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      <title>SPLINE4</title>
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      <div class="title_refTopic" id="xps10_pagetitle">SPLINE4 </div>
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      <h4 class="refClassification">Surface Spline Methods </h4>
      <p class="para_refTopic">Defines a curved surface spline for interpolating motion and/or forces for aeroelastic problems on general aerodynamic geometries using either the Infinite Plate, Thin Plate or Finite Plate splining method. </p>
      <div class="title_refCategory">Format: </div>
      <div class="refCategoryContent">
         <table border="1" width="100%" align="center">
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                     <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>
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                     <p class="para_th">4 </p>
                  </th>
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                     <p class="para_th">5 </p>
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                     <p class="para_th">6 </p>
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                     <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">SPLINE4 </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">AELIST </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">SETG </p>
                  </td>
                  <td align="center" colspan="1" rowspan="1">
                     <p class="para_td">DZ </p>
                  </td>
                  <td align="center" colspan="1" rowspan="1">
                     <p class="para_td">METH </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">NELEM </p>
                  </td>
                  <td align="center" colspan="1" rowspan="1">
                     <p class="para_td">MELEM </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>
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                  <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">Example: </div>
      <div class="refCategoryContent">
         <table border="1" width="100%" align="center">
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                     <p class="para_td">SPLINE4 </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">111 </p>
                  </td>
                  <td align="center" colspan="1" rowspan="1">
                     <p class="para_td">115 </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">14 </p>
                  </td>
                  <td align="center" colspan="1" rowspan="1">
                     <p class="para_td">0. </p>
                  </td>
                  <td align="center" colspan="1" rowspan="1">
                     <p class="para_td">IPS </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">
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                     <p class="para_th"><b class="uiTerm">Field </b></p>
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                     <p class="para_th"><b class="uiTerm">Contents </b></p>
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            </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">Aero panel ID that defines the interpolation surface.  (Integer &gt; 0) </p>
                  </td>
               </tr>
               <tr>
                  <td align="left" colspan="1" rowspan="1" valign="top">
                     <p class="para_td">AELIST </p>
                  </td>
                  <td align="left" colspan="1" rowspan="1" valign="top">
                     <p class="para_td">Identification of an AELIST entry listing boxes with motions that are interpolated using this spline; see Remark <a class="links" href="javascript:void(0)" onclick="top.openFile('QRG/19topic_76.html#ref3ejq1calori');return(false);">104-3</a> when using Mach Box method.  (Integer &gt; 0) 
                     </p>
                  </td>
               </tr>
               <tr>
                  <td align="left" colspan="1" rowspan="1" valign="top">
                     <p class="para_td">SETG </p>
                  </td>
                  <td align="left" colspan="1" rowspan="1" valign="top">
                     <p class="para_td">Refers to the SETi entry that lists the structural grid points to which the spline is attached.  (Integer &gt; 0) </p>
                  </td>
               </tr>
               <tr>
                  <td align="left" colspan="1" rowspan="1" valign="top">
                     <p class="para_td">DZ </p>
                  </td>
                  <td align="left" colspan="1" rowspan="1" valign="top">
                     <p class="para_td">Linear attachment flexibility.  (Real &ge; 0.0) </p>
                  </td>
               </tr>
               <tr>
                  <td align="left" colspan="1" rowspan="1" valign="top">
                     <p class="para_td">METH </p>
                  </td>
                  <td align="left" colspan="1" rowspan="1" valign="top">
                     <p class="para_td">Method for the spline fit.  One of IPS, TPS or FPS.  See Remark <a class="links" href="javascript:void(0)" onclick="top.openFile('QRG/19topic_76.html#refCRZnq21blori');return(false);">104-1. </a> (Character, Default=IPS) 
                     </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_76.html#ref39476');return(false);">104-4. </a> (Character, Default=BOTH) 
                     </p>
                  </td>
               </tr>
               <tr>
                  <td align="left" colspan="1" rowspan="1" valign="top">
                     <p class="para_td">NELEM </p>
                  </td>
                  <td align="left" colspan="1" rowspan="1" valign="top">
                     <p class="para_td">The number of FE elements along the local spline x-axis if using the FPS option. (Integer &gt; 0; Default=10) </p>
                  </td>
               </tr>
               <tr>
                  <td align="left" colspan="1" rowspan="1" valign="top">
                     <p class="para_td">MELEM </p>
                  </td>
                  <td align="left" colspan="1" rowspan="1" valign="top">
                     <p class="para_td">The number of FE elements along the local spline y-axis if using the FPS option. (integer &gt; 0; Default=10) </p>
                  </td>
               </tr>
            </tbody>
         </table><br></div>
      <div class="title_refCategory">Remarks: </div>
      <div class="refCategoryContent">
         <ol type="1" start="1">
            <li><a name="refCRZnq21blori"></a><p class="para_item">The default METHOD will result in the use of the Harder-Desmarais Infinite Plate Spline (IPS).  The other options are the Thin Plate Spline (TPS) and the Finite Plate Spline (FPS). The continuation applies only to the FPS option and is required only if the defaults are not adequate. </p>
            </li>
            <li>
               <p class="para_item">The attachment flexibility (units of area) is used for smoothing the interpolation.  If DZ=0.0, the spline will pass through all deflected grid points.  If DZ is much greater than the spline area, a least squares plane fit will be applied.  Intermediate values will provide smoothing. </p>
            </li>
            <li><a name="ref3ejq1calori"></a><p class="para_item">When using the Mach Box method, the AELIST boxes refer to the ID number of the first and last aerodynamic grids (x,y pairs on the AEFACT entry) which will be used for interpolation to structural grids.  They do not refer to Mach Boxes. </p>
            </li>
            <li><a name="ref39476"></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. </p>
               <p class="para_item">(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>
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