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      <title>DEQATN</title>
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      <div class="title_refTopic" id="xps10_pagetitle">DEQATN </div>
      <hr noshade="true">
      <h4 class="refClassification">Design Equation Definition </h4>
      <p class="para_refTopic">Defines one or more equations for use in design sensitivity or p-element analysis. </p>
      <div class="title_refCategory">Format: </div>
      <div class="refCategoryContent">
         <table border="1" width="100%" align="center">
            <colgroup span="1">
               <col span="1" width="11.63*">
               <col span="1" width="10.02*">
               <col span="1" width="10.02*">
               <col span="1" width="10.02*">
               <col span="1" width="10.02*">
               <col span="1" width="10.02*">
               <col span="1" width="10.02*">
               <col span="1" width="10.02*">
               <col span="1" width="8.21*">
               <col span="1" width="10.02*">
            </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="center" colspan="1" rowspan="1">
                     <p class="para_td">DEQATN </p>
                  </td>
                  <td align="center" colspan="1" rowspan="1">
                     <p class="para_td">EQID </p>
                  </td>
                  <td align="center" colspan="7" rowspan="1">
                     <p class="para_td">EQUATION </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="8" rowspan="1">
                     <p class="para_td">EQUATION (Cont.) </p>
                  </td>
                  <td align="center" colspan="1" rowspan="1">
                     <p class="para_td">&nbsp; </p>
                  </td>
               </tr>
            </tbody>
         </table><br></div>
      <div class="title_refCategory">Example: </div>
      <div class="refCategoryContent">
         <table border="1" width="100%" align="center">
            <colgroup span="1">
               <col span="1" width="11.71*">
               <col span="1" width="9.92*">
               <col span="1" width="9.92*">
               <col span="1" width="9.92*">
               <col span="1" width="9.92*">
               <col span="1" width="9.92*">
               <col span="1" width="9.92*">
               <col span="1" width="9.92*">
               <col span="1" width="9.92*">
               <col span="1" width="8.92*">
            </colgroup>
            <tbody>
               <tr>
                  <td align="center" colspan="1" rowspan="1">
                     <p class="para_td">DEQATN </p>
                  </td>
                  <td align="center" colspan="1" rowspan="1">
                     <p class="para_td">14 </p>
                  </td>
                  <td align="center" colspan="7" rowspan="1">
                     <p class="para_td">F1 (A, B, C, D, R) = A + B · C − (D ** 3 + 10.0) + sin (PI (1 · R)) </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="8" rowspan="1">
                     <p class="para_td">+ A**2/ (B − C) ; F = A + B − F1 · D </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="21.51*">
               <col span="1" width="78.49*">
            </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">EQID </p>
                  </td>
                  <td align="left" colspan="1" rowspan="1" valign="top">
                     <p class="para_td">Unique equation identification number.  (Integer&gt;0) </p>
                  </td>
               </tr>
               <tr>
                  <td align="left" colspan="1" rowspan="1" valign="top">
                     <p class="para_td">EQUATION </p>
                  </td>
                  <td align="left" colspan="1" rowspan="1" valign="top">
                     <p class="para_td">Equation(s).  See Remarks.  (Character) </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">EQUATION is a single equation or a set of nested equations and is specified in fields 3 through 9 on the first entry and may be continued on fields 2 through 9 on the continuation entries.  On the continuation entries, no commas can appear in columns 1 through 8.  All data in fields 2 through 9 must be specified in columns 9 through 72.  The large-field format is not allowed. </p>
               <p class="para_item">A single equation has the following format: </p>
               <p class="para_item">variable-1 (x1, x2, ..., xn)=expression-1 </p>
               <p class="para_item">A set of nested equations is separated by semicolons and has the format: </p>
               <p align="center"><img align="bottom" src="graphics/bulkde-ufig01.gif"></p>
               <p class="para_item">Expression-i is a collection of constants, real variables, and real functions, separated by operators, and must produce a single real value.  (x1, x2, ..., xn) is the list of all the variable names (except variable-i) that appear in all expressions.  Variable-i may be used in subsequent expressions.  The last equation, variable-m=expression-m, provides the value that is returned to the Bulk Data entry that references EQID; e.g., DRESP2.  The example above represents the following mathematical equations: </p>
               <p align="center"><img align="bottom" src="graphics/bulkde-equ04.gif"></p>
               <p class="para_item">where SIN and PI are intrinsic functions.  See Remark <a class="links" href="javascript:void(0)" onclick="top.openFile('QRG/15topic_9.html#ref38669');return(false);">8-4. </a></p>
            </li>
            <li>
               <p class="para_item">EQUATION may contain embedded blanks.  EQUATION must contain less than 32,000 nonblank characters. If more characters are required for use with a DRESP2 entry, the DRESP2 can be divided into two or more DRESP2 entries with a master DRESP2 referencing subsequent DRESP2s. </p>
            </li>
            <li>
               <p class="para_item">The syntax of the expressions follows FORTRAN language standards.  The allowable arithmetic operations are shown in <a class="links" href="javascript:void(0)" onclick="top.openFile('QRG/15topic_9.html#ref42128');return(false);">Table 14-1</a> in the order of execution precedence.  Parenthesis are used to change the order of precedence.  Operations within parentheses are performed first with the usual order of precedence being maintained within the parentheses. 
