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<p><b><span style="font-size: 18pt;" lang="EN-GB">4.10
HEXAHEDRON NO.10 WITH 20 NODES</span></b><span style="" lang="EN-GB"><o:p></o:p></span></p>
<p><span style="" lang="EN-GB">This is a curvilinear
Serendipity volume element with square shape functions. The
transformation is
isoparametric. The integration is carried out numerically in all 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 good. This element calculates both displacements and
stresses very
exactly. The quality of the displacement and stress calculations are
far better
than the results of the </span><a href="e88e1.htm"><span style=""
lang="EN-GB">hexahedron element No.1</span></a><span style=""
lang="EN-GB">. <o:p></o:p></span></p>
<p><span style="" lang="EN-GB">Hexahedron No.1 also
applies well for thick plate elements, if the plate's thickness is not
too
small compared to the other dimensions. <o:p></o:p></span></p>
<p class="MsoNormal" style="text-align: justify;"><span style=""
lang="EN-GB">The element causes an enormous
computing load and needs an extreme amount of memory because the
element
stiffness matrix has the order 60*60. Pay attention to surface and
pressure
loads when using forces, cf. <a href="e88i2.htm">chapter 3.4</a>. It
is easier
to enter these loads via the surface and pressure loads file <a
href="e88i5.htm">Z88I5.TXT</a>.<o:p></o:p></span></p>
<p><img id="_x0000_i1025" src="g88e1001.gif" border="0" height="357"
width="470"><span style="" lang="EN-GB"><o:p></o:p></span></p>
<p><b><span style="" lang="EN-GB">The nodal numbering of
the element No.10 must be done carefully and must exactly match the
sketch
below. Pay attention to the location of the axis system ! The possible
error
message " Jacobi determinant zero or negative " is a hint for
incorrect node numbering.</span></b><span style="" lang="EN-GB"><o:p></o:p></span></p>
<p><span style="" lang="EN-GB">Hexahedron No.10 can be generated
by the </span><a href="e88n.htm"><span style="" lang="EN-GB">mesh
generator Z88N</span></a><span style="" lang="EN-GB"> from super
elements Hexahedron No.10. Thus, the Hexahedron No.10 is
well suited as super element. Hexahedron No.10 can also generate </span><a
href="e88e1.htm"><span style="" lang="EN-GB">8-node
Hexahedrons No.1</span></a><span style="" lang="EN-GB">,
see chapter 4.1. <o:p></o:p></span></p>
<p><u><span style="" lang="EN-GB">Hexahedron No.10 is
recommended for all sort of deflection and stress computation in space</span></u><span
style="" lang="EN-GB">. Though its need for memory and
computing power is enormous, this element gives precise results for
displacements and stresses. Or use it as superelements for meshing
Hexahedrons
No.1 with 8 nodes. <o:p></o:p></span></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): <br>
Upper plane: 1 - 9 - 2 - 10 - 3 - 11 - 4 -12 - 1, quit LINE function <br>
Lower plane: 5 - 13 - 6 - 14 - 7 - 15 - 8 - 16 - 5, quit LINE function<br>
1 - 17 - 5, quit LINE function<br>
2 - 18 - 6, quit LINE function<br>
3 - 19 - 7, quit LINE function<br>
4 - 20 - 8, quit LINE function<o:p></o:p></span></p>
<p class="MsoNormal" style=""><a href="e88i1.htm"><b><span style=""
lang="EN-GB">Z88I1.TXT</span></b></a><span style="" lang="EN-GB"><br>
<i style="">> KFLAG for cartesian (0) or
cylindrical coordinates (1) <br>
> IQFLAG=1 if surface and pressure loads for this element are filed
in
Z88I5.TXT<br>
> 3 degrees of freedom for each node <br>
> Element type is 10</i> <br>
<i style="">> 20 nodes per element</i> <br>
<i>> Cross-section parameter QPARA is 0 or any value, has no
influence</i> <br>
<i>> Integration order INTORD for each mat info line. 3 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>> Integration order INTORD</i> for stress calculation: Can be
different
from INTORD in Z88I1.TXT. <br>
0 = Calculation of stresses in the corner nodes <br>
1,2,3,4 = Calculation of 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">, any, has no influence<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 surface and pressure loads applied onto
element no.10:<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<span style=""> </span>[Long]<o:p></o:p></span></i></p>
<p class="MsoNormal"><i style=""><span style="" lang="EN-GB">>
Pressure, positive if poiting towards the
surface <span style=""> </span>[Double]<o:p></o:p></span></i></p>
<p class="MsoNormal"><i style=""><span style="" lang="EN-GB">>
Tangential shear, positive in local r
direction<span style=""> </span>[Double]<o:p></o:p></span></i></p>
<p class="MsoNormal"><i style=""><span style="" lang="EN-GB">>
Tangential shear, positive in local s
direction<span style=""> </span>[Double]<o:p></o:p></span></i></p>
<p class="MsoNormal"><i style=""><span style="" lang="EN-GB">> 4
nodes of the loaded surface <span style=""> </span>[4 x Long]</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="text-align: justify;"><span style=""
lang="EN-GB">The local r direction is defined by
the nodes 1-2, the local s direction is defined by the nodes 1-4. 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="g88e1002.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"> in X, Y and Z<br>
<b>Stresses:</b> SIGXX, SIGYY, SIGZZ, TAUXY, TAUYZ, TAUZX, respectively
for
corner nodes or Gauss points. Optional von Mises stresses. <br>
<b>Nodal forces</b> in X, Y and Z for each element and each node. <o:p></o:p></span></p>
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