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      <title>The Finite Element Model</title>
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      <div class="title_topic3" id="xps10_pagetitle">The Finite Element Model</div>
      <hr noshade="true">
      <div class="title_division">Designing the Model</div><a name="gsfem_10465"></a><p class="para_division">First, we need to examine the structure to verify that it can reasonably qualify as a thin plate.  The thickness is 1/60 of the next largest dimension (3 inches), which is satisfactory.</p><a name="gsfem_10466"></a><p class="para_division">Next, we observe by inspection that the maximum deflection, regardless of the actual value, should occur at the center of the free edge.  Thus, it will be helpful to locate a grid point there to recover the maximum displacement.</p><a name="gsfem_10467"></a><p class="para_division">As a matter of good practice, we wish to design a model with the fewest elements that will do the job.  In our case, doing the job means good displacement accuracy.  The model shown in Figure <a class="links" href="javascript:void(0)" onclick="top.openFile('get_start/03topic_6.html#gsfem_10660');return(false);">2-</a> contains 20 GRID points and 12 CQUAD4 elements, which we hope will yield reasonable displacement results.  If we have reason to question the accuracy of the solution, we can always rerun the model with a finer mesh.
      </p><a name="gsfem_10660"></a><div class="figure">
         <p align="left"><img align="bottom" src="graphics/gsfema.gif"></p>
      </div>
      <div class="title_figure">Figure. Plate Finite Element Model</div><a name="gsfem_10661"></a><div class="title_division">Applying the Load</div><a name="gsfem_10662"></a><p class="para_division">The uniform pressure load is applied to all plate elements using the PLOAD2 entry.  Only one PLOAD2 entry is required by using the &ldquo;THRU&rdquo; feature (elements 1 THRU 12).  The positive normal to each plate element (as dictated by the GRID point ordering sequence) is in the negative z axis direction, which is the same direction as the pressure load.  Therefore, the value of pressure in Field 3 of the PLOAD2 entry is positive.</p>
      <div class="title_division">Applying the Constraints</div><a name="gsfem_10666"></a><p class="para_division">SPC1 entries are used to model the structure&rsquo;s constraints.  The SPC1 entries have a set ID of 10, which is selected by the Case Control command SPC = 100.  The constraints on the structure are shown in Figure <a class="links" href="javascript:void(0)" onclick="top.openFile('get_start/03topic_6.html#gsfem_10858');return(false);">2-</a>.
      </p><a name="gsfem_10858"></a><div class="figure">
         <p align="left"><img align="bottom" src="graphics/gsfem28.gif"></p>
      </div>
      <div class="title_figure">Figure. Constraints on the Plate Structure </div>
      <table border="0">
         <tr>
            <td valign="top" align="left"><img align="left" src="../graphics/note.gif" alt="Note" title="Note"></td>
            <td valign="bottom" align="left" width="100%">
               <div class="para_note">
                  <ol type="1" start="1">
                     <li><a name="gsfem_10853"></a><p class="para_note_body">1. The out-of-plane rotational DOF (degree of freedom 6) is constrained for all grids in the model. This is a requirement of a CQUAD4 flat plate element, and has nothing to do with this specific problem.</p>
                     </li>
                     <li><a name="gsfem_10854"></a><p class="para_note_body">2. Grids 16 and 20, shared with the fixed edge, are fixed&mdash;the greater constraint governs. For the remaining grids:</p>
                     </li>
                     <li><a name="gsfem_10855"></a><p class="para_note_body">Displacements Allowed: Rotation about y-axis (DOF 5)</p>
                     </li>
                     <li><a name="gsfem_10856"></a><p class="para_note_body">Displacements Not Allowed: Rotation about x-axis (DOF 4)  Translation in x, y, or z (DOFs 1, 2, 3)</p>
                     </li>
