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<DT> 20 <tt> ISEPE</tt>
<DD>
<P>

the number of internal nodes in a pentahedron,
<P>
 </DL>
<P>

<DL COMPACT>


<DT> 21 <tt> ISEHE</tt>
<DD>
<P>

the number internal nodes in a hexahedron,
<P>
 </DL>
<P>

<DL COMPACT>


<DT> 22 <tt> NP</tt>
<DD>
<P>

the number points,
<P>
 </DL>
<P>

<DL COMPACT>


<DT> 23 <tt> NTYCOO</tt>
<DD>
<P>

the type of coordinate values (2 here, see <b> NOP1</b>),
<P>
 </DL>
<P>

<DL COMPACT>


<DT> 24 <tt> LPGDN</tt>
<DD>
<P>

The largest difference between  the node numbers of an element +1,
<P>
 </DL>
<P>

<DL COMPACT>


<DT> 25 <tt> NBEGM</tt>
<DD>
<P>

the number of super-elements or descriptions in array <i> NOP3</i>,
<P>
 </DL>
<P>

<DL COMPACT>


<DT> 26 <tt> LNOP5</tt>
<DD>
<P>

the number of words in array <i> NOP5</i>,
<P>
 </DL>
<P>

<DL COMPACT>


<DT> 27 <tt> NTACOO</tt>
<DD>
<P>

the type of coordinate axis: 1 <b>x,y,z</b> ; 2 <IMG BORDER=0 ALIGN=MIDDLE ALT="" SRC="img124.gif"> ; 3  <IMG BORDER=0 ALIGN=MIDDLE ALT="" SRC="img140.gif">.
<P>
 </DL>
<P>
<DT>Array NOP3:
<DD> An eventual pointer. <BR>
<P>
If NBEGM (array <b> NOP2</b>) is non-zero, this integer array contains in one variable
an information item relative to each super-element or description (this array  is not actually
used).
<P>
<DT>Array NOP4:
<DD> Vertex coordinates. <BR>
<P>
This  NTYCOO type array contains the NDIM.NP coordinates of the vertices: <BR> 
<i> X1, Y1, X2, Y2, ...</i> or   <BR> 
<i> X1, Y1, Z1, X2, ... </i>
<P>
<DT>Array NOP5:
<DD> Sequential description of the elements. <BR>
<P>
This integer array describes each element in the mesh sequentially. It contains:
<P>
<UL><LI>
  Loop i from 1 to NE
  <UL><LI> NCGE, the element geometry code (1 = node, 2 = segment, 3 = triangle,
      4 = quadrilateral, 5 = tetrahedron, 6 = pentahedron, 7 = hexahedron, 8 = super-element, ...)
     <LI> NMAE, the number of words required to store the reference numbers of the faces, edges and vertices,
     <LI> NDSDE, the element sub-domain number,
     <LI> NNO, the number of nodes per element,
     <LI> Loop j from 1 to NNO
     <UL><LI> NONO(j), the number of node j of the element,
     </UL> 
     End of loop j
     <LI> if NCOPNP (see array <b> NOP2</b>) is zero:
     <UL><LI> NPO, the number of points in the element,
       <LI> Loop j from 1 to NPO
        <OL><LI> NOPO(j), the number of point j of the element,
        </OL> 
        End of loop j
     </UL>
     <LI> if  NMAE is non-zero:
        <UL><LI> INING, an indicator for reference number information.
If INING = 3 only the reference numbers of the vertices are given, for INING = 2 the reference numbers
 of the edges followed by the the vertex reference numbers are given, and for  INING = 1 the 
reference numbers of the faces, edges and vertices are given.
           <LI> Loop from 2 to NMAE
           <OL><LI> if INING = 3, references of the vertices,
              <LI> if INING = 2, references of the edges followed by the vertices,
              <LI> if INING = 1, references of the faces, followed by the edges and vertices.
           </OL> 
           End of loop
        </UL></UL> 
  End of loop i
</UL>
<P>
 </DL>
<P>

