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      <div class="title_refTopic" id="xps10_pagetitle">TSTEPNL </div>
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      <h4 class="refClassification">Parameters for Nonlinear Transient Analysis </h4>
      <p class="para_refTopic">Defines parametric controls and data for nonlinear transient structural or heat transfer analysis.  TSTEPNL is intended for SOLs 129, 159, and 99. </p>
      <div class="title_refCategory">Format: </div>
      <div class="refCategoryContent">
         <table border="1" width="100%" align="center">
            <colgroup span="1">
               <col span="1" width="10.96*">
               <col span="1" width="10.02*">
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               <col span="1" width="10.39*">
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               <col span="1" width="10.96*">
               <col span="1" width="9.45*">
               <col span="1" width="8.14*">
            </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">TSTEPNL </p>
                  </td>
                  <td align="center" colspan="1" rowspan="1">
                     <p class="para_td">ID </p>
                  </td>
                  <td align="center" colspan="1" rowspan="1">
                     <p class="para_td">NDT </p>
                  </td>
                  <td align="center" colspan="1" rowspan="1">
                     <p class="para_td">DT </p>
                  </td>
                  <td align="center" colspan="1" rowspan="1">
                     <p class="para_td">NO </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">KSTEP </p>
                  </td>
                  <td align="center" colspan="1" rowspan="1">
                     <p class="para_td">MAXITER </p>
                  </td>
                  <td align="center" colspan="1" rowspan="1">
                     <p class="para_td">CONV </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">EPSU </p>
                  </td>
                  <td align="center" colspan="1" rowspan="1">
                     <p class="para_td">EPSP </p>
                  </td>
                  <td align="center" colspan="1" rowspan="1">
                     <p class="para_td">EPSW </p>
                  </td>
                  <td align="center" colspan="1" rowspan="1">
                     <p class="para_td">MAXDIV </p>
                  </td>
                  <td align="center" colspan="1" rowspan="1">
                     <p class="para_td">MAXQN </p>
                  </td>
                  <td align="center" colspan="1" rowspan="1">
                     <p class="para_td">MAXLS </p>
                  </td>
                  <td align="center" colspan="1" rowspan="1">
                     <p class="para_td">FSTRESS </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" colspan="1" rowspan="1">
                     <p class="para_td">MAXBIS </p>
                  </td>
                  <td align="center" colspan="1" rowspan="1">
                     <p class="para_td">ADJUST </p>
                  </td>
                  <td align="center" colspan="1" rowspan="1">
                     <p class="para_td">MSTEP </p>
                  </td>
                  <td align="center" colspan="1" rowspan="1">
                     <p class="para_td">RB </p>
                  </td>
                  <td align="center" colspan="1" rowspan="1">
                     <p class="para_td">MAXR </p>
                  </td>
                  <td align="center" colspan="1" rowspan="1">
                     <p class="para_td">UTOL </p>
                  </td>
                  <td align="center" colspan="1" rowspan="1">
                     <p class="para_td">RTOLB </p>
                  </td>
                  <td align="center" bgcolor="gray" 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>
               </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="11.46*">
               <col span="1" width="10.13*">
               <col span="1" width="10.13*">
               <col span="1" width="10.13*">
               <col span="1" width="10.13*">
               <col span="1" width="10.13*">
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               <col span="1" width="10.13*">
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            </colgroup>
            <tbody>
               <tr>
                  <td align="left" colspan="1" rowspan="1" valign="top">
                     <p class="para_td">TSTEPNL </p>
                  </td>
                  <td align="center" colspan="1" rowspan="1">
                     <p class="para_td">250 </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">.01 </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">&nbsp; </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">10 </p>
                  </td>
                  <td align="center" colspan="1" rowspan="1">
                     <p class="para_td">PW </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">1.E-2 </p>
