<!DOCTYPE html
  PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN">

<!--
Copyright (c) 2006 UGS Corp.

All Rights Reserved.

This software and related documentation are proprietary to UGS Corp.
-->
<html>
   <head>
      <meta http-equiv="Content-Type" content="text/html; charset=UTF-8">
      <title>NLPARM</title>
      <script language="javaScript">
        abridged="false";
        displayConditions=new Array();
      </script>
      <link type="text/css" href="../css/main_styles.css" rel="stylesheet">
   </head>
   <body class="bodydocs" onload="top.pageLoader()" bgcolor="#FFFFFF">
      <hr noshade="true">
      <div class="title_refTopic" id="xps10_pagetitle">NLPARM </div>
      <hr noshade="true">
      <h4 class="refClassification">Parameters for Nonlinear Static Analysis Control </h4>
      <p class="para_refTopic">Defines a set of parameters for nonlinear static analysis iteration strategy. </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="7.91*">
               <col span="1" width="12.09*">
               <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">NLPARM </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">NINC </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">KMETHOD </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">INTOUT </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" colspan="1" rowspan="1">
                     <p class="para_td">LSTOL </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" 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>
                  <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">MAXR </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">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="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">NLPARM </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">5 </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">ITER </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">
            <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">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">NINC </p>
                  </td>
                  <td align="left" colspan="1" rowspan="1" valign="top">
                     <p class="para_td">Number of increments. See Remark 16. (0 &lt; Integer &lt; 1000; Default=10) </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">Incremental time interval for creep analysis.  See Remark 3. (Real &ge; 0.0; Default = 0.0 for no creep.) </p>
                  </td>
               </tr>
               <tr>
                  <td align="left" colspan="1" rowspan="1" valign="top">
                     <p class="para_td">KMETHOD </p>
                  </td>
                  <td align="left" colspan="1" rowspan="1" valign="top">
                     <p class="para_td">Method for controlling stiffness updates.  See Remark 4. (Character = &ldquo;AUTO&rdquo;, &ldquo;ITER&rdquo;, or &ldquo;SEMI&rdquo;; Default = &ldquo;AUTO&rdquo;.) </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">Number of iterations before the stiffness update for ITER method.  See Remark <b class="uiTerm">5. </b> (Integer &ge; 1; Default = 5) 
                     </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 load increment.  See Remark 6. (Integer &gt; 0; Default = 25) </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 7. (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">INTOUT </p>
                  </td>
                  <td align="left" colspan="1" rowspan="1" valign="top">
                     <p class="para_td">Intermediate output flag.  See Remark 8. (Character = &ldquo;YES&rdquo;, &ldquo;NO&rdquo;, or &ldquo;ALL&rdquo;; Default = NO) </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. See Remark <b class="uiTerm">16. </b> (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. See Remark 16. (Real &gt; 0.0; Usual default = 1.0E-2) </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. See Remark 16. (Real &gt; 0.0; Usual default = 1.0E-2) </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 probable divergence conditions per iteration before the solution is assumed to diverge.  See Remark 9. (Integer &ne; 0; Default = 3) </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 10. (Integer &ge; 0; Default = MAXITER) </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 for each iteration.  See Remark 11. (Integer &ge; 0; Default = 4) </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/bulkmno-ufig09.gif" border="0"> used to limit the subincrement size in the material routines.  See Remark 12. (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">LSTOL </p>