<P>
<P>
<H2><A NAME=SECTION051142000000000000000>1.13.2 Element definitions</A></H2>
<P>
<P>
<P>
Having chosen the first vertex, each element is defined by:
<P>
<OL><P><A NAME=6579>&#160;</A><IMG BORDER=0 ALIGN=BOTTOM ALT="" SRC="img141.gif">
<BR><STRONG>Figure 1.4:</STRONG> <i> Segment, triangle and quadrilateral</i><A NAME=6575iSegmenttriangleandquadrilaterali6575>&#160;</A><BR>
<P>
<P>
<LI> The segment<A NAME=6305>&#160;</A>: <BR> 
   <IMG BORDER=0 ALIGN=BOTTOM ALT="" SRC="img142.gif"> (1) <IMG BORDER=0 ALIGN=BOTTOM ALT="" SRC="img10.gif"> (2)
<P>
<LI> The triangle<A NAME=6306>&#160;</A>: numbering anti-clockwise in the
two-dimensional case (in the three-dimensional case, there is no orientation).
   <IMG BORDER=0 ALIGN=BOTTOM ALT="" SRC="img142.gif"> edge [1]: (1) <IMG BORDER=0 ALIGN=BOTTOM ALT="" SRC="img10.gif"> (2)  (nodes 4, 5,
   ... if there are supplementary nodes) <BR> 
   <IMG BORDER=0 ALIGN=BOTTOM ALT="" SRC="img142.gif"> edge [2]: (2) <IMG BORDER=0 ALIGN=BOTTOM ALT="" SRC="img10.gif"> (3)  (...) <BR> 
   <IMG BORDER=0 ALIGN=BOTTOM ALT="" SRC="img142.gif"> edge [3]: (3) <IMG BORDER=0 ALIGN=BOTTOM ALT="" SRC="img10.gif"> (1)
<P>
<LI> The quadrilateral<A NAME=6307>&#160;</A>: numbering anti-clockwise
(same remark as for the triangle) <BR> 
   <IMG BORDER=0 ALIGN=BOTTOM ALT="" SRC="img142.gif"> edge [1]: (1) <IMG BORDER=0 ALIGN=BOTTOM ALT="" SRC="img10.gif"> (2) (nodes 5, 6, ...) <BR> 
   <IMG BORDER=0 ALIGN=BOTTOM ALT="" SRC="img142.gif"> edge [2]: (2) <IMG BORDER=0 ALIGN=BOTTOM ALT="" SRC="img10.gif"> (3) (...) <BR> 
   <IMG BORDER=0 ALIGN=BOTTOM ALT="" SRC="img142.gif"> edge [3]: (3) <IMG BORDER=0 ALIGN=BOTTOM ALT="" SRC="img10.gif"> (4) <BR> 
   <IMG BORDER=0 ALIGN=BOTTOM ALT="" SRC="img142.gif"> edge [4]: (4) <IMG BORDER=0 ALIGN=BOTTOM ALT="" SRC="img10.gif"> (1)
<P>
<P><A NAME=6589>&#160;</A><IMG BORDER=0 ALIGN=BOTTOM ALT="" SRC="img143.gif">
<BR><STRONG>Figure 1.5:</STRONG> <i> Tetrahedron, pentahedron and hexahedron</i><A NAME=6585iTetrahedronpentahedronandhexahedroni6585>&#160;</A><BR>
<P>
<P>
<LI> The tetrahedron<A NAME=6311>&#160;</A>: trihedral
 <IMG BORDER=0 ALIGN=MIDDLE ALT="" SRC="img144.gif"> direct (<IMG BORDER=0 ALIGN=MIDDLE ALT="" SRC="img145.gif"> designates the
vector from point i to point j). <BR> 
   <IMG BORDER=0 ALIGN=BOTTOM ALT="" SRC="img142.gif"> edge [1]: (1) <IMG BORDER=0 ALIGN=BOTTOM ALT="" SRC="img10.gif"> (2)  (nodes 5, ...) <BR> 