                  </td>
                  <td align="center" colspan="1" rowspan="1">
                     <p class="para_td">1.E-3 </p>
                  </td>
                  <td align="center" colspan="1" rowspan="1">
                     <p class="para_td">1.E-6 </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">10 </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">.02 </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">5 </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">0 </p>
                  </td>
                  <td align="center" colspan="1" rowspan="1">
                     <p class="para_td">0.75 </p>
                  </td>
                  <td align="center" colspan="1" rowspan="1">
                     <p class="para_td">16.0 </p>
                  </td>
                  <td align="center" colspan="1" rowspan="1">
                     <p class="para_td">0.1 </p>
                  </td>
                  <td align="center" colspan="1" rowspan="1">
                     <p class="para_td">20. </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="16.45*">
               <col span="1" width="83.55*">
            </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">ID </p>
                  </td>
                  <td align="left" colspan="1" rowspan="1" valign="top">
                     <p class="para_td">Identification number.  (Integer &gt; 0) </p>
                  </td>
               </tr>
               <tr>
                  <td align="left" colspan="1" rowspan="1" valign="top">
                     <p class="para_td">NDT </p>
                  </td>
                  <td align="left" colspan="1" rowspan="1" valign="top">
                     <p class="para_td">Number of time steps of value DT.  See Remark <a class="links" href="javascript:void(0)" onclick="top.openFile('QRG/20topic_30.html#ref13234');return(false);">41-2. </a> (Integer &ge; 4) 
                     </p>
                  </td>
               </tr>
               <tr>
                  <td align="left" colspan="1" rowspan="1" valign="top">
                     <p class="para_td">DT </p>
                  </td>
                  <td align="left" colspan="1" rowspan="1" valign="top">
                     <p class="para_td">Time increment.  See Remark <a class="links" href="javascript:void(0)" onclick="top.openFile('QRG/20topic_30.html#ref13234');return(false);">41-2. </a> (Real &gt; 0.0) 
                     </p>
                  </td>
               </tr>
               <tr>
                  <td align="left" colspan="1" rowspan="1" valign="top">
                     <p class="para_td">NO </p>
                  </td>
                  <td align="left" colspan="1" rowspan="1" valign="top">
                     <p class="para_td">Time step interval for output.  Every NO-th step will be saved for output.  See Remark <a class="links" href="javascript:void(0)" onclick="top.openFile('QRG/20topic_30.html#ref64358');return(false);">41-3. </a> (Integer &gt; 0; Default=1) 
                     </p>
                  </td>
               </tr>
               <tr>
                  <td align="left" colspan="1" rowspan="1" valign="top">
                     <p class="para_td">KSTEP </p>
                  </td>
                  <td align="left" colspan="1" rowspan="1" valign="top">
                     <p class="para_td">KSTEP is the number of converged bisection solutions between stiffness updates. (Integer &gt; 0; Default=2) </p>
                  </td>
               </tr>
               <tr>
                  <td align="left" colspan="1" rowspan="1" valign="top">
                     <p class="para_td">MAXITER </p>
                  </td>
                  <td align="left" colspan="1" rowspan="1" valign="top">
                     <p class="para_td">Limit on number of iterations for each time step.  See Remark <a class="links" href="javascript:void(0)" onclick="top.openFile('QRG/20topic_30.html#ref95962');return(false);">41-4. </a> (Integer &ne; 0; Default=10) 
                     </p>
                  </td>
               </tr>
               <tr>
                  <td align="left" colspan="1" rowspan="1" valign="top">
                     <p class="para_td">CONV </p>
                  </td>
                  <td align="left" colspan="1" rowspan="1" valign="top">
                     <p class="para_td">Flags to select convergence criteria.  See Remark <a class="links" href="javascript:void(0)" onclick="top.openFile('QRG/20topic_30.html#ref95423');return(false);">41-5. </a> (Character:  &ldquo;U&rdquo;, &ldquo;P&rdquo;, &ldquo;W&rdquo;, or any combination; Default=&ldquo;PW.&rdquo;) 
                     </p>
                  </td>
               </tr>
               <tr>
                  <td align="left" colspan="1" rowspan="1" valign="top">
                     <p class="para_td">EPSU </p>
                  </td>
                  <td align="left" colspan="1" rowspan="1" valign="top">
                     <p class="para_td">Error tolerance for displacement (U) criterion.  (Real &gt; 0.0; Default=1.0E-2) </p>