               </p><a name="ref42128"></a><div class="title_tableWrapper">Table 14-1. DEQATN Entry Operators </div>
               <table border="1" width="100%" align="center">
                  <colgroup span="1">
                     <col span="1" width="17.64*">
                     <col span="1" width="36*">
                     <col span="1" width="23.12*">
                     <col span="1" width="23.24*">
                  </colgroup>
                  <thead>
                     <tr>
                        <th align="center" colspan="1" rowspan="1">
                           <p class="para_th"><b class="uiTerm">Operator </b></p>
                        </th>
                        <th align="center" colspan="1" rowspan="1">
                           <p class="para_th"><b class="uiTerm">Operation </b></p>
                        </th>
                        <th align="center" colspan="1" rowspan="1">
                           <p class="para_th"><b class="uiTerm">Sample Expressions </b></p>
                        </th>
                        <th align="center" colspan="1" rowspan="1">
                           <p class="para_th"><b class="uiTerm">Interpreted As </b></p>
                        </th>
                     </tr>
                  </thead>
                  <tbody>
                     <tr>
                        <td align="center" colspan="1" rowspan="1">
                           <p class="para_td">-, + </p>
                        </td>
                        <td align="left" colspan="1" rowspan="1" valign="top">
                           <p class="para_td">Negative or Positive immediately preceded by exponentiation </p>
                        </td>
                        <td align="center" colspan="1" rowspan="1">
                           <p class="para_td">X * * -Y </p>
                        </td>
                        <td align="center" colspan="1" rowspan="1">
                           <p class="para_td">X * * (-Y) </p>
                        </td>
                     </tr>
                     <tr>
                        <td align="center" colspan="1" rowspan="1">
                           <p class="para_td">* * </p>
                        </td>
                        <td align="left" colspan="1" rowspan="1" valign="top">
                           <p class="para_td">Exponentiation </p>
                        </td>
                        <td align="center" colspan="1" rowspan="1">
                           <p class="para_td">-X * * Y </p>
                        </td>
                        <td align="center" colspan="1" rowspan="1">
                           <p class="para_td">(-X * * Y) </p>
                        </td>
                     </tr>
                     <tr>
                        <td align="center" colspan="1" rowspan="1">
                           <p class="para_td">-, + </p>
                        </td>
                        <td align="left" colspan="1" rowspan="1" valign="top">
                           <p class="para_td">Negative or Positive </p>
                        </td>
                        <td align="center" colspan="1" rowspan="1">
                           <p class="para_td">-X-Y </p>
                        </td>
                        <td align="center" colspan="1" rowspan="1">
                           <p class="para_td">(-X)-Y </p>
                        </td>
                     </tr>
                     <tr>
                        <td align="center" colspan="1" rowspan="1">
                           <p class="para_td">*, / </p>
                        </td>
                        <td align="left" colspan="1" rowspan="1" valign="top">
                           <p class="para_td">Multiplication or Division </p>
                        </td>
                        <td align="center" colspan="1" rowspan="1">
                           <p class="para_td">X * Y-Z </p>
                        </td>
                        <td align="center" colspan="1" rowspan="1">
                           <p class="para_td">(X * Y)-Z </p>
                        </td>
                     </tr>
                     <tr>
                        <td align="center" colspan="1" rowspan="1">
                           <p class="para_td">+, - </p>
                        </td>
                        <td align="left" colspan="1" rowspan="1" valign="top">
                           <p class="para_td">Addition or Subtraction </p>
                        </td>
                        <td align="center" colspan="1" rowspan="1">
                           <p class="para_td">X+Y </p>
                        </td>
                        <td align="center" colspan="1" rowspan="1">
                           <p class="para_td">X+Y </p>
                        </td>
                     </tr>
                  </tbody>
               </table><br></li>
            <li><a name="ref38669"></a><p class="para_item">The expressions may contain intrinsic functions.  <a class="links" href="javascript:void(0)" onclick="top.openFile('QRG/15topic_9.html#ref71633');return(false);">Table 14-2</a> contains the format and descriptions of functions that may appear in the expressions.  The use of functions that may be discontinuous must be used with caution because they can cause discontinuous derivatives.  These are ABS, DIM, MAX, MIN, and MOD.  For examples and further details see the <em><a class="links" href="javascript:void(0)" onclick="top.popUpPage('QRG/linkInter_target_not_resolved.html#dmap:ref86112:-aux,-home','linkInter','menubar=yes,status=yes,resizable=yes,toolbar=yes,scrollbars=yes,location=no,directories=no');return(false);">NX Nastran DMAP Programmer&rsquo;s Guide</a></em>. 