   <IMG BORDER=0 ALIGN=BOTTOM ALT="" SRC="img142.gif"> edge [2]: (2) <IMG BORDER=0 ALIGN=BOTTOM ALT="" SRC="img10.gif"> (3)  (...) <BR> 
   <IMG BORDER=0 ALIGN=BOTTOM ALT="" SRC="img142.gif"> edge [3]: (3) <IMG BORDER=0 ALIGN=BOTTOM ALT="" SRC="img10.gif"> (1)  <BR> 
   <IMG BORDER=0 ALIGN=BOTTOM ALT="" SRC="img142.gif"> edge [4]: (1) <IMG BORDER=0 ALIGN=BOTTOM ALT="" SRC="img10.gif"> (4) <BR> 
   <IMG BORDER=0 ALIGN=BOTTOM ALT="" SRC="img142.gif"> edge [5]: (2) <IMG BORDER=0 ALIGN=BOTTOM ALT="" SRC="img10.gif"> (4) <BR> 
   <IMG BORDER=0 ALIGN=BOTTOM ALT="" SRC="img142.gif"> edge [6]: (3) <IMG BORDER=0 ALIGN=BOTTOM ALT="" SRC="img10.gif"> (4) (nodes ...,
   <b>p</b>)
<P>
   All faces, seen from the exterior, are described anti-clockwise:   <BR> 
   <IMG BORDER=0 ALIGN=BOTTOM ALT="" SRC="img142.gif"> face [1]: (1) (3) (2) (nodes p+1, ...) <BR> 
   <IMG BORDER=0 ALIGN=BOTTOM ALT="" SRC="img142.gif"> face [2]: (1) (4) (3) (...)  <BR> 
   <IMG BORDER=0 ALIGN=BOTTOM ALT="" SRC="img142.gif"> face [3]: (1) (2) (4) <BR> 
   <IMG BORDER=0 ALIGN=BOTTOM ALT="" SRC="img142.gif"> face [4]: (2) (3) (4)
<P>
<LI> The pentahedron<A NAME=6316>&#160;</A>: trihedral
      <IMG BORDER=0 ALIGN=MIDDLE ALT="" SRC="img144.gif">  direct <BR> 
   <IMG BORDER=0 ALIGN=BOTTOM ALT="" SRC="img142.gif"> edge [1]: (1) <IMG BORDER=0 ALIGN=BOTTOM ALT="" SRC="img10.gif"> (2)  (nodes 7, ...) <BR> 
   <IMG BORDER=0 ALIGN=BOTTOM ALT="" SRC="img142.gif"> edge [2]: (2) <IMG BORDER=0 ALIGN=BOTTOM ALT="" SRC="img10.gif"> (3)  (...) <BR> 
   <IMG BORDER=0 ALIGN=BOTTOM ALT="" SRC="img142.gif"> edge [3]: (3) <IMG BORDER=0 ALIGN=BOTTOM ALT="" SRC="img10.gif"> (1)  <BR> 
   <IMG BORDER=0 ALIGN=BOTTOM ALT="" SRC="img142.gif"> edge [4]: (1) <IMG BORDER=0 ALIGN=BOTTOM ALT="" SRC="img10.gif"> (4) <BR> 
   <IMG BORDER=0 ALIGN=BOTTOM ALT="" SRC="img142.gif"> edge [5]: (2) <IMG BORDER=0 ALIGN=BOTTOM ALT="" SRC="img10.gif"> (5) <BR> 
   <IMG BORDER=0 ALIGN=BOTTOM ALT="" SRC="img142.gif"> edge [6]: (3) <IMG BORDER=0 ALIGN=BOTTOM ALT="" SRC="img10.gif"> (6) <BR> 
   <IMG BORDER=0 ALIGN=BOTTOM ALT="" SRC="img142.gif"> edge [7]: (4) <IMG BORDER=0 ALIGN=BOTTOM ALT="" SRC="img10.gif"> (5) <BR> 
   <IMG BORDER=0 ALIGN=BOTTOM ALT="" SRC="img142.gif"> edge [8]: (5) <IMG BORDER=0 ALIGN=BOTTOM ALT="" SRC="img10.gif"> (6) <BR> 
   <IMG BORDER=0 ALIGN=BOTTOM ALT="" SRC="img142.gif"> edge [9]: (6) <IMG BORDER=0 ALIGN=BOTTOM ALT="" SRC="img10.gif"> (4) (nodes ..., p)
<P>