                  </td>
               </tr>
               <tr>
                  <td align="left" colspan="1" rowspan="1" valign="top">
                     <p class="para_td">EPSP </p>
                  </td>
                  <td align="left" colspan="1" rowspan="1" valign="top">
                     <p class="para_td">Error tolerance for load (P) criterion.  (Real &gt; 0.0; Default=1.0E-3) </p>
                  </td>
               </tr>
               <tr>
                  <td align="left" colspan="1" rowspan="1" valign="top">
                     <p class="para_td">EPSW </p>
                  </td>
                  <td align="left" colspan="1" rowspan="1" valign="top">
                     <p class="para_td">Error tolerance for work (W) criterion.  (Real &gt; 0.0; Default=1.0E-6) </p>
                  </td>
               </tr>
               <tr>
                  <td align="left" colspan="1" rowspan="1" valign="top">
                     <p class="para_td">MAXDIV </p>
                  </td>
                  <td align="left" colspan="1" rowspan="1" valign="top">
                     <p class="para_td">Limit on the number of diverging conditions for a time step before the solution is assumed to diverge.  See Remark <a class="links" href="javascript:void(0)" onclick="top.openFile('QRG/20topic_30.html#ref55813');return(false);">41-6. </a> (Integer &gt; 0; Default=2) 
                     </p>
                  </td>
               </tr>
               <tr>
                  <td align="left" colspan="1" rowspan="1" valign="top">
                     <p class="para_td">MAXQN </p>
                  </td>
                  <td align="left" colspan="1" rowspan="1" valign="top">
                     <p class="para_td">Maximum number of quasi-Newton correction vectors to be saved on the database.  See Remark <a class="links" href="javascript:void(0)" onclick="top.openFile('QRG/20topic_30.html#ref57818');return(false);">41-7. </a> (Integer &ge; 0; Default=10) 
                     </p>
                  </td>
               </tr>
               <tr>
                  <td align="left" colspan="1" rowspan="1" valign="top">
                     <p class="para_td">MAXLS </p>
                  </td>
                  <td align="left" colspan="1" rowspan="1" valign="top">
                     <p class="para_td">Maximum number of line searches allowed per iteration.  See Remark <a class="links" href="javascript:void(0)" onclick="top.openFile('QRG/20topic_30.html#ref57818');return(false);">41-7. </a> (Integer &ge; 0; Default=2) 
                     </p>
                  </td>
               </tr>
               <tr>
                  <td align="left" colspan="1" rowspan="1" valign="top">
                     <p class="para_td">FSTRESS </p>
                  </td>
                  <td align="left" colspan="1" rowspan="1" valign="top">
                     <p class="para_td">Fraction of effective stress <img align="bottom" src="graphics/bulktuv-ufig03.gif" border="0"> used to limit the subincrement size in the material routines.  See Remark <a class="links" href="javascript:void(0)" onclick="top.openFile('QRG/20topic_30.html#ref54470');return(false);">41-8. </a> (0.0 &lt; Real &lt; 1.0; Default=0.2) 
                     </p>
                  </td>
               </tr>
               <tr>
                  <td align="left" colspan="1" rowspan="1" valign="top">
                     <p class="para_td">MAXBIS </p>
                  </td>
                  <td align="left" colspan="1" rowspan="1" valign="top">
                     <p class="para_td">Maximum number of bisections allowed for each time step.  See Remark <a class="links" href="javascript:void(0)" onclick="top.openFile('QRG/20topic_30.html#ref68099');return(false);">41-9. </a> (-9 &le; Integer &le; 9; Default=5) 
                     </p>
                  </td>
               </tr>
               <tr>
                  <td align="left" colspan="1" rowspan="1" valign="top">
                     <p class="para_td">ADJUST </p>
                  </td>
                  <td align="left" colspan="1" rowspan="1" valign="top">
                     <p class="para_td">Time step skip factor for automatic time step adjustment.  See Remark <a class="links" href="javascript:void(0)" onclick="top.openFile('QRG/20topic_30.html#ref19689');return(false);">41-10. </a> (Integer &ge; 0; Default=5) 
                     </p>
                  </td>
               </tr>
               <tr>
                  <td align="left" colspan="1" rowspan="1" valign="top">
                     <p class="para_td">MSTEP </p>
                  </td>
                  <td align="left" colspan="1" rowspan="1" valign="top">
                     <p class="para_td">Number of steps to obtain the dominant period response.  See Remark <a class="links" href="javascript:void(0)" onclick="top.openFile('QRG/20topic_30.html#ref80222');return(false);">41-11. </a> (10 &le; Integer &le; 200; Default=variable between 20 and 40.) 