                  </td>
                  <td align="left" colspan="1" rowspan="1" valign="top">
                     <p class="para_td">Line search tolerance.  See Remark 11. (0.01 &lt; Real &lt; 0.9; Default = 0.5) </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 load increment.  See Remark 13. (-10 &le; MAXBIS &le; 10; Default = 5) </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 arc-length increment relative to the initial value.  See Remark 14. (1.0 &le; MAXR &le; 40.0; Default = 20.0) </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 15. (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 NLPARM entry is selected by the Case Control command NLPARM = ID.  Each solution subcase requires an NLPARM command. </p>
            </li>
            <li>
               <p class="para_item">In cases of static analysis (DT = 0.0) using Newton methods, NINC is the number of equal subdivisions of the load change defined for the subcase.  Applied loads, gravity loads, temperature sets, enforced displacements, etc., define the new loading conditions.  The differences from the previous case are divided by NINC to define the incremental values.  In cases of static analysis (DT = 0.0) using arc-length methods, NINC is used to determine the initial arc-length for the subcase, and the number of load subdivisions will not be equal to NINC.  In cases of creep analysis (DT &gt; 0.0), NINC is the number of time step increments. </p>
            </li>
            <li>
               <p class="para_item">The unit of DT must be consistent with the unit used on the CREEP entry that defines the creep characteristics.  Total creep time for the subcase is DT multiplied by the value in the field NINC; i.e., DT*NINC. </p>
            </li>
            <li>
               <p class="para_item">The stiffness update strategy is selected in the KMETHOD field. </p>
               <ul>
                  <li>
                     <p class="para_item">If the AUTO option is selected, the program automatically selects the most efficient strategy based on convergence rates.  At each step the number of iterations required to converge is estimated.  Stiffness is updated, if (i) estimated number of iterations to converge exceeds MAXITER, (ii) estimated time required for convergence with current stiffness exceeds the estimated time required for convergence with updated stiffness, and (iii) solution diverges.  See Remarks 9 and 13. and for diverging solutions. </p>
                  </li>
                  <li>
                     <p class="para_item">If the SEMI option is selected, the program for each load increment (i) performs a single iteration based upon the new load, (ii) updates the stiffness matrix, and (iii) resumes the normal AUTO option. </p>
                  </li>
                  <li>
                     <p class="para_item">If the ITER option is selected, the program updates the stiffness matrix at every KSTEP iterations and on convergence if KSTEP &le; MAXITER.  However, if KSTEP &gt; MAXITER, stiffness matrix is never updated.  Note that the Newton-Raphson iteration strategy is obtained by selecting the ITER option and KSTEP = 1, while the Modified Newton-Raphson iteration strategy is obtained by selecting the ITER option and KSTEP = MAXITER. </p>
                  </li>
               </ul>
            </li>
            <li>
               <p class="para_item">For AUTO and SEMI options, the stiffness matrix is updated on convergence if KSTEP is less than the number of iterations that were required for convergence with the current stiffness. </p>
            </li>
            <li>
               <p class="para_item">The number of iterations for a load increment is limited to MAXITER.  If the solution does not converge in MAXITER iterations, the load increment is bisected and the analysis is repeated.  If the load increment cannot be bisected (i.e., MAXBIS is attained or MAXBIS = 0) and MAXDIV is positive, the best attainable solution is computed and the analysis is continued to the next load increment.  If MAXDIV is negative, the analysis is terminated. </p>
            </li>
            <li>
               <p class="para_item">The test flags (U = displacement error, P = load equilibrium error, and W = work error) and the tolerances (EPSU, EPSP, and EPSW) define the convergence criteria.  All the requested criteria (combination of U, P, and/or W) are satisfied upon convergence.  See the <em>NX Nastran Handbook for Nonlinear Analysis</em> for more details on convergence criteria. 