   All faces, seen from the exterior, are described anti-clockwise. <BR> 
   <IMG BORDER=0 ALIGN=BOTTOM ALT="" SRC="img142.gif"> face [1] : (1) (3) (2)        (nodes p+1, ...) <BR> 
   <IMG BORDER=0 ALIGN=BOTTOM ALT="" SRC="img142.gif"> face [2] : (1) (4) (6) (3)     <BR> 
   <IMG BORDER=0 ALIGN=BOTTOM ALT="" SRC="img142.gif"> face [3] : (1) (2) (5) (4) <BR> 
   <IMG BORDER=0 ALIGN=BOTTOM ALT="" SRC="img142.gif"> face [4] : (4) (5) (6) <BR> 
   <IMG BORDER=0 ALIGN=BOTTOM ALT="" SRC="img142.gif"> face [5] : (2) (3) (5) (6)
<P>
<LI> The hexahedron<A NAME=6320>&#160;</A>: trihedral
      <IMG BORDER=0 ALIGN=MIDDLE ALT="" SRC="img146.gif"> direct <BR> 
   <IMG BORDER=0 ALIGN=BOTTOM ALT="" SRC="img142.gif"> edge [1]: (1) <IMG BORDER=0 ALIGN=BOTTOM ALT="" SRC="img10.gif"> (2)  (nodes 9, ...) <BR> 
   <IMG BORDER=0 ALIGN=BOTTOM ALT="" SRC="img142.gif"> edge [2]: (2) <IMG BORDER=0 ALIGN=BOTTOM ALT="" SRC="img10.gif"> (3)  (...) <BR> 
   <IMG BORDER=0 ALIGN=BOTTOM ALT="" SRC="img142.gif"> edge [3]: (3) <IMG BORDER=0 ALIGN=BOTTOM ALT="" SRC="img10.gif"> (4)  <BR> 
   <IMG BORDER=0 ALIGN=BOTTOM ALT="" SRC="img142.gif"> edge [4]: (4) <IMG BORDER=0 ALIGN=BOTTOM ALT="" SRC="img10.gif"> (1) <BR> 
   <IMG BORDER=0 ALIGN=BOTTOM ALT="" SRC="img142.gif"> edge [5]: (1) <IMG BORDER=0 ALIGN=BOTTOM ALT="" SRC="img10.gif"> (5) <BR> 
   <IMG BORDER=0 ALIGN=BOTTOM ALT="" SRC="img142.gif"> edge [6]: (2) <IMG BORDER=0 ALIGN=BOTTOM ALT="" SRC="img10.gif"> (6) <BR> 
   <IMG BORDER=0 ALIGN=BOTTOM ALT="" SRC="img142.gif"> edge [7]: (3) <IMG BORDER=0 ALIGN=BOTTOM ALT="" SRC="img10.gif"> (7) <BR> 
   <IMG BORDER=0 ALIGN=BOTTOM ALT="" SRC="img142.gif"> edge [8]: (4) <IMG BORDER=0 ALIGN=BOTTOM ALT="" SRC="img10.gif"> (8) <BR> 
   <IMG BORDER=0 ALIGN=BOTTOM ALT="" SRC="img142.gif"> edge [9]: (5) <IMG BORDER=0 ALIGN=BOTTOM ALT="" SRC="img10.gif"> (6) <BR> 
   <IMG BORDER=0 ALIGN=BOTTOM ALT="" SRC="img142.gif"> edge [10]: (6) <IMG BORDER=0 ALIGN=BOTTOM ALT="" SRC="img10.gif"> (7) <BR> 
   <IMG BORDER=0 ALIGN=BOTTOM ALT="" SRC="img142.gif"> edge [11]: (7) <IMG BORDER=0 ALIGN=BOTTOM ALT="" SRC="img10.gif"> (8) <BR> 
   <IMG BORDER=0 ALIGN=BOTTOM ALT="" SRC="img142.gif"> edge [12]: (8) <IMG BORDER=0 ALIGN=BOTTOM ALT="" SRC="img10.gif"> (5) (nodes ..., p)
<P>
   All faces, seen from the exterior, are described anti-clockwise. <BR> 
   <IMG BORDER=0 ALIGN=BOTTOM ALT="" SRC="img142.gif"> face [1] : (1) (4) (3) (2)  (nodes p+1, ...) <BR> 
