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      <title>NOLIN2</title>
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      <div class="title_refTopic" id="xps10_pagetitle">NOLIN2 </div>
      <hr noshade="true">
      <h4 class="refClassification">Nonlinear Transient Load as the Product of Two Variables </h4>
      <p class="para_refTopic">Defines nonlinear transient forcing functions of the form </p>
      <p class="para_refTopic"><img align="bottom" src="graphics/bulkmno-equ47.gif" border="0"></p>
      <p class="para_refTopic">where <em>X<sub class="subscript">j</sub></em>(<em>t</em>) and <em>X<sub class="subscript">k</sub></em>(<em>t</em>) can be either displacement or velocity at points GJ and GK in the directions of CJ and CK. 
      </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*">
               <col span="1" width="10*">
               <col span="1" width="10*">
               <col span="1" width="10*">
               <col span="1" width="10*">
               <col span="1" width="10*">
               <col span="1" width="10*">
               <col span="1" width="10*">
               <col span="1" width="10*">
               <col span="1" width="10*">
            </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">NOLIN2 </p>
                  </td>
                  <td align="center" colspan="1" rowspan="1">
                     <p class="para_td">SID </p>
                  </td>
                  <td align="center" colspan="1" rowspan="1">
                     <p class="para_td">GI </p>
                  </td>
                  <td align="center" colspan="1" rowspan="1">
                     <p class="para_td">CI </p>
                  </td>
                  <td align="center" colspan="1" rowspan="1">
                     <p class="para_td">S </p>
                  </td>
                  <td align="center" colspan="1" rowspan="1">
                     <p class="para_td">GJ </p>
                  </td>
                  <td align="center" colspan="1" rowspan="1">
                     <p class="para_td">CJ </p>
                  </td>
                  <td align="center" colspan="1" rowspan="1">
                     <p class="para_td">GK </p>
                  </td>
                  <td align="center" colspan="1" rowspan="1">
                     <p class="para_td">CK </p>
                  </td>
                  <td align="center" bgcolor="gray" 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*">
               <col span="1" width="10*">
               <col span="1" width="10*">
               <col span="1" width="10*">
               <col span="1" width="10*">
               <col span="1" width="10*">
               <col span="1" width="10*">
               <col span="1" width="10*">
               <col span="1" width="10*">
            </colgroup>
            <tbody>
               <tr>
                  <td align="left" colspan="1" rowspan="1" valign="top">
                     <p class="para_td">NOLIN2 </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">2 </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">2.9 </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">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">&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">SID </p>
                  </td>
                  <td align="left" colspan="1" rowspan="1" valign="top">
                     <p class="para_td">Nonlinear load set identification number.  (Integer &gt; 0) </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, scalar, or extra point identification number at which nonlinear load is to be applied.  (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 number for GI.  (0 &le; Integer &le; 6; blank or zero if GI is a scalar or extra point.) </p>
                  </td>
               </tr>
               <tr>
                  <td align="left" colspan="1" rowspan="1" valign="top">
                     <p class="para_td">S </p>
                  </td>
                  <td align="left" colspan="1" rowspan="1" valign="top">
                     <p class="para_td">Scale factor.  (Real) </p>
                  </td>
               </tr>
               <tr>
                  <td align="left" colspan="1" rowspan="1" valign="top">
                     <p class="para_td">GJ, GK </p>
                  </td>
                  <td align="left" colspan="1" rowspan="1" valign="top">
                     <p class="para_td">Grid, scalar, or extra point identification number.  (Integer &gt; 0) </p>
                  </td>
               </tr>
               <tr>
                  <td align="left" colspan="1" rowspan="1" valign="top">
                     <p class="para_td">CJ, CK </p>
                  </td>
                  <td align="left" colspan="1" rowspan="1" valign="top">
                     <p class="para_td">Component number for GJ, GK according to the following table: </p>
                  </td>
               </tr>
            </tbody>
         </table><br><table border="1" width="100%" align="center">
            <colgroup span="1">
               <col span="1" width="30.40*">
               <col span="1" width="33.29*">
               <col span="1" width="36.30*">
            </colgroup>
            <thead>
               <tr>
                  <th align="center" colspan="1" rowspan="1">
                     <p class="para_th"><b class="uiTerm">Type of Point </b></p>
                  </th>
                  <th align="center" colspan="1" rowspan="1">
                     <p class="para_th"><b class="uiTerm">Displacement </b></p>
                  </th>
                  <th align="center" colspan="1" rowspan="1">
                     <p class="para_th"><b class="uiTerm">Velocity </b></p>
                  </th>
               </tr>
            </thead>
            <tbody>
               <tr>
                  <td align="center" colspan="1" rowspan="1">
                     <p class="para_td">Grid </p>
                  </td>
                  <td align="center" colspan="1" rowspan="1">
                     <p class="para_td">1 &le; Integer &le; 6 </p>
                  </td>
                  <td align="center" colspan="1" rowspan="1">
                     <p class="para_td">11 &le; Integer &le; 16 </p>
                  </td>
               </tr>
               <tr>
                  <td align="center" colspan="1" rowspan="1">
                     <p class="para_td">Scalar </p>
                  </td>
                  <td align="center" colspan="1" rowspan="1">
                     <p class="para_td">Blank or zero </p>
                  </td>
                  <td align="center" colspan="1" rowspan="1">
                     <p class="para_td">Integer = 10 </p>
                  </td>
               </tr>
               <tr>
                  <td align="center" colspan="1" rowspan="1">
                     <p class="para_td">Extra </p>
                  </td>
                  <td align="center" colspan="1" rowspan="1">
                     <p class="para_td">Blank or zero </p>
                  </td>
                  <td align="center" colspan="1" rowspan="1">
                     <p class="para_td">Integer = 10 </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">Nonlinear loads must be selected with the Case Control command NONLINEAR=SID. </p>
            </li>
            <li>
               <p class="para_item">Nonlinear loads may not be referenced on a DLOAD entry. </p>
            </li>
            <li>
               <p class="para_item">All degrees-of-freedom referenced on NOLIN2 entries must be members of the solution set.  This means the e-set for modal formulation and the d-set for direct formulation. </p>
            </li>
            <li>
               <p class="para_item">GI-CI, GJ-CJ, and GK-CK may be the same point. </p>
            </li>
            <li>
               <p class="para_item">Nonlinear loads may be a function of displacement (<em>X</em> = <em>u</em>) or velocity <img align="bottom" src="graphics/bulkmno-ufig11.gif" border="0">.  Velocities are denoted by a component number ten greater than the actual component number; i.e., a component of 10 is component 0 (velocity).  The velocity is determined by 
               </p>
               <p align="center"><img align="bottom" src="graphics/bulkmno-equ48.gif"></p>
               <p class="para_item">where &Delta;<em>t</em>is the time step interval and <em>u</em><sub class="subscript"><em>t</em>−1</sub> is the displacement of GJ-CJ or GK-CK for the previous time step. 
               </p>
            </li>
         </ol>
      </div>
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