>
               <tr>
                  <td align="left" colspan="1" rowspan="1" valign="top">
                     <p class="para_td">CAERO </p>
                  </td>
                  <td align="left" colspan="1" rowspan="1" valign="top">
                     <p class="para_td">Identification number of the macro-element on which the element to be interpolated lies.  (Integer &gt; 0) </p>
                  </td>
               </tr>
               <tr>
                  <td align="left" colspan="1" rowspan="1" valign="top">
                     <p class="para_td">BOXID </p>
                  </td>
                  <td align="left" colspan="1" rowspan="1" valign="top">
                     <p class="para_td">Identification number of the aerodynamic element; i.e., the box number.  (Integer &gt; 0) </p>
                  </td>
               </tr>
               <tr>
                  <td align="left" colspan="1" rowspan="1" valign="top">
                     <p class="para_td">COMP </p>
                  </td>
                  <td align="left" colspan="1" rowspan="1" valign="top">
                     <p class="para_td">The component of motion to be interpolated.  See Remark <a class="links" href="javascript:void(0)" onclick="top.openFile('QRG/19topic_75.html#ref33739');return(false);">103-4. </a> (One of the Integers 1, 2, 3, 4, 5, or 6.) 
                     </p>
                  </td>
               </tr>
               <tr>
                  <td align="left" colspan="1" rowspan="1" valign="top">
                     <p class="para_td">Gi </p>
                  </td>
                  <td align="left" colspan="1" rowspan="1" valign="top">
                     <p class="para_td">Grid point identification number of the  independent grid point.  (Integer &gt; 0) </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 in the displacement coordinate system.  (One of the Integers 1 through 6 for grid points, or 0 for scalar points.)</p>
                  </td>
               </tr>
               <tr>
                  <td align="left" colspan="1" rowspan="1" valign="top">
                     <p class="para_td">Ai </p>
                  </td>
                  <td align="left" colspan="1" rowspan="1" valign="top">
                     <p class="para_td">Coefficient of the constraint relationship.  (Real) </p>
                  </td>
               </tr>
               <tr>
                  <td align="left" colspan="1" rowspan="1" valign="top">
                     <p class="para_td">USAGE </p>
                  </td>
                  <td align="left" colspan="1" rowspan="1" valign="top">
                     <p class="para_td">Spline usage flag to determine whether this spline applies to the force transformation, displacement transformation or both.  FORCE, DISP or BOTH. See Remark <a class="links" href="javascript:void(0)" onclick="top.openFile('QRG/19topic_75.html#ref69497');return(false);">103-6. </a> (Character, Default=BOTH). 
                     </p>
                  </td>
               </tr>
            </tbody>
         </table><br></div>
      <div class="title_refCategory">Remarks: </div>
      <div class="refCategoryContent">
         <ol type="1" start="1">
            <li>
               <p class="para_item">The independent grid points and components must refer to degrees-of-freedom in the g-set. </p>
            </li>
            <li>
               <p class="para_item">The constraint is given by </p>
               <p align="center"><img align="bottom" src="graphics/bulkqrs-equ11.gif"></p>
               <p class="para_item">where </p>
               <table width="100%" align="center">
                  <colgroup span="1">
                     <col span="1" width="4.15*">
                     <col span="1" width="3.37*">
                     <col span="1" width="92.49*">
                  </colgroup>
                  <tbody>
                     <tr>
                        <td align="right" colspan="1" rowspan="1">
                           <p class="para_td"><em>u<sub class="subscript">d</sub></em></p>
                        </td>
                        <td align="center" colspan="1" rowspan="1">
                           <p class="para_td">= </p>
                        </td>
                        <td align="left" colspan="1" rowspan="1" valign="top">
                           <p class="para_td">value of the dependent component of the aerodynamic element </p>
                        </td>
                     </tr>
                     <tr>
                        <td align="right" colspan="1" rowspan="1">
                           <p class="para_td"><em>u<sub class="subscript">i</sub></em></p>
                        </td>
                        <td align="center" colspan="1" rowspan="1">
                           <p class="para_td">= </p>