               </p>
            </li>
            <li>
               <p class="para_item">INTOUT controls the output requests for displacements, element forces and stresses, etc.  YES or ALL must be specified in order to be able to perform a subsequent restart from the middle of a subcase. </p>
               <table border="1" cellpadding="8" width="100%" align="center">
                  <colgroup span="1">
                     <col span="1" width="17.89*">
                     <col span="1" width="82.11*">
                  </colgroup>
                  <thead>
                     <tr>
                        <th align="center" colspan="1" rowspan="1">
                           <p class="para_th"><b class="uiTerm">INTOUT </b></p>
                        </th>
                        <th align="center" colspan="1" rowspan="1">
                           <p class="para_th"><b class="uiTerm">Output Processed </b></p>
                        </th>
                     </tr>
                  </thead>
                  <tbody>
                     <tr>
                        <td align="center" colspan="1" rowspan="1">
                           <p class="para_td">YES </p>
                        </td>
                        <td align="left" colspan="1" rowspan="1" valign="top">
                           <p class="para_td">For every computed load increment. </p>
                        </td>
                     </tr>
                     <tr>
                        <td align="center" colspan="1" rowspan="1">
                           <p class="para_td">NO </p>
                        </td>
                        <td align="left" colspan="1" rowspan="1" valign="top">
                           <p class="para_td">For the last load of the subcase. </p>
                        </td>
                     </tr>
                     <tr>
                        <td align="center" colspan="1" rowspan="1">
                           <p class="para_td">ALL </p>
                        </td>
                        <td align="left" colspan="1" rowspan="1" valign="top">
                           <p class="para_td">For every computed and user-specified load increment. </p>
                        </td>
                     </tr>
                  </tbody>
               </table><br><ul>
                  <li>
                     <p class="para_item">For the Newton family of iteration methods (i.e., when no NLPCI command is specified), the option ALL is equivalent to option YES since the computed load increment is always equal to the user-specified load increment. </p>
                  </li>
                  <li>
                     <p class="para_item">For arc-length methods (i.e., when the NLPCI command is specified) the computed load increment in general is not going to be equal to the user-specified load increment, and is not known in advance.  The option ALL allows the user to obtain solutions at the desired intermediate load increments. </p>
                  </li>
               </ul>
            </li>
            <li>
               <p class="para_item">The ratio of energy errors before and after the iteration is defined as divergence rate (<em>E<sup class="superscript">i</sup></em>), i.e., 
               </p>
               <p align="center"><img align="bottom" src="graphics/bulkmno-equ34.gif"></p>
               <p class="para_item">Depending on the divergence rate, the number of diverging iteration (NDIV) is incremented as follows: </p>
               <p align="center"><img align="bottom" src="graphics/bulkmno-equ35.gif"></p>
               <p align="center"><img align="bottom" src="graphics/bulkmno-equ36.gif"></p>
               <p class="para_item">The solution is assumed to diverge when NDIV &ge; |MAXDIV|.  If the solution diverges and the load increment cannot be further bisected (i.e., MAXBIS is attained or MAXBIS is zero), the stiffness is updated based on the previous iteration and the analysis is continued.  If the solution diverges again in the same load increment while MAXDIV is positive, the best solution is computed and the analysis is continued to the next load increment.  If MAXDIV is negative, the analysis is terminated on the second divergence. </p>
            </li>
            <li>
               <p class="para_item">The BFGS update is performed if MAXQN &gt; 0.  As many as MAXQN quasi-Newton vectors can be accumulated.  The BFGS update with these QN vectors provides a secant modulus in the search direction.  If MAXQN is reached, no additional ON vectors will be accumulated.  Accumulated QN vectors are purged when the stiffness is updated and the accumulation is resumed. </p>
            </li>
            <li>
               <p class="para_item">The line search is performed as required, if MAXLS &gt; 0.  In the line search, the displacement increment is scaled to minimize the energy error.  The line search is not performed if the absolute value of the relative energy error is less than the value specified in LSTOL. </p>
            </li>
            <li>
               <p class="para_item">The number of subincrements in the material routines (elastoplastic and creep) is determined so that the subincrement size is approximately </p>
               <p class="para_item"><img align="bottom" src="graphics/bulkmno-ufig09.gif" border="0"> (equivalent stress).  
