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      <div class="title_refTopic" id="xps10_pagetitle">PGAP </div>
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      <h4 class="refClassification">Gap Element Property </h4>
      <p class="para_refTopic">Defines the properties of the gap element (CGAP entry). </p>
      <div class="title_refCategory">Format: </div>
      <div class="refCategoryContent">
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                     <p class="para_th">1 </p>
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                     <p class="para_th">2 </p>
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                     <p class="para_th">3 </p>
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                     <p class="para_th">4 </p>
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                     <p class="para_th">5 </p>
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                     <p class="para_th">6 </p>
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                     <p class="para_th">7 </p>
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                     <p class="para_th">8 </p>
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                     <p class="para_th">9 </p>
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                     <p class="para_th">10 </p>
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            <tbody>
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                  <td align="left" colspan="1" rowspan="1" valign="top">
                     <p class="para_td">PGAP </p>
                  </td>
                  <td align="center" colspan="1" rowspan="1">
                     <p class="para_td">PID </p>
                  </td>
                  <td align="center" colspan="1" rowspan="1">
                     <p class="para_td">U0 </p>
                  </td>
                  <td align="center" colspan="1" rowspan="1">
                     <p class="para_td">F0 </p>
                  </td>
                  <td align="center" colspan="1" rowspan="1">
                     <p class="para_td">KA </p>
                  </td>
                  <td align="center" colspan="1" rowspan="1">
                     <p class="para_td">KB </p>
                  </td>
                  <td align="center" colspan="1" rowspan="1">
                     <p class="para_td">KT </p>
                  </td>
                  <td align="center" colspan="1" rowspan="1">
                     <p class="para_td">MU1 </p>
                  </td>
                  <td align="center" colspan="1" rowspan="1">
                     <p class="para_td">MU2 </p>
                  </td>
                  <td align="center" colspan="1" rowspan="1">
                     <p class="para_td">&nbsp; </p>
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                  <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">TMAX </p>
                  </td>
                  <td align="center" colspan="1" rowspan="1">
                     <p class="para_td">MAR </p>
                  </td>
                  <td align="center" colspan="1" rowspan="1">
                     <p class="para_td">TRMIN </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>
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                     <p class="para_td">&nbsp; </p>
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                     <p class="para_td">&nbsp; </p>
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                  <td align="center" bgcolor="gray" colspan="1" rowspan="1">
                     <p class="para_td">&nbsp; </p>
                  </td>
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                     <p class="para_td">&nbsp; </p>
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      <div class="title_refCategory">Example: </div>
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                     <p class="para_td">PGAP </p>
                  </td>
                  <td align="center" colspan="1" rowspan="1">
                     <p class="para_td">2 </p>
                  </td>
                  <td align="center" colspan="1" rowspan="1">
                     <p class="para_td">.025 </p>
                  </td>
                  <td align="center" colspan="1" rowspan="1">
                     <p class="para_td">2.5 </p>
                  </td>
                  <td align="center" colspan="1" rowspan="1">
                     <p class="para_td">1.E6 </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">1.E6 </p>
                  </td>
                  <td align="center" colspan="1" rowspan="1">
                     <p class="para_td">0.25 </p>
                  </td>
                  <td align="center" colspan="1" rowspan="1">
                     <p class="para_td">0.25 </p>
                  </td>
                  <td align="center" colspan="1" rowspan="1">
                     <p class="para_td">&nbsp; </p>
                  </td>
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      <div class="title_refCategory">Fields:</div>
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                     <p class="para_th"><b class="uiTerm">Field </b></p>
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                     <p class="para_th"><b class="uiTerm">Contents </b></p>
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                     <p class="para_td">PID </p>
                  </td>
                  <td align="left" colspan="1" rowspan="1" valign="top">
                     <p class="para_td">Property identification number.  (Integer &gt; 0) </p>
                  </td>
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                     <p class="para_td">U0 </p>
                  </td>
                  <td align="left" colspan="1" rowspan="1" valign="top">
                     <p class="para_td">Initial gap opening.  See <a class="links" href="javascript:void(0)" onclick="top.openFile('QRG/18topic_36.html#ref85108');return(false);">Figure 17-</a>.  (Real; Default = 0.0) 
                     </p>
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                     <p class="para_td">F0 </p>
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                  <td align="left" colspan="1" rowspan="1" valign="top">