                        </td>
                        <td align="left" colspan="1" rowspan="1" valign="top">
                           <p class="para_td">displacement at grid Gi, component Ci. </p>
                        </td>
                     </tr>
                  </tbody>
               </table><br></li>
            <li>
               <p class="para_item">The SPLINE3 EID must be unique with respect to all SPLINEi entries. </p>
            </li>
            <li><a name="ref33739"></a><p class="para_item">The allowable components by CAEROi entry type are indicated by an &ldquo;X&rdquo; in the table below: </p>
               <table border="1" cellpadding="7" width="100%" align="center">
                  <colgroup span="1">
                     <col span="1" width="31.82*">
                     <col span="1" width="13.64*">
                     <col span="1" width="13.64*">
                     <col span="1" width="13.64*">
                     <col span="1" width="13.64*">
                     <col span="1" width="13.64*">
                  </colgroup>
                  <thead>
                     <tr>
                        <th align="center" colspan="1" rowspan="2">
                           <p class="para_th"><b class="uiTerm">Entry Type </b></p>
                        </th>
                        <th align="center" colspan="5" rowspan="1">
                           <p class="para_th"><b class="uiTerm">COMP </b></p>
                        </th>
                     </tr>
                     <tr>
                        <th align="center" colspan="1" rowspan="1">
                           <p class="para_th"><b class="uiTerm">1 </b></p>
                        </th>
                        <th align="center" colspan="1" rowspan="1">
                           <p class="para_th"><b class="uiTerm">2 </b></p>
                        </th>
                        <th align="center" colspan="1" rowspan="1">
                           <p class="para_th"><b class="uiTerm">3 </b></p>
                        </th>
                        <th align="center" colspan="1" rowspan="1">
                           <p class="para_th"><b class="uiTerm">5 </b></p>
                        </th>
                        <th align="center" colspan="1" rowspan="1">
                           <p class="para_th"><b class="uiTerm">6 </b></p>
                        </th>
                     </tr>
                  </thead>
                  <tbody>
                     <tr>
                        <td align="left" colspan="1" rowspan="1" valign="top">
                           <p class="para_td">CAERO1 </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>
                        <td align="center" colspan="1" rowspan="1">
                           <p class="para_td">X </p>
                        </td>
                        <td align="center" colspan="1" rowspan="1">
                           <p class="para_td">X </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">CAERO2 </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">X </p>
                        </td>
                        <td align="center" colspan="1" rowspan="1">
                           <p class="para_td">X </p>
                        </td>
                        <td align="center" colspan="1" rowspan="1">
                           <p class="para_td">X </p>
                        </td>
                        <td align="center" colspan="1" rowspan="1">
                           <p class="para_td">X </p>
                        </td>
                     </tr>
                     <tr>
                        <td align="left" colspan="1" rowspan="1" valign="top">
                           <p class="para_td">CAERO3 </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>
                        <td align="center" colspan="1" rowspan="1">
                           <p class="para_td">X </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">CAERO4 </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>
                        <td align="center" colspan="1" rowspan="1">
                           <p class="para_td">X </p>
                        </td>
                        <td align="center" colspan="1" rowspan="1">
                           <p class="para_td">X </p>
                        </td>
                        <td align="center" colspan="1" rowspan="1">
                           <p class="para_td">X </p>
                        </td>
                     </tr>
                     <tr>
                        <td align="left" colspan="1" rowspan="1" valign="top">
                           <p class="para_td">CAERO5 </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>
                        <td align="center" colspan="1" rowspan="1">
