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      <div class="title_topic3" id="xps10_pagetitle">NX Nastran Results</div>
      <hr noshade="true"><a name="gsfem_11093"></a><p class="para_topic">The NX Nastran results are shown in Table <a class="links" href="javascript:void(0)" onclick="top.openFile('get_start/03topic_7.html#gsfem_11033');return(false);">2-2</a>. 
      </p><a name="gsfem_11033"></a><div class="title_tableWrapper">Table 2-2. Rectangular Plate f06 Results File &nbsp;</div>
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               <p align="left"><img align="bottom" src="graphics/LIST_2-4_1.gif"></p>
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               <p align="left"><img align="bottom" src="graphics/LIST_2-4_2.gif"></p>
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               <p align="left"><img align="bottom" src="graphics/LIST_2-4_3.gif"></p>
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            <td colspan="1" rowspan="1">
               <p align="left"><img align="bottom" src="graphics/LIST_2-4_4.gif"></p>
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               <p align="left"><img align="bottom" src="graphics/LIST_2-4_5.gif"></p>
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               <p align="left"><img align="bottom" src="graphics/LIST_2-4_7.gif"></p>
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               <p align="left"><img align="bottom" src="graphics/LIST_2-4_9.gif"></p>
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               <p align="left"><img align="bottom" src="graphics/LIST_2-4_10.gif"></p>
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      </table><br><div class="title_division">Reviewing the Results</div><a name="gsfem_11095"></a><p class="para_division">The value of epsilon, listed on page 6 of the output, is small, indicating a numerically well-behaved problem. A plot of the deformed plate is shown in Figure <a class="links" href="javascript:void(0)" onclick="top.openFile('get_start/03topic_7.html#gsfem_11237');return(false);">2-</a>. As expected, the maximum displacement (-3.678445E-3 inches) occurs at grid point 3 in the -T3 direction. This deflection is approximately one-fourteenth the thickness of the plate, and is therefore a fairly reasonable &ldquo;small&rdquo; displacement.
      </p><a name="gsfem_11099"></a><p class="para_division">It is also useful to check the applied loads against the reaction forces. We have:</p>
      <p class="para_division">Total Lateral Applied Force = (0.25 lb/in<sup class="superscript">2</sup>)(3 in)(6 in) = 4.5 lbs
      </p><a name="gsfem_11104"></a><p class="para_division">which is in agreement with the T3 direction SPCFORCE resultant listed on page 7 of the output. Note that the SPCFORCE is positive, and the applied load is in the negative z (-T3) direction.</p><a name="gsfem_11237"></a><div class="figure">
         <p align="center"><img align="bottom" src="graphics/gsfem26.gif"></p>
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      <div class="title_figure">Figure. Deformed Shape</div>
      <div class="title_division">Comparison with Theory</div><a name="gsfem_11239"></a><p class="para_division">Article 46 of Timoshenko, Theory of Plates and Shells, 2nd ed., gives the analytical solution for the maximum deflection of a fixed-hinged-hinged-free plate with a uniform lateral load as:</p>
      <p class="para_division">W<sub class="subscript">max</sub> = (0.582 qb<sup class="superscript">4</sup> / D) (for b/a = 1/2)
      </p><a name="gsfem_11245"></a><p class="para_division"> where:  </p>
      <table width="100%" align="center">
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            <col span="1" width="19*">
            <col span="1" width="252*">
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            <td colspan="1" rowspan="1" valign="top"><a name="gsfem_11248"></a><p class="para_td">q</p>
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               <p class="para_td">=</p>
            </td>
            <td colspan="1" rowspan="1"><a name="gsfem_11252"></a><p class="para_td">lateral pressure = 0.25 lb/in<sup class="superscript">2</sup></p>
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            <td colspan="1" rowspan="1" valign="top"><a name="gsfem_11254"></a><p class="para_td">D</p>
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               <p class="para_td">=</p>
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            <td colspan="1" rowspan="1"><a name="gsfem_11261"></a><p class="para_td"><img align="bottom" src="graphics/gsfem3.gif" border="0"></p>
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      </table><br><a name="gsfem_11263"></a><p class="para_division">Therefore, the maximum deflection is:</p>
      <p align="left"><img align="bottom" src="graphics/gsfem4.gif"></p><a name="gsfem_11268"></a><p class="para_division">The NX Nastran solution at grid point 3 is:</p>
      <p class="para_division">W<sub class="subscript">max</sub> = 3.678445E-3 in
      </p><a name="gsfem_11273"></a><p class="para_division">The NX Nastran result (which includes transverse shear) is 7.2% greater than the theory solution. The theory solution does not account for transverse shear deflection. Rerunning the model without shear (by eliminating MID3 in field 7of the PSHELL entry) gives a deflection of:</p>
      <p class="para_division">W<sub class="subscript">max</sub> (no shear) = 3.664290E-3 in
      </p><a name="gsfem_11278"></a><p class="para_division">Thus, for this thin plate, adding shear deflection results in less than half a percent difference in the total deflection.</p>
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