               </p><a name="ref71633"></a><div class="title_tableWrapper">Table 14-2. DEQATN Entry Functions </div>
               <table border="1" cellpadding="8" width="100%" align="center">
                  <colgroup span="1">
                     <col span="1" width="21.24*">
                     <col span="1" width="20.77*">
                     <col span="1" width="57.99*">
                  </colgroup>
                  <thead>
                     <tr>
                        <th align="center" colspan="1" rowspan="1">
                           <p class="para_th"><b class="uiTerm">Format </b></p>
                        </th>
                        <th align="center" colspan="1" rowspan="1">
                           <p class="para_th"><b class="uiTerm">Description </b></p>
                        </th>
                        <th align="center" colspan="1" rowspan="1">
                           <p class="para_th"><b class="uiTerm">Mathematical Expressions </b></p>
                        </th>
                     </tr>
                  </thead>
                  <tbody>
                     <tr>
                        <td align="left" colspan="1" rowspan="1" valign="top">
                           <p class="para_td">ABS(x) </p>
                        </td>
                        <td align="left" colspan="1" rowspan="1" valign="top">
                           <p class="para_td">absolute value </p>
                        </td>
                        <td align="left" colspan="1" rowspan="1" valign="top">
                           <p class="para_td">|x| </p>
                        </td>
                     </tr>
                     <tr>
                        <td align="left" colspan="1" rowspan="1" valign="top">
                           <p class="para_td">ACOS(x) </p>
                        </td>
                        <td align="left" colspan="1" rowspan="1" valign="top">
                           <p class="para_td">arccosine </p>
                        </td>
                        <td align="left" colspan="1" rowspan="1" valign="top">
                           <p class="para_td">cos<sup class="superscript">-1</sup> x 
                           </p>
                        </td>
                     </tr>
                     <tr>
                        <td align="left" colspan="1" rowspan="1" valign="top">
                           <p class="para_td">ACOSH(x) </p>
                        </td>
                        <td align="left" colspan="1" rowspan="1" valign="top">
                           <p class="para_td">hyperbolic arccosine </p>
                        </td>
                        <td align="left" colspan="1" rowspan="1" valign="top">
                           <p class="para_td">cosh<sup class="superscript">-1</sup> x 
                           </p>
                        </td>
                     </tr>
                     <tr>
                        <td align="left" colspan="1" rowspan="1" valign="top">
                           <p class="para_td">ASIN(x) </p>
                        </td>
                        <td align="left" colspan="1" rowspan="1" valign="top">
                           <p class="para_td">arcsine </p>
                        </td>
                        <td align="left" colspan="1" rowspan="1" valign="top">
                           <p class="para_td">sin<sup class="superscript">-1</sup> x 
                           </p>
                        </td>
                     </tr>
                     <tr>
                        <td align="left" colspan="1" rowspan="1" valign="top">
                           <p class="para_td">ASINH(x) </p>
                        </td>
                        <td align="left" colspan="1" rowspan="1" valign="top">
                           <p class="para_td">hyperbolic arcsine </p>
                        </td>
                        <td align="left" colspan="1" rowspan="1" valign="top">
                           <p class="para_td">sinh<sup class="superscript">-1</sup> x 
                           </p>
                        </td>
                     </tr>
                     <tr>
                        <td align="left" colspan="1" rowspan="1" valign="top">
                           <p class="para_td">ATAN(x) </p>
                        </td>
                        <td align="left" colspan="1" rowspan="1" valign="top">
                           <p class="para_td">arctangent </p>
                        </td>
                        <td align="left" colspan="1" rowspan="1" valign="top">
                           <p class="para_td">tan<sup class="superscript">-1</sup> x 
                           </p>
                        </td>
                     </tr>
                     <tr>
                        <td align="left" colspan="1" rowspan="1" valign="top">
                           <p class="para_td">ATAN2(x,y) </p>
                        </td>
                        <td align="left" colspan="1" rowspan="1" valign="top">
                           <p class="para_td">arctangent of quotient </p>