               </p>
               <p class="para_item">FSTRESS is also used to establish a tolerance for error correction in the elastoplastic material; i.e., </p>
               <p align="center"><img align="bottom" src="graphics/bulkmno-equ37.gif"></p>
               <p class="para_item">If the limit is exceeded at the converging state, the program will exit with a fatal message.  Otherwise, the stress state is adjusted to the current yield surface. </p>
            </li>
            <li>
               <p class="para_item">The number of bisections for a load increment/arc-length is limited to the absolute value of MAXBIS.  Different actions are taken when the solution diverges depending on the sign of MAXBIS.  If MAXBIS is positive, the stiffness is updated on the first divergence, and the load is bisected on the second divergence.  If MAXBIS is negative, the load is bisected every time the solution diverges until the limit on bisection is reached.  If the solution does not converge after |MAXBIS| bisections, the analysis is continued or terminated depending on the sign of MAXDIV.  See Remark 9.</p>
            </li>
            <li>
               <p class="para_item">MAXR is used in the adaptive load increment/arc-length method to define the overall upper and lower bounds on the load increment/arc-length in the subcase; i.e., </p>
               <p align="center"><img align="bottom" src="graphics/bulkmno-equ38.gif"></p>
               <p class="para_item">where &Delta;<em>l<sub class="subscript">n</sub></em> is the arc-length at step <em>n</em> and &Delta;<em>l<sub class="subscript">o</sub></em> is the original arc-length.  The arc-length method for load increments is selected by an NLPCI Bulk Data entry.  This entry must have the same ID as the NLPARM Bulk Data entry. 
               </p>
            </li>
            <li>
               <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>, or &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>
            <li><a name="ref53132"></a><p class="para_item">Default tolerance sets are determined based on model type and desired accuracy. Accuracy is under user control and can be specified on the PARAM, NLTOL entry. NLTOL&rsquo;s value is used only if the CONV, EPSU, EPSP and EPSW fields are blank, and if NINC is set to a value of 10 or larger. Otherwise, the NLTOL selection will be overridden. The tables below list tolerances according to NLTOL selections: </p><a name="tbl135"></a><div class="title_tableWrapper">Table 16-4. Default Tolerances for Static Nonlinear SOL 106 Models Without Gaps, Contact or Heat Transfer </div>
               <table border="1" width="100%" align="center">
                  <colgroup span="1">
                     <col span="1" width="17.01*">
                     <col span="1" width="20.14*">
                     <col span="1" width="14.30*">
                     <col span="1" width="17.01*">
                     <col span="1" width="15.76*">
                     <col span="1" width="15.76*">
                  </colgroup>
                  <thead>
                     <tr>
                        <th align="center" colspan="1" rowspan="1">
                           <p class="para_th"><b class="uiTerm">NLTOL </b></p>
                        </th>
                        <th align="center" colspan="1" rowspan="1">
                           <p class="para_th"><b class="uiTerm">Designation </b></p>
                        </th>
                        <th align="center" colspan="1" rowspan="1">
                           <p class="para_th"><b class="uiTerm">CONV </b></p>
                        </th>
                        <th align="center" colspan="1" rowspan="1">
                           <p class="para_th"><b class="uiTerm">EPSU </b></p>
                        </th>
                        <th align="center" colspan="1" rowspan="1">
                           <p class="para_th"><b class="uiTerm">EPSP </b></p>
                        </th>
                        <th align="center" colspan="1" rowspan="1">
                           <p class="para_th"><b class="uiTerm">EPSW </b></p>
                        </th>
                     </tr>
                  </thead>
                  <tbody>
                     <tr>
                        <td align="center" colspan="1" rowspan="1">
                           <p class="para_td">0 </p>
                        </td>
                        <td align="left" colspan="1" rowspan="1" valign="top">
                           <p class="para_td">Very high </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">_______ </p>
                        </td>
                        <td align="center" colspan="1" rowspan="1">
                           <p class="para_td">1.0E-3 </p>
                        </td>
                        <td align="center" colspan="1" rowspan="1">
                           <p class="para_td">1.0E-7 </p>
                        </td>
                     </tr>
                     <tr>
                        <td align="center" colspan="1" rowspan="1">
                           <p class="para_td">1 </p>
                        </td>
