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      <div class="title_topic3" id="xps10_pagetitle">NX Nastran Results</div>
      <hr noshade="true"><a name="gsfem_10221"></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_4.html#gsfem10164');return(false);">2-1</a>.
      </p><a name="gsfem10164"></a><div class="title_tableWrapper">Table 2-1. Cantilever Beam f06 Results File &nbsp;</div>
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      </table><br><div class="title_division">Reviewing the Results</div><a name="gsfem_10223"></a><p class="para_division">First, we review the .f06 output file for any warning or error messages.  None are present in this file.  Next, look at epsilon on page 6 of the output.  Its value of -7.77E-17 is indeed very small, showing no evidence of numerical difficulties.  Finally, we review the reaction forces (forces of single point constraint, or SPC forces) at the wall.  As a check, a free body diagram of the structure is used to solve for reaction forces as follows:</p><a name="gsfem_10278"></a><p class="para_division"><img align="bottom" src="graphics/gsfem15.gif" border="0"></p><a name="gsfem_10279"></a><p class="para_division">Solving for the reactions at the wall, we obtain:</p><a name="gsfem_10316"></a><p class="para_division"><img align="bottom" src="graphics/gsfem17.gif" border="0"></p><a name="gsfem_10317"></a><p class="para_division">The SPC forces are listed on page 9 of the NX Nastran results.  The T2 reaction (force at grid point 1 in the y direction) is +660 lbs.  The R3 reaction (moment about the z axis) is +9780 lb.  Thus, we can be confident that the loads were applied correctly, and at least the static equilibrium of the problem makes sense.</p><a name="gsfem_10318"></a><p class="para_division">The displacement results are shown on page 8 of the .f06 file.  Note that all displacements at the wall (GRID 1) are exactly zero, as they should be.  The free end deflection in the y direction (T2 of GRID 4) is -1.086207E-1 in.</p><a name="gsfem_10319"></a><p class="para_division">As a final observation, note that there is no axial shortening of the beam as it deflects downward (all T1&rsquo;s are exactly zero).  This is a consequence of the simplifying small displacement assumptions built into slender beam theory and beam elements when used in linear analysis.  If the load on the beam is such that large displacement occurs, nonlinear analysis must be used to update the element matrices as the structure deforms.  The shortening terms will then be part of the solution.</p>
      <div class="title_division">Comparison with Theory</div><a name="gsfem_10322"></a><p class="para_division">The theory solution to this problem is as follows:</p><a name="gsfem_10364"></a><p class="para_division"><img align="bottom" src="graphics/gsfem19.gif" border="0"></p><a name="gsfem_10365"></a><p class="para_division">Using superposition, the net deflection at free end is given by:</p>
      <p align="left"><img align="bottom" src="graphics/gsfem25.gif"></p><a name="gsfem_10370"></a><p class="para_division">Thus, we are in exact agreement with the NX Nastran result.</p><a name="gsfem_10371"></a><p class="para_division">It should be noted that simple beam bending problems such as this give exact answers, even with one element.  This is a very special case and is by no means typical of real world problems.</p>
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