                        </td>
                        <td align="left" colspan="1" rowspan="1" valign="top">
                           <p class="para_td">tan<sup class="superscript">-1</sup> (x/y) 
                           </p>
                        </td>
                     </tr>
                     <tr>
                        <td align="left" colspan="1" rowspan="1" valign="top">
                           <p class="para_td">ATANH(x) </p>
                        </td>
                        <td align="left" colspan="1" rowspan="1" valign="top">
                           <p class="para_td">hyperbolic arctangent </p>
                        </td>
                        <td align="left" colspan="1" rowspan="1" valign="top">
                           <p class="para_td">tanh<sup class="superscript">-1</sup> x 
                           </p>
                        </td>
                     </tr>
                     <tr>
                        <td align="left" colspan="1" rowspan="1" valign="top">
                           <p class="para_td">ATANH2(x,y) </p>
                        </td>
                        <td align="left" colspan="1" rowspan="1" valign="top">
                           <p class="para_td">hyperbolic arctangent of quotient </p>
                        </td>
                        <td align="left" colspan="1" rowspan="1" valign="top">
                           <p class="para_td">tanh<sup class="superscript">-1</sup> (x/y) 
                           </p>
                        </td>
                     </tr>
                     <tr>
                        <td align="left" colspan="1" rowspan="1" valign="top">
                           <p class="para_td">AVG(X<sub class="subscript">1</sub>, X<sub class="subscript">2</sub>, .., Xn) 
                           </p>
                        </td>
                        <td align="left" colspan="1" rowspan="1" valign="top">
                           <p class="para_td">average </p>
                        </td>
                        <td align="left" colspan="1" rowspan="1" valign="top">
                           <p align="center"><img align="bottom" src="graphics/bulkde-equ05.gif"></p>
                        </td>
                     </tr>
                     <tr>
                        <td align="left" colspan="1" rowspan="1" valign="top">
                           <p class="para_td">COS(x) </p>
                        </td>
                        <td align="left" colspan="1" rowspan="1" valign="top">
                           <p class="para_td">cosine </p>
                        </td>
                        <td align="left" colspan="1" rowspan="1" valign="top">
                           <p class="para_td">cos x </p>
                        </td>
                     </tr>
                     <tr>
                        <td align="left" colspan="1" rowspan="1" valign="top">
                           <p class="para_td">COSH(x) </p>
                        </td>
                        <td align="left" colspan="1" rowspan="1" valign="top">
                           <p class="para_td">hyperbolic cosine </p>
                        </td>
                        <td align="left" colspan="1" rowspan="1" valign="top">
                           <p class="para_td">cosh x </p>
                        </td>
                     </tr>
                     <tr>
                        <td align="left" colspan="1" rowspan="1" valign="top">
                           <p class="para_td">DB(P, PREF) </p>
                        </td>
                        <td align="left" colspan="1" rowspan="1" valign="top">
                           <p class="para_td">sound pressure in decibel </p>
                        </td>
                        <td align="left" colspan="1" rowspan="1" valign="top">
                           <p align="center"><img align="bottom" src="graphics/bulkde-equ06.gif"></p>
                        </td>
                     </tr>
                     <tr>
                        <td align="left" colspan="1" rowspan="1" valign="top">
                           <p class="para_td">DBA(P, PREF, F) </p>
                        </td>
                        <td align="left" colspan="1" rowspan="1" valign="top">
                           <p class="para_td">sound pressure in decibel (perceived) </p>
                        </td>
                        <td align="left" colspan="1" rowspan="1" valign="top">
                           <p align="center"><img align="bottom" src="graphics/bulkde-equ07.gif"></p>
                        </td>
                     </tr>
                     <tr>
                        <td align="left" colspan="1" rowspan="1" valign="top">
                           <p class="para_td">DIM(x,y) </p>
                        </td>
                        <td align="left" colspan="1" rowspan="1" valign="top">
                           <p class="para_td">positive difference </p>
                        </td>
                        <td align="left" colspan="1" rowspan="1" valign="top">