                     <li><a name="gsfem_10857"></a><p class="para_note_body">3. The non-corner grids of the free edge have no additional constraints.</p>
                     </li>
                  </ol>
               </div>
            </td>
         </tr>
      </table><a name="gsfem_10859"></a><p class="para_division">The SPC1 entries are written as follows:</p>
      <p class="para_division"><b class="uiTerm">Format:</b></p>
      <table border="1" width="100%" align="center">
         <tr>
            <th colspan="1" rowspan="1"><a name="gsfem_10862"></a><p class="para_th">1</p>
            </th>
            <th colspan="1" rowspan="1"><a name="gsfem_10864"></a><p class="para_th">2</p>
            </th>
            <th colspan="1" rowspan="1"><a name="gsfem_10866"></a><p class="para_th">3</p>
            </th>
            <th colspan="1" rowspan="1"><a name="gsfem_10868"></a><p class="para_th">4</p>
            </th>
            <th colspan="1" rowspan="1"><a name="gsfem_10870"></a><p class="para_th">5</p>
            </th>
            <th colspan="1" rowspan="1"><a name="gsfem_10872"></a><p class="para_th">6</p>
            </th>
            <th colspan="1" rowspan="1"><a name="gsfem_10874"></a><p class="para_th">7</p>
            </th>
            <th colspan="1" rowspan="1"><a name="gsfem_10876"></a><p class="para_th">8</p>
            </th>
            <th colspan="1" rowspan="1"><a name="gsfem_10878"></a><p class="para_th">9</p>
            </th>
            <th colspan="1" rowspan="1"><a name="gsfem_10880"></a><p class="para_th">10</p>
            </th>
         </tr>
         <tr>
            <td align="center" colspan="1" rowspan="1"><a name="gsfem_10882"></a><p class="para_td">SPC1</p>
            </td>
            <td align="center" colspan="1" rowspan="1"><a name="gsfem_10884"></a><p class="para_td">SID</p>
            </td>
            <td align="center" colspan="1" rowspan="1"><a name="gsfem_10886"></a><p class="para_td">C</p>
            </td>
            <td align="center" colspan="1" rowspan="1"><a name="gsfem_10888"></a><p class="para_td">G1</p>
            </td>
            <td align="center" colspan="1" rowspan="1"><a name="gsfem_10890"></a><p class="para_td">G2</p>
            </td>
            <td align="center" colspan="1" rowspan="1"><a name="gsfem_10892"></a><p class="para_td">G3</p>
            </td>
            <td align="center" colspan="1" rowspan="1"><a name="gsfem_10894"></a><p class="para_td">G4</p>
            </td>
            <td align="center" colspan="1" rowspan="1"><a name="gsfem_10896"></a><p class="para_td">G5</p>
            </td>
            <td align="center" colspan="1" rowspan="1"><a name="gsfem_10898"></a><p class="para_td">G6</p>
            </td>
            <td colspan="1" rowspan="1"></td>
         </tr>
         <tr>
            <td align="center" colspan="1" rowspan="1"></td>
            <td align="center" colspan="1" rowspan="1"><a name="gsfem_10904"></a><p class="para_td">G7</p>
            </td>
            <td align="center" colspan="1" rowspan="1"><a name="gsfem_10906"></a><p class="para_td">G8</p>
            </td>
            <td align="center" colspan="1" rowspan="1"><a name="gsfem_10908"></a><p class="para_td">G9</p>
            </td>
            <td align="center" colspan="1" rowspan="1"><a name="gsfem_10910"></a><p class="para_td">-etc.-</p>
            </td>
            <td align="center" colspan="1" rowspan="1"></td>
            <td align="center" colspan="1" rowspan="1"></td>
            <td align="center" colspan="1" rowspan="1"></td>
            <td align="center" colspan="1" rowspan="1"></td>
            <td colspan="1" rowspan="1"></td>
         </tr>
      </table><br><p class="para_division"><b class="uiTerm">Alternate Format:</b></p>
      <table border="1" width="100%" align="center">
         <colgroup span="1">
            <col align="center" span="1" width="103*">
            <col align="center" span="1" width="99*">
            <col align="center" span="1" width="99*">
            <col align="center" span="1" width="99*">