                        <td align="left" colspan="1" rowspan="1" valign="top">
                           <p class="para_td">High </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">_______ </p>
                        </td>
                        <td align="center" colspan="1" rowspan="1">
                           <p class="para_td">1.0E-2 </p>
                        </td>
                        <td align="center" colspan="1" rowspan="1">
                           <p class="para_td">1.0E-3 </p>
                        </td>
                     </tr>
                     <tr>
                        <td align="center" colspan="1" rowspan="1">
                           <p class="para_td">2 </p>
                        </td>
                        <td align="left" colspan="1" rowspan="1" valign="top">
                           <p class="para_td">Engineering </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">_______ </p>
                        </td>
                        <td align="center" colspan="1" rowspan="1">
                           <p class="para_td">1.0E-2 </p>
                        </td>
                        <td align="center" colspan="1" rowspan="1">
                           <p class="para_td">1.0E-2 </p>
                        </td>
                     </tr>
                     <tr>
                        <td align="center" colspan="1" rowspan="1">
                           <p class="para_td">3 </p>
                        </td>
                        <td align="left" colspan="1" rowspan="1" valign="top">
                           <p class="para_td">Prelim Design </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">_______ </p>
                        </td>
                        <td align="center" colspan="1" rowspan="1">
                           <p class="para_td">1.0E-1 </p>
                        </td>
                        <td align="center" colspan="1" rowspan="1">
                           <p class="para_td">1.0E-1 </p>
                        </td>
                     </tr>
                     <tr>
                        <td align="center" colspan="1" rowspan="1">
                           <p class="para_td">None </p>
                        </td>
                        <td align="left" colspan="1" rowspan="1" valign="top">
                           <p class="para_td">Engineering </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">_______ </p>
                        </td>
                        <td align="center" colspan="1" rowspan="1">
                           <p class="para_td">1.0E-2 </p>
                        </td>
                        <td align="center" colspan="1" rowspan="1">
                           <p class="para_td">1.0E-2 </p>
                        </td>
                     </tr>
                  </tbody>
               </table><br><a name="tbl136"></a><div class="title_tableWrapper">Table 16-5. Default Tolerances for Static Nonlinear SOL 106 Models With Gaps or Contact (Enter NLTOL Values of 0 or 2 Only or Omit the Parameter) </div>
               <table border="1" width="100%" align="center">
                  <colgroup span="1">
                     <col span="1" width="17.01*">
                     <col span="1" width="20.14*">
                     <col span="1" width="14.30*">
                     <col span="1" width="17.01*">
                     <col span="1" width="15.76*">
                     <col span="1" width="15.76*">
                  </colgroup>
                  <thead>
                     <tr>
                        <th align="center" colspan="1" rowspan="1">
                           <p class="para_th"><b class="uiTerm">NLTOL </b></p>
                        </th>
                        <th align="center" colspan="1" rowspan="1">
                           <p class="para_th"><b class="uiTerm">Designation </b></p>
                        </th>
                        <th align="center" colspan="1" rowspan="1">
                           <p class="para_th"><b class="uiTerm">CONV </b></p>
                        </th>
                        <th align="center" colspan="1" rowspan="1">
                           <p class="para_th"><b class="uiTerm">EPSU </b></p>
                        </th>
                        <th align="center" colspan="1" rowspan="1">
                           <p class="para_th"><b class="uiTerm">EPSP </b></p>
                        </th>
                        <th align="center" colspan="1" rowspan="1">
                           <p class="para_th"><b class="uiTerm">EPSW </b></p>
                        </th>
                     </tr>
                  </thead>
                  <tbody>
                     <tr>
                        <td align="center" colspan="1" rowspan="1">
                           <p class="para_td">0 </p>
                        </td>
                        <td align="left" colspan="1" rowspan="1" valign="top">
                           <p class="para_td">Very high </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">_______ </p>
                        </td>
                        <td align="center" colspan="1" rowspan="1">
                           <p class="para_td">1.0E-3 </p>