                           <p class="para_td">x-MIN(x,y) </p>
                        </td>
                     </tr>
                     <tr>
                        <td align="left" colspan="1" rowspan="1" valign="top">
                           <p class="para_td">EXP(x) </p>
                        </td>
                        <td align="left" colspan="1" rowspan="1" valign="top">
                           <p class="para_td">exponential </p>
                        </td>
                        <td align="left" colspan="1" rowspan="1" valign="top">
                           <p class="para_td">e<sup class="superscript">x</sup></p>
                        </td>
                     </tr>
                     <tr>
                        <td align="left" colspan="1" rowspan="1" valign="top">
                           <p class="para_td">INVDB(DB, PREF) </p>
                        </td>
                        <td align="left" colspan="1" rowspan="1" valign="top">
                           <p class="para_td">inverse Db </p>
                        </td>
                        <td align="left" colspan="1" rowspan="1" valign="top">
                           <p align="center"><img align="bottom" src="graphics/bulkde-equ08.gif"></p>
                        </td>
                     </tr>
                     <tr>
                        <td align="left" colspan="1" rowspan="1" valign="top">
                           <p class="para_td">INVDBA(DBA, PREF, F) </p>
                        </td>
                        <td align="left" colspan="1" rowspan="1" valign="top">
                           <p class="para_td">inverse Dba </p>
                        </td>
                        <td align="left" colspan="1" rowspan="1" valign="top">
                           <p align="center"><img align="bottom" src="graphics/bulkde-equ09.gif"></p>
                        </td>
                     </tr>
                     <tr>
                        <td align="left" colspan="1" rowspan="1" valign="top">
                           <p class="para_td">LOG(x) </p>
                        </td>
                        <td align="left" colspan="1" rowspan="1" valign="top">
                           <p class="para_td">natural logarithm </p>
                        </td>
                        <td align="left" colspan="1" rowspan="1" valign="top">
                           <p class="para_td">log<sub class="subscript">e</sub> x 
                           </p>
                        </td>
                     </tr>
                     <tr>
                        <td align="left" colspan="1" rowspan="1" valign="top">
                           <p class="para_td">LOG10(x) </p>
                        </td>
                        <td align="left" colspan="1" rowspan="1" valign="top">
                           <p class="para_td">common logarithm </p>
                        </td>
                        <td align="left" colspan="1" rowspan="1" valign="top">
                           <p class="para_td">log<sub class="subscript">10</sub> x 
                           </p>
                        </td>
                     </tr>
                     <tr>
                        <td align="left" colspan="1" rowspan="1" valign="top">
                           <p class="para_td">LOGX(x,y) </p>
                        </td>
                        <td align="left" colspan="1" rowspan="1" valign="top">
                           <p class="para_td">base x logarithm </p>
                        </td>
                        <td align="left" colspan="1" rowspan="1" valign="top">
                           <p class="para_td">log<sub class="subscript">x</sub> y 
                           </p>
                        </td>
                     </tr>
                     <tr>
                        <td align="left" colspan="1" rowspan="1" valign="top">
                           <p class="para_td">MAX(x<sub class="subscript">1</sub>, x<sub class="subscript">2</sub>, ..) 
                           </p>
                        </td>
                        <td align="left" colspan="1" rowspan="1" valign="top">
                           <p class="para_td">maximum </p>
                        </td>
                        <td align="left" colspan="1" rowspan="1" valign="top">
                           <p class="para_td">maximum of x<sub class="subscript">1</sub>, etc. 
                           </p>
                        </td>
                     </tr>
                     <tr>
                        <td align="left" colspan="1" rowspan="1" valign="top">
                           <p class="para_td">MIN(x<sub class="subscript">1</sub>, x<sub class="subscript">2</sub>, ...) 
                           </p>
                        </td>
                        <td align="left" colspan="1" rowspan="1" valign="top">
                           <p class="para_td">minimum </p>
                        </td>
                        <td align="left" colspan="1" rowspan="1" valign="top">
                           <p class="para_td">minimum of x<sub class="subscript">1</sub>, etc. 