            <col align="center" span="1" width="99*">
            <col align="center" span="1" width="97*">
            <col align="center" span="1" width="99*">
            <col span="1" width="99*">
            <col span="1" width="99*">
            <col span="1" width="99*">
         </colgroup>
         <tr>
            <td colspan="1" rowspan="1"><a name="gsfem_10924"></a><p class="para_td">SPC1</p>
            </td>
            <td colspan="1" rowspan="1"><a name="gsfem_10926"></a><p class="para_td">SID</p>
            </td>
            <td colspan="1" rowspan="1"><a name="gsfem_10928"></a><p class="para_td">C</p>
            </td>
            <td colspan="1" rowspan="1"><a name="gsfem_10930"></a><p class="para_td">G1</p>
            </td>
            <td colspan="1" rowspan="1"><a name="gsfem_10932"></a><p class="para_td">&ldquo;THRU&rdquo;</p>
            </td>
            <td colspan="1" rowspan="1"><a name="gsfem_10934"></a><p class="para_td">G2</p>
            </td>
            <td colspan="1" rowspan="1"></td>
            <td colspan="1" rowspan="1"></td>
            <td colspan="1" rowspan="1"></td>
            <td colspan="1" rowspan="1"></td>
         </tr>
      </table><br><p class="para_division"><b class="uiTerm">Out-of-plane Rotations:</b></p>
      <table border="1" width="100%" align="center">
         <colgroup span="1">
            <col align="center" span="1">
            <col align="center" span="1">
            <col align="center" span="1">
            <col align="center" span="1">
            <col align="center" span="1">
            <col align="center" span="1">
            <col span="1">
            <col span="1">
            <col span="1">
            <col span="1">
         </colgroup>
         <tr>
            <td colspan="1" rowspan="1"><a name="gsfem_10946"></a><p class="para_td">SPC1</p>
            </td>
            <td colspan="1" rowspan="1"><a name="gsfem_10948"></a><p class="para_td">100</p>
            </td>
            <td colspan="1" rowspan="1"><a name="gsfem_10950"></a><p class="para_td">6</p>
            </td>
            <td colspan="1" rowspan="1"><a name="gsfem_10952"></a><p class="para_td">1</p>
            </td>
            <td colspan="1" rowspan="1"><a name="gsfem_10954"></a><p class="para_td">THRU</p>
            </td>
            <td colspan="1" rowspan="1"><a name="gsfem_10956"></a><p class="para_td">20</p>
            </td>
            <td colspan="1" rowspan="1"></td>
            <td colspan="1" rowspan="1"></td>
            <td colspan="1" rowspan="1"></td>
            <td colspan="1" rowspan="1"></td>
         </tr>
      </table><br><p class="para_division"><b class="uiTerm">Hinged Edges:</b></p>
      <table border="1" width="100%" align="center">
         <colgroup span="1">
            <col align="center" span="1">
            <col align="center" span="1">
            <col align="center" span="1">
            <col align="center" span="1">
            <col align="center" span="1">
            <col align="center" span="1">
            <col align="center" span="1">
            <col align="center" span="1">
            <col align="center" span="1">
            <col span="1">
         </colgroup>
         <tr>
            <td colspan="1" rowspan="1"><a name="gsfem_10968"></a><p class="para_td">spc1</p>
            </td>
            <td colspan="1" rowspan="1"><a name="gsfem_10970"></a><p class="para_td">100</p>
            </td>
            <td colspan="1" rowspan="1"><a name="gsfem_10972"></a><p class="para_td">1234</p>
            </td>
            <td colspan="1" rowspan="1"><a name="gsfem_10974"></a><p class="para_td">1</p>
            </td>
            <td colspan="1" rowspan="1"><a name="gsfem_10976"></a><p class="para_td">6</p>
            </td>
            <td colspan="1" rowspan="1"><a name="gsfem_10978"></a><p class="para_td">11</p>
            </td>
            <td colspan="1" rowspan="1"><a name="gsfem_10980"></a><p class="para_td">5</p>
            </td>
            <td colspan="1" rowspan="1"><a name="gsfem_10982"></a><p class="para_td">10</p>
            </td>