                     <p class="para_td">Preload.  See <a class="links" href="javascript:void(0)" onclick="top.openFile('QRG/18topic_36.html#ref85108');return(false);">Figure 17-</a>.  (Real &ge; 0.0; Default = 0.0) 
                     </p>
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                     <p class="para_td">KA </p>
                  </td>
                  <td align="left" colspan="1" rowspan="1" valign="top">
                     <p class="para_td">Axial stiffness for the closed gap; i.e., <em>U<sub class="subscript">a</sub></em> − <em>U<sub class="subscript">b</sub></em>&gt; <em>U</em>0.  See <a class="links" href="javascript:void(0)" onclick="top.openFile('QRG/18topic_36.html#ref85108');return(false);">Figure 17-</a>.  (Real &ge; 0.0) 
                     </p>
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                     <p class="para_td">KB </p>
                  </td>
                  <td align="left" colspan="1" rowspan="1" valign="top">
                     <p class="para_td">Axial stiffness for the open gap; i.e., <em>U<sub class="subscript">a</sub></em> − <em>U<sub class="subscript">b</sub></em>&lt; <em>U</em>0.  See <a class="links" href="javascript:void(0)" onclick="top.openFile('QRG/18topic_36.html#ref85108');return(false);">Figure 17-</a>.  See Remark <a class="links" href="javascript:void(0)" onclick="top.openFile('QRG/18topic_36.html#refzOjHi39clori');return(false);">55-2. </a> (Real &ge; 0.0; Default = MU1 · KA) 
                     </p>
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                     <p class="para_td">KT </p>
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                     <p class="para_td">Transverse stiffness when the gap is closed.  See <a class="links" href="javascript:void(0)" onclick="top.openFile('QRG/18topic_36.html#ref38846');return(false);">Figure 17-</a>.  It is recommended that KT &ge; (0.1 · KA).  (Real &ge; 0.0; Default = MUI · KA) 
                     </p>
                  </td>
               </tr>
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                  <td align="left" colspan="1" rowspan="1" valign="top">
                     <p class="para_td">MU1 </p>
                  </td>
                  <td align="left" colspan="1" rowspan="1" valign="top">
                     <p class="para_td">Coefficient of static friction (&mu;<em><sub class="subscript">s</sub></em>) for the adaptive gap element or coefficient of friction in the y transverse direction (&mu;<em><sub class="subscript">y</sub></em>) for the nonadaptive gap element.  See Remark <a class="links" href="javascript:void(0)" onclick="top.openFile('QRG/18topic_36.html#ref15554');return(false);">55-3. </a> and <a class="links" href="javascript:void(0)" onclick="top.openFile('QRG/18topic_36.html#ref38846');return(false);">Figure 17-</a>.  (Real &ge; 0.0; Default = 0.0) 
                     </p>
                  </td>
               </tr>
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                  <td align="left" colspan="1" rowspan="1" valign="top">
                     <p class="para_td">MU2 </p>
                  </td>
                  <td align="left" colspan="1" rowspan="1" valign="top">
                     <p class="para_td">Coefficient of kinetic friction (&mu;<em><sub class="subscript">k</sub></em>) for the adaptive gap element or coefficient of friction in the z transverse direction (&mu;<em><sub class="subscript">z</sub></em>) for the nonadaptive gap element.  See Remark <a class="links" href="javascript:void(0)" onclick="top.openFile('QRG/18topic_36.html#ref15554');return(false);">55-3. </a> and <a class="links" href="javascript:void(0)" onclick="top.openFile('QRG/18topic_36.html#ref38846');return(false);">Figure 17-</a>.  (Real &ge; 0.0 for the adaptive gap element, MU2 &le; MU1; Default = MU1) 
                     </p>
                  </td>
               </tr>
               <tr>
                  <td align="left" colspan="1" rowspan="1" valign="top">
                     <p class="para_td">TMAX </p>
                  </td>
                  <td align="left" colspan="1" rowspan="1" valign="top">
                     <p class="para_td">Maximum allowable penetration used in the adjustment of penalty values.  The positive value activates the penalty value adjustment.  See Remark <a class="links" href="javascript:void(0)" onclick="top.openFile('QRG/18topic_36.html#ref83469');return(false);">55-4. </a> (Real; Default = 0.0) 
                     </p>
                  </td>
               </tr>
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                  <td align="left" colspan="1" rowspan="1" valign="top">
                     <p class="para_td">MAR </p>
                  </td>
                  <td align="left" colspan="1" rowspan="1" valign="top">
                     <p class="para_td">Maximum allowable adjustment ratio for adaptive penalty values KA and KT.  See Remark <a class="links" href="javascript:void(0)" onclick="top.openFile('QRG/18topic_36.html#ref63948');return(false);">55-5. </a> (1.0 &lt; Real &lt; 10<sup class="superscript">6</sup>; Default = 100.0) 
                     </p>
                  </td>
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                  <td align="left" colspan="1" rowspan="1" valign="top">
                     <p class="para_td">TRMIN </p>
                  </td>
                  <td align="left" colspan="1" rowspan="1" valign="top">
                     <p class="para_td">Fraction of TMAX defining the lower bound for the allowable penetration.  See Remark <a class="links" href="javascript:void(0)" onclick="top.openFile('QRG/18topic_36.html#ref67324');return(false);">55-6. </a> (0.0 &le; Real &le; 1.0; Default = 0.001) 
                     </p>
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         </table><br></div>
      <div class="title_refCategory">Remarks: </div>
      <div class="refCategoryContent">
         <ol type="1" start="1">
            <li>
               <p class="para_item"><a class="links" href="javascript:void(0)" onclick="top.openFile('QRG/18topic_36.html#ref72072');return(false);">Figure 17-</a>, <a class="links" href="javascript:void(0)" onclick="top.openFile('QRG/18topic_36.html#ref85108');return(false);">Figure 17-</a>, and <a class="links" href="javascript:void(0)" onclick="top.openFile('QRG/18topic_36.html#ref38846');return(false);">Figure 17-</a> show the gap element and the force-displacement curves used in the stiffness and force computations for the element. 