                     </p>
                  </td>
               </tr>
               <tr>
                  <td align="left" colspan="1" rowspan="1" valign="top">
                     <p class="para_td">RB </p>
                  </td>
                  <td align="left" colspan="1" rowspan="1" valign="top">
                     <p class="para_td">Define bounds for maintaining the same time step for the stepping function during the adaptive process.  See Remark <a class="links" href="javascript:void(0)" onclick="top.openFile('QRG/20topic_30.html#ref80222');return(false);">41-11. </a> (0.1 &le; Real &le; 1.0; Default=0.75) 
                     </p>
                  </td>
               </tr>
               <tr>
                  <td align="left" colspan="1" rowspan="1" valign="top">
                     <p class="para_td">MAXR </p>
                  </td>
                  <td align="left" colspan="1" rowspan="1" valign="top">
                     <p class="para_td">Maximum ratio for the adjusted incremental time relative to DT allowed for time step adjustment.  See Remark <a class="links" href="javascript:void(0)" onclick="top.openFile('QRG/20topic_30.html#ref41821');return(false);">41-12. </a> (1.0 &le; Real &le; 32.0; Default=16.0) 
                     </p>
                  </td>
               </tr>
               <tr>
                  <td align="left" colspan="1" rowspan="1" valign="top">
                     <p class="para_td">UTOL </p>
                  </td>
                  <td align="left" colspan="1" rowspan="1" valign="top">
                     <p class="para_td">Tolerance on displacement or temperature increment below which a special provision is made for numerical stability.  See Remark <a class="links" href="javascript:void(0)" onclick="top.openFile('QRG/20topic_30.html#ref26101');return(false);">41-13. </a> (0.001 &lt; Real &le; 1.0; Default=0.1) 
                     </p>
                  </td>
               </tr>
               <tr>
                  <td align="left" colspan="1" rowspan="1" valign="top">
                     <p class="para_td">RTOLB </p>
                  </td>
                  <td align="left" colspan="1" rowspan="1" valign="top">
                     <p class="para_td">Maximum value of incremental rotation (in degrees) allowed per iteration to activate bisection.  See Remark <a class="links" href="javascript:void(0)" onclick="top.openFile('QRG/20topic_30.html#ref24383');return(false);">41-14. </a> (Real &gt; 2.0; Default=20.0) 
                     </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 TSTEPNL Bulk Data entry is selected by the Case Control command TSTEP=ID.  Each residual structure subcase requires a TSTEP entry and either applied loads via TLOADi data or initial values from a previous subcase.  Multiple subcases are assumed to occur sequentially in time with the initial values of time and displacement conditions of each subcase defined by the end conditions of the previous subcase. </p>
            </li>
            <li><a name="ref13234"></a><p class="para_item">NDT is used to define the total duration for analysis, which is NDT * DT. Since DT is adjusted during the analysis , the actual number of time steps, in general, will not be equal to NDT).  Also, DT is used only as an initial value for the time increment. </p>
            </li>
            <li><a name="ref64358"></a><p class="para_item">For printing and plotting the solution, data recovery is performed at time steps 0, NO, 2 * NO, ..., and the last converged step.  The Case Control command OTIME may also be used to control the output times. </p>
            </li>
            <li><a name="ref95962"></a><p class="para_item">The number of iterations for a time step is limited to MAXITER.  If MAXITER is negative, the analysis is terminated when the divergence condition is encountered twice during the same time step or the solution diverges for five consecutive time steps.  If MAXITER is positive, the program computes the best solution and continues the analysis until divergence occurs again.  If the solution does not converge in MAXITER iterations, the process is treated as a divergent process.  See Remark <a class="links" href="javascript:void(0)" onclick="top.openFile('QRG/20topic_30.html#ref55813');return(false);">41-6. </a></p>
            </li>
            <li><a name="ref95423"></a><p class="para_item">The convergence test flags (U=displacement error test, P=load equilibrium error test, W=work error test) and the error tolerances (EPSU, EPSP, and EPSW) define the convergence criteria.  All requested criteria (combination of U, P, and/or W) are satisfied upon convergence.  Note that at least two iterations are necessary to check the displacement convergence criterion. </p>
            </li>