            <td colspan="1" rowspan="1"><a name="gsfem_10984"></a><p class="para_td">15</p>
            </td>
            <td colspan="1" rowspan="1"></td>
         </tr>
      </table><br><p class="para_division"><b class="uiTerm">Fixed Edge:</b></p><a name="gsfem_11010"></a><p class="para_division">Note that some constraints are redundantly specified. For example, GRID 17 is constrained in all 6 DOFs with the fixed edge SPC1, and again in DOF 6 with the out-of-plane rotational constraint. This is perfectly acceptable, and keeps the constraint bookkeeping a little tidier.</p>
      <table border="1" width="100%" align="center">
         <colgroup span="1">
            <col align="center" span="1">
            <col align="center" span="1">
            <col align="center" span="1">
            <col align="center" span="1">
            <col align="center" span="1">
            <col align="center" span="1">
            <col span="1">
            <col span="1">
            <col span="1">
            <col span="1">
         </colgroup>
         <tr>
            <td colspan="1" rowspan="1"><a name="gsfem_10990"></a><p class="para_td">SPC1</p>
            </td>
            <td colspan="1" rowspan="1"><a name="gsfem_10992"></a><p class="para_td">100</p>
            </td>
            <td colspan="1" rowspan="1"><a name="gsfem_10994"></a><p class="para_td">123456</p>
            </td>
            <td colspan="1" rowspan="1"><a name="gsfem_10996"></a><p class="para_td">16</p>
            </td>
            <td colspan="1" rowspan="1"><a name="gsfem_10998"></a><p class="para_td">THRU</p>
            </td>
            <td colspan="1" rowspan="1"><a name="gsfem_11000"></a><p class="para_td">20</p>
            </td>
            <td colspan="1" rowspan="1"></td>
            <td colspan="1" rowspan="1"></td>
            <td colspan="1" rowspan="1"></td>
            <td colspan="1" rowspan="1"></td>
         </tr>
      </table><br><div class="title_division">Output Requests</div><a name="gsfem_11012"></a><p class="para_division">The problem statement requires displacements. As a matter of good practice, we will also request SPC forces to check the model&rsquo;s reactions. Thus, the following output requests are included in the Case Control Section:</p><a name="gsfem_11013"></a><pre class="indent"> DISP=ALL SPCF=ALL </pre><div class="title_division">The Input File</div><a name="gsfem_11018"></a><p class="para_division">The complete input file is shown in Listing <a class="links" href="javascript:void(0)" onclick="top.openFile('get_start/03topic_6.html#gsfem_11020');return(false);">2-2</a>.
      </p><a name="gsfem_11020"></a><div class="figure"><a name="gsfem_11021"></a><pre class="indent"> ID MPM,EXAMPLE3 
SOL 101 
TIME 100 
CEND 
SPCF=ALL 
DISP=ALL 
TITLE=PLATE EXAMPLE 
SUBTITLE=FIXED-HINGED-HINGED-FREE 
LABEL=UNIFORM LATERAL PRESSURE LOAD (0.25 lb/in**2) 
SPC=100 
ECHO=BOTH 
LOAD=5 
$ 
BEGIN BULK 
$ DEFINE GRID POINTS 
GRID,1,,0.,0.,0. 
GRID,2,,1.5,0.,0. 
GRID,3,,3.0,0.,0. 
GRID,4,,4.5,0.,0. 
GRID,5,,6.0,0.,0. 
GRID,6,,0.,1.,0. 
GRID,7,,1.5,1.,0. 
GRID,8,,3.0,1.,0. 
GRID,9,,4.5,1.,0. 
GRID,10,,6.0,1.,0. 
GRID,11,,0.,2.,0. 
GRID,12,,1.5,2.,0. 
GRID,13,,3.0,2.,0. 
GRID,14,,4.5,2.,0. 
GRID,15,,6.0,2.,0. 
GRID,16,,0.,3.,0. 
GRID,17,,1.5,3.,0. 
GRID,18,,3.0,3.,0. 
GRID,19,,4.5,3.,0. 
GRID,20,,6.0,3.,0. 
$ 
$ DEFINE PLATE ELEMENTS 
CQUAD4,1,101,1,6,7,2 
CQUAD4,2,101,2,7,8,3 
CQUAD4,3,101,3,8,9,4 
CQUAD4,4,101,4,9,10,5 
CQUAD4,5,101,6,11,12,7 
CQUAD4,6,101,7,12,13,8 
CQUAD4,7,101,8,13,14,9 
CQUAD4,8,101,9,14,15,10 
CQUAD4,9,101,11,16,17,12 
CQUAD4,10,101,12,17,18,13 
CQUAD4,11,101,13,18,19,14 
CQUAD4,12,101,14,19,20,15 
$ 
$ DEFINE PRESSURE LOAD ON PLATES 
PLOAD2,5,0.25,1,THRU,12 
$ DEFINE PROPERTIES OF PLATE ELEMENTS 
PSHELL,101,105,.05,105,,105 
MAT1,105,30.E6,,0.3 
$ 
$ DEFINE FIXED EDGE 
SPC1,100,123456,16,THRU,20 
$ 
$ DEFINE HINGED EDGES 
SPC1,100,1234,1,6,11,5,10,15 
$ 
$ CONSTRAIN OUT-OF-PLANE ROTATION FOR ALL GRIDS 
SPC1,100,6,1,THRU,20 
ENDDATA </pre></div>
      <div class="title_figure">Listing 2-2. </div>
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