                           </p>
                        </td>
                     </tr>
                     <tr>
                        <td align="left" colspan="1" rowspan="1" valign="top">
                           <p class="para_td">MOD(x,y) </p>
                        </td>
                        <td align="left" colspan="1" rowspan="1" valign="top">
                           <p class="para_td">remainder (modulo) </p>
                        </td>
                        <td align="left" colspan="1" rowspan="1" valign="top">
                           <p class="para_td">x − y · (INT (x / y)) </p>
                        </td>
                     </tr>
                     <tr>
                        <td align="left" colspan="1" rowspan="1" valign="top">
                           <p class="para_td">PI(x) </p>
                        </td>
                        <td align="left" colspan="1" rowspan="1" valign="top">
                           <p class="para_td">multiples of pi (&pi;) </p>
                        </td>
                        <td align="left" colspan="1" rowspan="1" valign="top">
                           <p class="para_td">x · &pi; </p>
                        </td>
                     </tr>
                     <tr>
                        <td align="left" colspan="1" rowspan="1" valign="top">
                           <p class="para_td">RSS(X<sub class="subscript">1</sub>, ..., Xn) 
                           </p>
                        </td>
                        <td align="left" colspan="1" rowspan="1" valign="top">
                           <p class="para_td">square root of sum of squares </p>
                        </td>
                        <td align="left" colspan="1" rowspan="1" valign="top">
                           <p align="center"><img align="bottom" src="graphics/bulkde-equ10.gif"></p>
                        </td>
                     </tr>
                     <tr>
                        <td align="left" colspan="1" rowspan="1" valign="top">
                           <p class="para_td">SIN(x) </p>
                        </td>
                        <td align="left" colspan="1" rowspan="1" valign="top">
                           <p class="para_td">sine </p>
                        </td>
                        <td align="left" colspan="1" rowspan="1" valign="top">
                           <p class="para_td">sin x </p>
                        </td>
                     </tr>
                     <tr>
                        <td align="left" colspan="1" rowspan="1" valign="top">
                           <p class="para_td">SINH(x) </p>
                        </td>
                        <td align="left" colspan="1" rowspan="1" valign="top">
                           <p class="para_td">hyperbolic sine </p>
                        </td>
                        <td align="left" colspan="1" rowspan="1" valign="top">
                           <p class="para_td">sinh x </p>
                        </td>
                     </tr>
                     <tr>
                        <td align="left" colspan="1" rowspan="1" valign="top">
                           <p class="para_td">SQRT(x) </p>
                        </td>
                        <td align="left" colspan="1" rowspan="1" valign="top">
                           <p class="para_td">square root </p>
                        </td>
                        <td align="left" colspan="1" rowspan="1" valign="top">
                           <p align="center"><img align="bottom" src="graphics/bulkde-equ11.gif"></p>
                        </td>
                     </tr>
                     <tr>
                        <td align="left" colspan="1" rowspan="1" valign="top">
                           <p class="para_td">SSQ(X<sub class="subscript">1</sub>, ..., Xn) 
                           </p>
                        </td>
                        <td align="left" colspan="1" rowspan="1" valign="top">
                           <p class="para_td">sum of squares </p>
                        </td>
                        <td align="left" colspan="1" rowspan="1" valign="top">
                           <p align="center"><img align="bottom" src="graphics/bulkde-equ12.gif"></p>
                        </td>
                     </tr>
                     <tr>
                        <td align="left" colspan="1" rowspan="1" valign="top">
                           <p class="para_td">SUM(X<sub class="subscript">1</sub>, ..., Xn) 
                           </p>
                        </td>
                        <td align="left" colspan="1" rowspan="1" valign="top">
                           <p class="para_td">summation </p>
                        </td>
                        <td align="left" colspan="1" rowspan="1" valign="top">
                           <p align="center"><img align="bottom" src="graphics/bulkde-equ13.gif"></p>
                        </td>
                     </tr>
                     <tr>
                        <td align="left" colspan="1" rowspan="1" valign="top">
                           <p class="para_td">TAN(x) </p>
                        </td>
                        <td align="left" colspan="1" rowspan="1" valign="top">
                           <p class="para_td">tangent </p>
                        </td>
                        <td align="left" colspan="1" rowspan="1" valign="top">
                           <p class="para_td">tan x </p>
                        </td>
                     </tr>
                     <tr>
                        <td align="left" colspan="1" rowspan="1" valign="top">
                           <p class="para_td">TANH(x) </p>
                        </td>
                        <td align="left" colspan="1" rowspan="1" valign="top">
