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<title>4</title>
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<div class="Section1">
<p><b><span style="font-size: 18pt;" lang="EN-GB">4.11
PLANE STRESS ELEMENT NO.11 WITH 12 NODES </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 is a curvilinear Serendipity
plane stress element with cubic shape functions. The transformation is
isoparametric. The integration is carried out numerically in both
axises
according to Gauss- Legendre. Thus, the integration order can be
selected in </span><a href="e88i1.htm"><span style="" lang="EN-GB">Z88I1.TXT</span></a><span
style="" lang="EN-GB"> in the material information lines. The
order 3 is mostly the best choice. This element calculates both
displacements
and stresses with outstanding precision. 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). Because of its 24*24 element stiffness matrices the
element
No.11 needs a lot of memory and computing power. Pay attention to edge
loads
when using forces, cf. <a href="e88i2.htm">chapter 3.4</a>. It is
easier to
enter edge loads via the surface and pressure loads file <a
href="e88i5.htm">Z88I5.TXT</a>.<o:p></o:p></span></p>
<p><a href="e88e7.htm"><span style="" lang="EN-GB">Plane
Stress Elements No.7</span></a><span style="" lang="EN-GB">
can be generated by the </span><a href="e88n.htm"><span style=""
lang="EN-GB">net generator Z88N</span></a><span style="" lang="EN-GB">
from super elements Plane Stress Elements
No.11. Thus, the Plane Stress Element No.11 is well suited as super
element. But
Plane Stress Elements No.11 cannot be generated by the net generator
Z88N from
super elements Plane Stress Elements No.11. <o:p></o:p></span></p>
<p><img id="_x0000_i1025" src="g88e1101.gif" border="0" height="304"
width="384"></p>
<p><b><span style="font-size: 13.5pt;" 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><span
style="" lang="EN-GB"> (see chapter 2.7.2): <i>1-5-6-2-7-8-3-9-10-4-11-12-1
</i><o:p></o:p></span></p>
<p><a href="e88i1.htm"><b><span style="" lang="EN-GB">Z88I1.TXT</span></b></a><span
style="" lang="EN-GB"><br>
> KFLAG for cartesian (0) or polar coordinates (1) <br>
> IQFLAG=1 if edge loads for this element are filed in Z88I5.TXT<br>
> 2 degrees of freedom for each node <br>
<span style="">> Element type is 11</span> <br>
<span style="">> 12 nodes per element</span> <br>
<span style="">> Cross-section parameter QPARA is
the element thickness</span> <br>
<span style="">> Integration order INTORD per each
mat info line. 3 is usually good.</span><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>> 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">> KFLAG</span></i><span style=""
lang="EN-GB"> = 0: Calculation of SIGXX, SIGYY
and TAUXY <br>
<i>> KFLAG</i> = 1: Additional calculation of SIGRR, SIGTT and TAURT<o:p></o:p></span></p>
<p><i><span style="" lang="EN-GB">> 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=""><span style="" lang="EN-GB">This file is
optional and only used if in
addition to nodal forces edge loads applied onto element no.11:<o:p></o:p></span></p>
<p class="MsoNormal" style=""><span style="" lang="EN-GB"><o:p> </o:p></span></p>
<p class="MsoNormal"><i style=""><span style="" lang="EN-GB">>
Element number with surface and pressure load
<o:p></o:p></span></i></p>
<p class="MsoNormal"><i style=""><span style="" lang="EN-GB">>
Pressure, positive if poiting towards the
edge <o:p></o:p></span></i></p>
<p class="MsoNormal"><i style=""><span style="" lang="EN-GB">>
Tangential shear, positive in local r
direction<o:p></o:p></span></i></p>
<p class="MsoNormal"><i style=""><span style="" lang="EN-GB">> 2
corner nodes and 2 mid nodes of the
loaded surface</span></i><!--[if supportFields]><i style='mso-bidi-font-style:
normal'><span style='mso-element:field-begin'></span></i><i style='mso-bidi-font-style:
normal'><span lang=EN-GB style='mso-ansi-language:EN-GB'> XE "Verschiebung"
</span></i><![endif]--><!--[if supportFields]><i style='mso-bidi-font-style:
normal'><span style='mso-element:field-end'></span></i><![endif]--><!--[if supportFields]><i
style='mso-bidi-font-style:normal'><span style='mso-element:field-begin'></span></i><i
style='mso-bidi-font-style:normal'><span lang=EN-GB style='mso-ansi-language:
EN-GB'><span style='mso-spacerun:yes'></span>XE "Verschiebung" </span></i><![endif]--><!--[if supportFields]><i
style='mso-bidi-font-style:normal'><span style='mso-element:field-end'></span></i><![endif]--><i
style=""><span style="" lang="EN-GB"><o:p></o:p></span></i></p>
<p class="MsoNormal" style=""><span style="" lang="EN-GB"><o:p> </o:p></span></p>
<p class="MsoNormal" style=""><span style="" lang="EN-GB">The local r
direction is defined by the nodes
1-2. The local nodes 1, 2, 3, 4 may differ from the local nodes 1, 2,
3, 4 used
for the coincidence.<o:p></o:p></span></p>
<p><img src="g88e1102.gif"></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"> ino X and Y. <br>
<b>Stresses:</b> The stresses are calculated in the corner nodes or
Gauss
points and printed along with their locations. For KFLAG = 1 the radial
stresses SIGRR, the tangential stresses SIGTT and the accompanying
shear
stresses SIGRT are computed additionally (makes only sense if a
rotational-symmetric structure is available). For easier orientation
the
respective radiuses and angles of the nodes/points are printed.
Optional von
Mises stresses <br>
<b>Nodal forces</b> in X and Y for each elementand each node. <o:p></o:p></span></p>
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