                           <p class="para_td">X </p>
                        </td>
                        <td align="center" colspan="1" rowspan="1">
                           <p class="para_td">X </p>
                        </td>
                        <td align="center" colspan="1" rowspan="1">
                           <p class="para_td">X </p>
                        </td>
                     </tr>
                     <tr>
                        <td align="left" colspan="1" rowspan="1" valign="top">
                           <p class="para_td">3D Geometry </p>
                        </td>
                        <td align="center" colspan="1" rowspan="1">
                           <p class="para_td">X </p>
                        </td>
                        <td align="center" colspan="1" rowspan="1">
                           <p class="para_td">X </p>
                        </td>
                        <td align="center" colspan="1" rowspan="1">
                           <p class="para_td">X </p>
                        </td>
                        <td align="center" colspan="1" rowspan="1">
                           <p class="para_td">X </p>
                        </td>
                        <td align="center" colspan="1" rowspan="1">
                           <p class="para_td">X </p>
                        </td>
                     </tr>
                  </tbody>
               </table><br><p class="para_item">COMP=2:  lateral displacement </p>
               <p class="para_item">COMP=3  transverse displacement </p>
               <p class="para_item">COMP=5:  pitch angle </p>
               <p class="para_item">COMP=6:  relative control angle for CAERO4 and CAERO5 yaw angle for CAERO2. </p>
               <p class="para_item">For general 3D aerodynamic geometries the components numbers refer to axes of the Aerodynamic Coordinate System (<em>u<sub class="subscript">x</sub></em>, <em>u<sub class="subscript">y</sub></em>, <em>u<sub class="subscript">z</sub></em>, &theta;<em><sub class="subscript">x</sub></em>, &theta;<em><sub class="subscript">y</sub></em>, &theta;<em><sub class="subscript">z</sub></em>). 
               </p>
            </li>
            <li>
               <p class="para_item">For Strip theory and Piston theory, the COMP=6 control surface relative angle is positive when the trailing edge has a negative z-deflection in the element coordinate system (see the <em><a class="links" href="javascript:void(0)" onclick="top.popUpPage('QRG/linkInter_target_not_resolved.html#aero:ref86112:-aux,-home','linkInter','menubar=yes,status=yes,resizable=yes,toolbar=yes,scrollbars=yes,location=no,directories=no');return(false);">NX Nastran Aeroelastic Analysis User&rsquo;s Guide</a></em>.)
               </p>
            </li>
            <li><a name="ref69497"></a><p class="para_item">The USAGE field allows you to specify that the particular spline interpolant defined in this entry is to be used for just the force transformation (FORCE) or just the displacement transformation (DISP) or for both (BOTH). </p>
               <p class="para_item"><em>Fg</em>=[<em>GPkg</em>]<sup class="superscript"><em>T</em></sup> {<em>Pk</em>} (FORCE/BOTH splines are in the transform) 
               </p>
               <p class="para_item"><em>Uk</em>=[<em>GDkg</em>] {<em>Ug</em>} (DISP/BOTH splines are in the transform) 
               </p>
               <p class="para_item">In general, the two transforms are done with distinct matrices.  Only when ALL splines are of type BOTH is the familiar transpose relationship <em>GPgk</em>]<sup class="superscript"><em>T</em></sup>]=[<em>GDkg</em>] satisfied. The default behavior (BOTH for all splines) is compatible with versions of MSC.Nastran prior to Version 70.5. 
               </p>
               <p class="para_item">In general, the USAGE field can be used to apply aerodynamic forces to the structure from aerodynamic panels that are intended NOT to move (USAGE=FORCE) or to apply structural displacements to aerodynamic grids whose forces are not to be applied to the structure (USAGE=DISP). The DISP option is somewhat esoteric in that you are then suggesting that the aeroelastic effect of the surface is important while its forces are not.  (In other words, only the forces arising from tis effects on other surfaces is important.) While there may be circumstances where this is true, it is unlikely.  Take care that you included all the FORCEs from aerodynamic panels that are important by including them in either FORCE or BOTH spline(s).  NX Nastran will NOT issue a warning unless ALL forces are omitted.  All displacements may be omitted without warning (and is a means to perform &ldquo;rigid aerodynamic&rdquo; analyses). </p>
            </li>
         </ol>
      </div>
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