                           <p class="para_td">hyperbolic tangent </p>
                        </td>
                        <td align="left" colspan="1" rowspan="1" valign="top">
                           <p class="para_td">tanh x </p>
                        </td>
                     </tr>
                  </tbody>
               </table><br><table cellpadding="9" width="100%" align="center">
                  <colgroup span="1">
                     <col span="1" width="21.63*">
                     <col span="1" width="9.31*">
                     <col span="1" width="69.05*">
                  </colgroup>
                  <tbody>
                     <tr>
                        <td align="right" colspan="1" rowspan="1">
                           <p class="para_td">X<sub class="subscript">1</sub>, X<sub class="subscript">2</sub>, .., Xn,P 
                           </p>
                        </td>
                        <td align="center" colspan="1" rowspan="1">
                           <p class="para_td">= </p>
                        </td>
                        <td align="left" colspan="1" rowspan="1" valign="top">
                           <p class="para_td">structure responses or acoustic pressure </p>
                        </td>
                     </tr>
                     <tr>
                        <td align="right" colspan="1" rowspan="1">
                           <p class="para_td">PREF </p>
                        </td>
                        <td align="center" colspan="1" rowspan="1">
                           <p class="para_td">= </p>
                        </td>
                        <td align="left" colspan="1" rowspan="1" valign="top">
                           <p class="para_td">reference pressure </p>
                        </td>
                     </tr>
                     <tr>
                        <td align="right" 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="left" colspan="1" rowspan="1" valign="top">
                           <p class="para_td">forcing frequency </p>
                        </td>
                     </tr>
                     <tr>
                        <td align="right" colspan="1" rowspan="1">
                           <p class="para_td">DB </p>
                        </td>
                        <td align="center" colspan="1" rowspan="1">
                           <p class="para_td">= </p>
                        </td>
                        <td align="left" colspan="1" rowspan="1" valign="top">
                           <p class="para_td">acoustic pressure in Decibel </p>
                        </td>
                     </tr>
                     <tr>
                        <td align="right" colspan="1" rowspan="1">
                           <p class="para_td">DBA </p>
                        </td>
                        <td align="center" colspan="1" rowspan="1">
                           <p class="para_td">= </p>
                        </td>
                        <td align="left" colspan="1" rowspan="1" valign="top">
                           <p class="para_td">perceived acoustic pressure in Decibel </p>
                        </td>
                     </tr>
                     <tr>
                        <td align="right" colspan="1" rowspan="1">
                           <p class="para_td"><em>T<sub class="subscript">a</sub></em>1 
                           </p>
                        </td>
                        <td align="center" colspan="1" rowspan="1">
                           <p class="para_td">= </p>
                        </td>
                        <td align="left" colspan="1" rowspan="1" valign="top">
                           <p align="center"><img align="bottom" src="graphics/bulkde-equ14.gif"></p>
                        </td>
                     </tr>
                     <tr>
                        <td align="right" colspan="1" rowspan="1">
                           <p class="para_td"><em>T<sub class="subscript">a</sub></em>2 
                           </p>
                        </td>
                        <td align="center" colspan="1" rowspan="1">
                           <p class="para_td">= </p>
                        </td>
                        <td align="left" colspan="1" rowspan="1" valign="top">
                           <p align="center"><img align="bottom" src="graphics/bulkde-equ15.gif"></p>
                        </td>
                     </tr>
                     <tr>
                        <td align="right" colspan="1" rowspan="1">
                           <p class="para_td"><em>K</em>1 
                           </p>
                        </td>
                        <td align="center" colspan="1" rowspan="1">
                           <p class="para_td">= </p>
                        </td>
                        <td align="left" colspan="1" rowspan="1" valign="top">
                           <p class="para_td">2.242882e+16 </p>
                        </td>
                     </tr>
                     <tr>
                        <td align="right" colspan="1" rowspan="1">
                           <p class="para_td"><em>K</em>3 
                           </p>
                        </td>
                        <td align="center" colspan="1" rowspan="1">
                           <p class="para_td">= </p>
                        </td>
                        <td align="left" colspan="1" rowspan="1" valign="top">
                           <p class="para_td">1.562339 </p>
                        </td>
                     </tr>
                     <tr>
                        <td align="right" colspan="1" rowspan="1">
                           <p class="para_td"><em>P</em>1 
                           </p>
                        </td>
                        <td align="center" colspan="1" rowspan="1">