                        </td>
                        <td align="center" colspan="1" rowspan="1">
                           <p class="para_td">1.0E-7 </p>
                        </td>
                     </tr>
                     <tr>
                        <td align="center" colspan="1" rowspan="1">
                           <p class="para_td">2 </p>
                        </td>
                        <td align="left" colspan="1" rowspan="1" valign="top">
                           <p class="para_td">Engineering </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">_______ </p>
                        </td>
                        <td align="center" colspan="1" rowspan="1">
                           <p class="para_td">1.0E-3 </p>
                        </td>
                        <td align="center" colspan="1" rowspan="1">
                           <p class="para_td">1.0E-5 </p>
                        </td>
                     </tr>
                     <tr>
                        <td align="center" colspan="1" rowspan="1">
                           <p class="para_td">None </p>
                        </td>
                        <td align="left" colspan="1" rowspan="1" valign="top">
                           <p class="para_td">Engineering </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">_______ </p>
                        </td>
                        <td align="center" colspan="1" rowspan="1">
                           <p class="para_td">1.0E-3 </p>
                        </td>
                        <td align="center" colspan="1" rowspan="1">
                           <p class="para_td">1.0E-5 </p>
                        </td>
                     </tr>
                  </tbody>
               </table><br><a name="tbl137"></a><div class="title_tableWrapper">Table 16-6. Default Tolerances for Static Nonlinear SOL 106 or 153 Models With Heat Transfer (Enter NLTOL Value of 0 Only or Omit the Parameter) </div>
               <table border="1" width="100%" align="center">
                  <colgroup span="1">
                     <col span="1" width="17.01*">
                     <col span="1" width="20.14*">
                     <col span="1" width="14.30*">
                     <col span="1" width="17.01*">
                     <col span="1" width="15.76*">
                     <col span="1" width="15.76*">
                  </colgroup>
                  <thead>
                     <tr>
                        <th align="center" colspan="1" rowspan="1">
                           <p class="para_th"><b class="uiTerm">NLTOL </b></p>
                        </th>
                        <th align="center" colspan="1" rowspan="1">
                           <p class="para_th"><b class="uiTerm">Designation </b></p>
                        </th>
                        <th align="center" colspan="1" rowspan="1">
                           <p class="para_th"><b class="uiTerm">CONV </b></p>
                        </th>
                        <th align="center" colspan="1" rowspan="1">
                           <p class="para_th"><b class="uiTerm">EPSU </b></p>
                        </th>
                        <th align="center" colspan="1" rowspan="1">
                           <p class="para_th"><b class="uiTerm">EPSP </b></p>
                        </th>
                        <th align="center" colspan="1" rowspan="1">
                           <p class="para_th"><b class="uiTerm">EPSW </b></p>
                        </th>
                     </tr>
                  </thead>
                  <tbody>
                     <tr>
                        <td align="center" colspan="1" rowspan="1">
                           <p class="para_td">0 </p>
                        </td>
                        <td align="left" colspan="1" rowspan="1" valign="top">
                           <p class="para_td">Very high </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">_______ </p>
                        </td>
                        <td align="center" colspan="1" rowspan="1">
                           <p class="para_td">1.0E-3 </p>
                        </td>
                        <td align="center" colspan="1" rowspan="1">
                           <p class="para_td">1.0E-7 </p>
                        </td>
                     </tr>
                     <tr>
                        <td align="center" colspan="1" rowspan="1">
                           <p class="para_td">None </p>
                        </td>
                        <td align="left" colspan="1" rowspan="1" valign="top">
                           <p class="para_td">Very high </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">_______ </p>
                        </td>
                        <td align="center" colspan="1" rowspan="1">
                           <p class="para_td">1.0E-3 </p>
                        </td>
                        <td align="center" colspan="1" rowspan="1">
                           <p class="para_td">1.0E-7 </p>
                        </td>
                     </tr>
                  </tbody>
               </table><br></li>
         </ol>
      </div>
   </body>
</html>