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<body style="" lang="DE" link="blue" vlink="blue">
<div class="Section1">
<p><b><span style="font-size: 18pt;" lang="EN-GB">4.19
PLATE NO.19 WITH 16 NODES</span></b><span style="" lang="EN-GB"><o:p></o:p></span></p>
<p><span style="" lang="EN-GB">This is a curvilinear <u>Lagrange</u>-
<i>Reissner- Mindlin</i> plate element with cubic shape functions. The
transformation is isoparametric. The integration is carried out
numerically in
both axises according to Gauss- Legendre. Consequently, the integration
order
can be selected in Z88I1.TXT in the material information lines. The
order 4 (=
4 x 4 points) is very good. This element calculates both displacements
and
stresses very precisely. The input amount is heavy, you should use the
mesher </span><a href="e88n.htm"><span style="" lang="EN-GB">Z88N</span></a><span
 style="" lang="EN-GB">. <o:p></o:p></span></p>
<p><span style="" lang="EN-GB">The integration order can
be chosen again for the stress calculation. The stresses are calculated
in the
corner nodes (good for an overview) or calculated in the Gauss points
(substantially more exactly). Area loads are defined in the appropriate
material lines, file </span><a href="e88i1.htm"><span style=""
 lang="EN-GB">Z88I1.TXT</span></a><span style="" lang="EN-GB">, instead
of Second moment of inertia RIYY. For
this element you need to set the plate flag IPFLAG to 1. Attention: In
contrary
to the usual rules of the classic mechanics Z88 defines ThetaX the
rotation
around the X- axis and ThetaY the rotation around the Y- axis.<o:p></o:p></span></p>
<p><i><span style="" lang="EN-GB">Mesh generation with
Z88N: Use </span><a href="e88e20.htm"><span style="" lang="EN-GB">plates
No.20</span></a></i><i><span style="" lang="EN-GB"> for super elements,
resulting in finite elements of type 19 (plates
No.20 may generated by AutoCAD or Pro/ENGINEER, ref. the chapters of
Z88X and
Z88G). A bit tricky, but works quite fine.</span></i><span style=""
 lang="EN-GB"> <o:p></o:p></span></p>
<p><i><span style="" lang="EN-GB">For example, some lines
from a mesh generator input file </span><a href="e88ni.htm"><span
 style="" lang="EN-GB">Z88NI.TXT</span></a></i><i><span style=""
 lang="EN-GB">: <br>
.....</span></i><span style="" lang="EN-GB"> <br>
<i>5 20 super element 5 of type 20</i> <br>
<i>20 25 27 22 24 26 28 21</i> <br>
<i>.....</i> <br>
<i>5 19 generate from super element 5 (which is of type 20 is, see
above)
finite elements of type 19 <br>
3 E 3 E .. and subdivide them threetimes equidistant in X-direction and
threetimes equidistant in Y- direction<br>
<br>
</i></span><i><img id="_x0000_i1025" src="pla1.gif" border="0"
 height="160" width="337"></i><i><span style="" lang="EN-GB"><br>
<br>
</span><img id="_x0000_i1026" src="g88e19.gif" border="0" height="340"
 width="370"></i><span style="" lang="EN-GB"><o:p></o:p></span></p>
<p><b><span style="" lang="EN-GB">Input:</span></b><span style=""
 lang="EN-GB"><o:p></o:p></span></p>
<p><a href="e88x.htm"><b><span style="" lang="EN-GB">CAD</span></b></a><b><span
 style="" lang="EN-GB"> :</span></b><i><span style="" lang="EN-GB">
1-2-3-4-5-6-7-8-9-10-11-12-13-14-15-16-1 ,</span></i><b><span style=""
 lang="EN-GB"> </span></b><span style="" lang="EN-GB">ref. chap.
2.7.2. Usually, you will not work in
this way. It's much more easier to build within a CAD program a super
elements
mesh with 8- node plates No.20. Export this mesh as a DXF file and use
Z88X to
produce a mesh generator input file </span><a href="e88ni.htm"><span
 style="" lang="EN-GB">Z88NI.TXT</span></a><span style="" lang="EN-GB">.