                           <p class="para_td">= </p>
                        </td>
                        <td align="left" colspan="1" rowspan="1" valign="top">
                           <p class="para_td">20.598997 </p>
                        </td>
                     </tr>
                     <tr>
                        <td align="right" colspan="1" rowspan="1">
                           <p class="para_td"><em>P</em>2 
                           </p>
                        </td>
                        <td align="center" colspan="1" rowspan="1">
                           <p class="para_td">= </p>
                        </td>
                        <td align="left" colspan="1" rowspan="1" valign="top">
                           <p class="para_td">107.65265 </p>
                        </td>
                     </tr>
                     <tr>
                        <td align="right" colspan="1" rowspan="1">
                           <p class="para_td"><em>P</em>3
                           </p>
                        </td>
                        <td align="center" colspan="1" rowspan="1">
                           <p class="para_td">= </p>
                        </td>
                        <td align="left" colspan="1" rowspan="1" valign="top">
                           <p class="para_td">737.86223 </p>
                        </td>
                     </tr>
                     <tr>
                        <td align="right" colspan="1" rowspan="1">
                           <p class="para_td"><em>P</em>4 
                           </p>
                        </td>
                        <td align="center" colspan="1" rowspan="1">
                           <p class="para_td">= </p>
                        </td>
                        <td align="left" colspan="1" rowspan="1" valign="top">
                           <p class="para_td">12194.22 </p>
                        </td>
                     </tr>
                  </tbody>
               </table><br></li>
            <li>
               <p class="para_item">If the DEQATN entry is referenced by the: </p>
               <ul>
                  <li>
                     <p class="para_item">DVPREL2 entry, then X<em><sub class="subscript">i</sub></em> represents the DVIDj and LABLk fields. 
                     </p>
                  </li>
                  <li>
                     <p class="para_item">DRESP2 entry, then X<em><sub class="subscript">i</sub></em> represents the DVIDj, LABLk, NRm,  Gp, DPIPq, DCICr, DMIMs, DPI2Pt, DCI2Cu, DMI2Mv, and NRRw fields in that order. 
                     </p>
                  </li>
                  <li>
                     <p class="para_item">GMLOAD, GMBC, or TEMPF entries, then </p>
                     <p class="para_item"><em>X</em><sub class="subscript">1</sub> represents x in the basic coordinate system, 
                     </p>
                     <p class="para_item"><em>X</em><sub class="subscript">2</sub> represents y in the basic coordinate system, and 
                     </p>
                     <p class="para_item"><em>X</em><sub class="subscript">3</sub> represents z in the basic coordinate system. 
                     </p>
                  </li>
                  <li>
                     <p class="para_item">GMCURV entry, then </p>
                     <p class="para_item"><em>X</em><sub class="subscript">1</sub> represents line parameter u. 
                     </p>
                  </li>
                  <li>
                     <p class="para_item">GMSURF entry, then </p>
                     <p class="para_item"><em>X</em><sub class="subscript">1</sub> represents surface parameter u and 
                     </p>
                     <p class="para_item"><em>X</em><sub class="subscript">2</sub> represents surface parameter v. 
                     </p>
                  </li>
               </ul>
            </li>
            <li>
               <p class="para_item">If the DEQATN entry is referenced by the GMLOAD, GMBC, TEMPF, GMCURV, or GMSURF entries and your computer has a short word length (e.g., 32 bits/word), then EQUATION is processed with double precision and constants may be specified in double precision; e.g., 1.2D0.  If your machine has a long word length (e.g., 64 bits/word) then EQUATION is processed in single precision and constants must be specified in single precision; e.g., 1.2. </p>
            </li>
            <li>
               <p class="para_item">The DMAP logical operators NOT, AND, OR, XOR, and XQV cannot be used as X<sub class="subscript">i</sub> names. 
               </p>
            </li>
            <li>
               <p class="para_item">Input errors on the DEQATN entry often result in poor messages.  Substituting a &ldquo;[&rdquo; for a parenthesis or violating the restriction against large field format are examples.  Known messages are UFM 215, SFM 233 and UFM 5199.  If any of these messages are encountered then, review the DEQATN entry input. </p>
            </li>
            <li>
               <p class="para_item">Intrinsic functions MAX and MIN are limited to &lt;100 arguments. If more arguments are desired, the functions may be concatenated. </p>
            </li>
            <li>
               <p class="para_item">Arithmetic is carried out using the type of the input data. For example, in the expression: </p>
               <p class="para_item"><em>X</em> = <em>A</em>**(1/2) 
               </p>
               <p class="para_item">both values in the exponent are integers so that the value returned for the exponent is calculated using integer arithmetic or 1/2 = 0. In this case 1/2 should be replaced by (.5). </p>
            </li>
         </ol>
      </div>
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