            <li><a name="ref55813"></a><p class="para_item">MAXDIV provides control over diverging solutions.  Depending on the rate of divergence, the number of diverging solutions (NDIV) is incremented by 1 or 2.  The solution is assumed to diverge when NDIV reaches MAXDIV during the iteration.  If the bisection option is used (allowed MAXBIS times) the time step is bisected upon divergence.  Otherwise, the solution for the time step is repeated with a new stiffness based on the converged state at the beginning of the time step.  If NDIV reaches MAXDIV again within the same time step, the analysis is terminated. </p>
            </li>
            <li><a name="ref57818"></a><p class="para_item">Nonzero values of MAXQN and MAXLS will activate the quasi-Newton update and the line search process, respectively. </p>
            </li>
            <li><a name="ref54470"></a><p class="para_item">The number of subincrements in the material routines is determined such that the subincrement size is approximately FSTRESS,</p>
               <p class="para_item"><img align="bottom" src="graphics/bulktuv-ufig04.gif" border="0">.  FSTRESS is also used to establish a tolerance for error correction in elastoplastic material, i.e., 
               </p>
               <p align="center"><img align="bottom" src="graphics/bulktuv-equ44.gif"></p>
               <p class="para_item">If the limit is exceeded at the converging state, the program will terminate with a fatal error message.  Otherwise, the stress state is adjusted to the current yield surface, resulting in &delta;=0. </p>
            </li>
            <li><a name="ref68099"></a><p class="para_item">The bisection process is activated when divergence occurs and MAXBIS &ne; 0.  The number of bisections for a time increment is limited to |MAXBIS|.  If MAXBIS is positive and the solution does not converge after MAXBIS bisections, the best solution is computed and the analysis is continued to the next time step.  If MAXBIS is negative and the solution does not converge in |MAXBIS| bisection, the analysis is terminated. </p>
            </li>
            <li><a name="ref19689"></a><p class="para_item">ADJUST controls the automatic time stepping.  Since the automatic time step adjustment is based on the mode of response and not on the loading pattern, it may be necessary to limit the adjustable step size when the period of the forcing function is much shorter than the period of dominant response frequency of the structure.  It is the user&rsquo;s responsibility to ensure that the loading history is properly traced with the ADJUST option.  The ADJUST option should be suppressed for the duration of short pulse loading.  If unsure, start with a value for DT that is much smaller than the pulse duration in order to properly represent the loading pattern. </p>
               <ul>
                  <li>
                     <p class="para_item">If ADJUST=0, then the automatic adjustment is deactivated.  This is recommended when the loading consists of short duration pulses. </p>
                  </li>
                  <li>
                     <p class="para_item">If ADJUST &gt; 0, the time increment is continually adjusted for the first few steps until a good value of &Delta;t is obtained.  After this initial adjustment, the time increment is adjusted every ADJUST-th time step only. </p>
                  </li>
                  <li>
                     <p class="para_item">If ADJUST is one order greater than NDT, then automatic adjustment is deactivated after the initial adjustment. </p>
                  </li>
               </ul>
            </li>
            <li><a name="ref80222"></a><p class="para_item">MSTEP and RB are used to adjust the time increment during analysis.  The recommended value of MSTEP for nearly linear problems is 20.  A larger value (e.g., 40) is required for highly nonlinear problems.  By default, the program automatically computes the value of MSTEP based on the changes in the stiffness. </p>
               <p class="para_item">The time increment adjustment is based on the number of time steps desired to capture the dominant frequency response accurately.  The time increment is adjusted as follows: </p>
               <p align="center"><img align="bottom" src="graphics/bulktuv-equ45.gif"></p>
               <p class="para_item">where </p>
               <p class="para_item"></p>
               <p align="center"><img align="bottom" src="graphics/bulktuv-equ46.gif"></p>
               <p class="para_item">with </p>
               <table cellpadding="7" width="100%" align="center">
                  <colgroup span="1">
                     <col span="1" width="6.65*">
                     <col span="1" width="9.34*">
                     <col span="1" width="15.31*">
                     <col span="1" width="16.08*">
                     <col span="1" width="52.63*">
                  </colgroup>
                  <tbody>
                     <tr>
                        <td align="center" colspan="1" rowspan="1">
                           <p class="para_td">f </p>
                        </td>
                        <td align="center" colspan="1" rowspan="1">
                           <p class="para_td">= </p>
                        </td>
                        <td align="center" colspan="1" rowspan="1">