Run the mesher </span><a href="e88n.htm"><span style="" lang="EN-GB">Z88N</span></a><span
 style="" lang="EN-GB"> and generate a finite elements mesh
with plates No.19. Plot this mesh using </span><a href="e88p.htm"><span
 style="" lang="EN-GB">Z88P</span></a><span style="" lang="EN-GB">,
read off the appropriate node numbers and
edit the boundary conditions file </span><a href="e88i2.htm"><span
 style="" lang="EN-GB">Z88I2.TXT</span></a><span style="" lang="EN-GB">.<o:p></o:p></span></p>
<p><img id="_x0000_i1027" src="g88x3.gif" border="0" height="441"
 width="480"></p>
<p><a href="e88i1.htm"><b><span style="" lang="EN-GB">Z88I1.TXT</span></b></a><span
 style="" lang="EN-GB"><br>
<i style="">&gt; KFLAG for cartesian (0) or
cylindrical coordinates (1) <br>
&gt; set plate flag IPFLAG to 1 (or 2, if you want to reduce the shear
influence) <br>
&gt; set surface and pressure loads flag IQFLAG to 0 for your
convenience. Then
the entry of the pressure is done via the "Second moment of inertia
RIYY", see below. If IQFLAG is set to 1, then the entry of the pressure
is
done via the surface and pressure loads file Z88I5.TXT<br>
<span style="">&gt; 3 degrees of freedom for each
node (w, ThetaX, ThetaY )</span></i> <br>
<i>&gt; Element type is 19</i> <br>
<i>&gt; 16 nodes per element</i> <br>
<i>&gt; Cross-section parameter QPARA is the element thickness</i> <br>
&gt; "<i>Second moment of inertia RIYY" is the area load</i> <br>
<i>&gt; Integration order INTORD per each mat info line. 4 is usually
good. </i><o:p></o:p></span></p>
<p><a href="e88i3.htm"><b><span style="" lang="EN-GB">Z88I3.TXT</span></b></a><span
 style="" lang="EN-GB"><br>
<i>&gt; Integration order INTORD</i>: Basically, it is a good idea to
use the
same value as chosen in Z88I1.TXT , but different values are permitted<br>
0 = Calculation of the stresses in the corner nodes <br>
1, 2, 3, 4 = Calculation of the stresses in the Gauss points <o:p></o:p></span></p>
<p><i><span style="" lang="EN-GB">&gt; KFLAG</span></i><span style=""
 lang="EN-GB"> has no meaning<o:p></o:p></span></p>
<p><i><span style="" lang="EN-GB">&gt; Reduced stress flag
ISFLAG:</span></i><span style="" lang="EN-GB"> <br>
</span><span style="" lang="EN-GB">0 = no calculation of reduced
stresses <br>
1 = von Mises stresses in the Gauss points ( INTORD not 0 !)<br>
2 = principal stresses in the Gauss points (INTORD not 0!)<br>
3 = Tresca </span><span style="" lang="EN-GB">stresses in the Gauss
points (INTORD not 0!)</span></p>
<p class="MsoNormal" style=""><b style=""><span style="" lang="EN-GB"><a
 href="e88i5.htm">Z88I5.TXT</a></span></b><span style="" lang="EN-GB"><o:p></o:p></span></p>
<p class="MsoNormal" style="text-align: justify;"><span style=""
 lang="EN-GB">This file is optional and normally
not used here because it is much more convenient to enter the pressure
data for
the plate elements into <a href="e88i1.htm">Z88I1.TXT</a> in the
section
material information. However, the possibility for entering the
pressure loads
by the surface and pressure loads file Z88I5.TXT, too, is implemented
for
universal use of this file. Then set IQFLAG to 1 and proceed as follows:<o:p></o:p></span></p>
<p class="MsoNormal" style=""><span style="" lang="EN-GB"><o:p>&nbsp;</o:p></span></p>
<p class="MsoNormal"><i style=""><span style="" lang="EN-GB">&gt;
Element number with pressure load <o:p></o:p></span></i></p>
<p class="MsoNormal"><i style=""><span style="" lang="EN-GB">&gt;
Pressure, positive if poiting towards the
edge <o:p></o:p></span></i></p>
<p><b><span style="font-size: 13.5pt;" lang="EN-GB">Results:</span></b><span
 style="" lang="EN-GB"><o:p></o:p></span></p>
<p><b><span style="" lang="EN-GB">Displacements</span></b><span style=""
 lang="EN-GB"> in Z (i.e. w) and rotations ThetaX
around X- axis and ThetaY around the Y- axis. <br>
<b>Stresses:</b> The stresses are calculated in the corner nodes or
Gauss
points and printed along with their locations. The following results
will be
presented: <o:p></o:p></span></p>
<ul type="disc">
  <li class="MsoNormal" style=""><span style="" lang="EN-GB">plate
bending moments M<sub>xx</sub> and M<sub>yy</sub> (unit: force x lenght
/ length) <o:p></o:p></span></li>
  <li class="MsoNormal" style=""><span style="" lang="EN-GB">plate
torsion moments M<sub>xy</sub> = M<sub>yx</sub> (unit: force x length /
length) <o:p></o:p></span></li>
  <li class="MsoNormal" style=""><span style="" lang="EN-GB">the shear
forces Q<sub>yz</sub> and Q<sub>zx</sub> (unit: force / length) <o:p></o:p></span></li>
  <li class="MsoNormal" style=""><span style="" lang="EN-GB">the true
stresses resulting from plate bending moments and plate torsion moments
    <o:p></o:p></span></li>
</ul>
<p><span style="" lang="EN-GB">Optional <i>von Mises</i>
stresses <br>
<b>Nodal forces</b> in X and Y for each element and each node. <o:p></o:p></span></p>
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