               </p>
            </li>
            <li><a name="refzOjHi39clori"></a><p class="para_item"> For most contact problems, KA (penalty value) should be chosen to be three orders of magnitude higher than the stiffness of the neighboring grid points.  A much larger KA value may slow convergence or cause divergence, while a much smaller KA value may result in inaccurate results.  The value is adjusted as necessary if TMAX &gt; 0.0. </p>
            </li>
            <li><a name="ref15554"></a><p class="para_item">When the gap is open, there is no transverse stiffness.  When the gap is closed and there is friction, the gap has the elastic stiffness (KT) in the transverse direction until the friction force is exceeded and slippage starts to occur. </p>
            </li>
            <li><a name="ref83469"></a><p class="para_item">There are two kinds of gap elements:  adaptive gap and nonadaptive gap.  If TMAX&ge;0.0, the adaptive gap element is selected by the program.  When TMAX=0.0, penalty values will not be adjusted, but other adaptive features will be active (i.e., the gap-induced stiffness update, gap-induced bisection, and subincremental process).  The value of TMAX = -1.0 selects the nonadaptive (old) gap element.  The recommended allowable penetration TMAX is about 10% of the element thickness for plates or the equivalent thickness for other elements that are connected to the gap. </p>
            </li>
            <li><a name="ref63948"></a><p class="para_item">The maximum adjustment ratio MAR is used only for the adaptive gap element.  Upper and lower bounds of the adjusted penalty are defined by </p>
               <p align="center"><img align="bottom" src="graphics/bulkp-equ31.gif"></p>
               <p class="para_item">where <em>K<sup class="superscript">init</sup></em> is either KA or KT. 
               </p>
            </li>
            <li><a name="ref67324"></a><p class="para_item">TRMIN is used only for the penalty value adjustment in the adaptive gap element.  The lower bound for the allowable penetration is computed by TRMIN * TMAX.  The penalty values are decreased if the penetration is below the lower bound. </p><a name="ref72072"></a><div class="figure">
                  <p align="center"><img align="bottom" src="graphics/bulkp-fig12.gif"></p>
               </div>
               <div class="title_figure">Figure. The CGAP Element Coordinate System </div><a name="ref85108"></a><div class="figure">
                  <p align="center"><img align="bottom" src="graphics/bulkp-fig13.gif"></p>
               </div>
               <div class="title_figure">Figure.   CGAP Element Force-Deflection Curve for Nonlinear Analysis </div><a name="ref38846"></a><div class="figure">
                  <p align="center"><img align="bottom" src="graphics/bulkp-fig14.gif"></p>
               </div>
               <div class="title_figure">Figure. Shear Force for CGAP Element </div>
            </li>
            <li>
               <p class="para_item">If U0 is specified negative and GA and GB are not coincident, then the direction for closing must be controlled by the use of the CID field on the CBAP entry. </p>
            </li>
         </ol>
      </div>
      <div class="title_refCategory">Remarks related to SOLs 601 and 701: </div>
      <div class="refCategoryContent">
         <ol type="1" start="1">
            <li>
               <p class="para_item">The gap element is simulated by a nonlinear spring element in SOLs 601 and 701 where the axial properties are represented but the transverse properties are ignored. </p>
            </li>
            <li>
               <p class="para_item">KT, MU1, MU2, TMAX, MAR, and TRMIN are ignored. </p>
            </li>
         </ol>
      </div>
      <div class="title_refCategory">Remarks related to SOL 101 with contact: </div>
      <div class="refCategoryContent">
         <ol type="1" start="1">
            <li>
               <p class="para_item">MU1 is used as the coefficient of friction in both transverse directions. </p>
            </li>
            <li>
               <p class="para_item">F0, KA, KB, KT, MU2, TMAX, MAR and TRMIN are ignored. </p>
            </li>
         </ol>
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