                           <p class="para_td">0.25 </p>
                        </td>
                        <td align="center" colspan="1" rowspan="1">
                           <p class="para_td">for </p>
                        </td>
                        <td align="left" colspan="1" rowspan="1" valign="top">
                           <p class="para_td"><em>r</em> &lt; 0.5 · RB 
                           </p>
                        </td>
                     </tr>
                     <tr>
                        <td align="center" colspan="1" rowspan="1">
                           <p class="para_td">f </p>
                        </td>
                        <td align="center" colspan="1" rowspan="1">
                           <p class="para_td">= </p>
                        </td>
                        <td align="center" colspan="1" rowspan="1">
                           <p class="para_td">0.5 </p>
                        </td>
                        <td align="center" colspan="1" rowspan="1">
                           <p class="para_td">for </p>
                        </td>
                        <td align="left" colspan="1" rowspan="1" valign="top">
                           <p class="para_td">0.5 · RB &le;<em>r</em> &lt; RB 
                           </p>
                        </td>
                     </tr>
                     <tr>
                        <td align="center" colspan="1" rowspan="1">
                           <p class="para_td">f </p>
                        </td>
                        <td align="center" colspan="1" rowspan="1">
                           <p class="para_td">= </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">for </p>
                        </td>
                        <td align="left" colspan="1" rowspan="1" valign="top">
                           <p class="para_td">RB &le; <em>r</em> &lt; 2.0 
                           </p>
                        </td>
                     </tr>
                     <tr>
                        <td align="center" colspan="1" rowspan="1">
                           <p class="para_td">f </p>
                        </td>
                        <td align="center" colspan="1" rowspan="1">
                           <p class="para_td">= </p>
                        </td>
                        <td align="center" colspan="1" rowspan="1">
                           <p class="para_td">2.0 </p>
                        </td>
                        <td align="center" colspan="1" rowspan="1">
                           <p class="para_td">for </p>
                        </td>
                        <td align="left" colspan="1" rowspan="1" valign="top">
                           <p class="para_td">2.0 &le; <em>r</em> &lt; 3.0/RB 
                           </p>
                        </td>
                     </tr>
                     <tr>
                        <td align="center" colspan="1" rowspan="1">
                           <p class="para_td">f </p>
                        </td>
                        <td align="center" colspan="1" rowspan="1">
                           <p class="para_td">= </p>
                        </td>
                        <td align="center" colspan="1" rowspan="1">
                           <p class="para_td">4.0 </p>
                        </td>
                        <td align="center" colspan="1" rowspan="1">
                           <p class="para_td">for </p>
                        </td>
                        <td align="left" colspan="1" rowspan="1" valign="top">
                           <p class="para_td"><em>r</em> &ge; 3.0/RB 
                           </p>
                        </td>
                     </tr>
                  </tbody>
               </table><br></li>
            <li><a name="ref41821"></a><p class="para_item">MAXR is used to define the upper and lower bounds for adjusted time step size, i.e., </p>
               <p align="center"><img align="bottom" src="graphics/bulktuv-equ47.gif"></p>
            </li>
            <li><a name="ref26101"></a><p class="para_item">UTOL is a tolerance used to filter undesirable time step adjustments; i.e., </p>
               <p align="center"><img align="bottom" src="graphics/bulktuv-equ48.gif"></p>
               <p class="para_item">Under this condition no time step adjustment is performed in a structural analysis (SOL 129).  In a heat transfer analysis (SOL 159) the time step is doubled. </p>
            </li>
            <li><a name="ref24383"></a><p class="para_item">The bisection is activated if the incremental rotation for any degree-of-freedom (&Delta;&theta;<em><sub class="subscript">x</sub></em>, &Delta;&theta;<em><sub class="subscript">y</sub></em>, &Delta;&theta;<em><sub class="subscript">z</sub></em>) exceeds the value specified by RTOLB.  This bisection strategy is based on the incremental rotation and controlled by MAXBIS. 
               </p>
            </li>
         </ol>
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