   <IMG BORDER=0 ALIGN=BOTTOM ALT="" SRC="img142.gif"> face [2] : (1) (5) (8) (4)   <BR> 
   <IMG BORDER=0 ALIGN=BOTTOM ALT="" SRC="img142.gif"> face [3] : (1) (2) (6) (5) <BR> 
   <IMG BORDER=0 ALIGN=BOTTOM ALT="" SRC="img142.gif"> face [4] : (5) (6) (7) (8) <BR> 
   <IMG BORDER=0 ALIGN=BOTTOM ALT="" SRC="img142.gif"> face [5] : (2) (3) (7) (6) <BR> 
   <IMG BORDER=0 ALIGN=BOTTOM ALT="" SRC="img142.gif"> face [6] : (3) (4) (8) (7)
<P>
</OL>
<P>
<b> Remark:</b>  Other elements, developed to treat  specific problems, are added to the above elements
corresponding to the usual geometric forms;
we can cite, for example, the connected elements<A NAME=6326>&#160;</A> used to  simulate a
hinge<A NAME=6327>&#160;</A> 
(junction between two beams<A NAME=6328>&#160;</A>, for instance two segments; between two planes, for instance
 two quadrilaterals in the space).   <IMG BORDER=0 ALIGN=BOTTOM ALT="" SRC="img126.gif">
<P>
<b> Remark:</b> In proportion to the requirements, new elements  may appear. It is thus necessary to
define them in a consistent manner.   <IMG BORDER=0 ALIGN=BOTTOM ALT="" SRC="img126.gif">
<P>
<P>
<P>
<H2><A NAME=SECTION051143000000000000000>1.13.3 Corresponding tools</A></H2>
<P>
<P>
<P>
<H3><A NAME=SECTION051143100000000000000> Reading and writing a DS NOPO</A></H3>
<P>
A DS residing in core is written, as a whole (it is a category 1 DS), on sequential file via
 module <b> SDECRI</b>.
<P>
Similarly,  a DS residing on file is read and transferred, as a whole, to main memory via
 module <b> SDLECT</b>.
<P>
 <P>
<P>
<H3><A NAME=SECTION051143200000000000000> Printing a DS NOPO and plotting a mesh</A></H3>
<P>
<P>
<P>
The contents (total or partial) of a DS <b> NOPO</b> can be printed  by the following modules:
<P>
<DL COMPACT><DT>IMNOPO:
<DD> The whole DS (according to the print parameter IMPRE):
<P>
<PRE>      SUBROUTINE  IMNOPO(M,NFNOPO,NINOPO,IMPRE)
C AIM : PRINT THE ARRAYS OF DS NOPO, INCREASING WITH IMPRE
C ---   FILE NFNOPO (OR MC IF 0), LEVEL NINOPO
</PRE>
<P>
<DT>IMNOPS:
<DD> The array <b> NOP2</b> and certain mesh elements:
<P>
<PRE>      SUBROUTINE IMNOPS(M,NFNOPO,NINOPO,ISTRES,INDIC,LINDIC)
C AIM : PRINT ARRAYS 2 AND 5 OF DS NOPO
C ---   FILE NFNOPO (OR MC IF 0 ), LEVEL NINOPO
C       ISTRES = 0 NO NOP2, IF NOT PRINT NOP2
C       INDIC(*) THE NUMBERS OF THE LINDIC ELEMENTS OF NOP5 TO PRINT
</PRE>
<P>
<DT>INFONO:
<DD> An arbitrary value contained in the DS:
<P>
<PRE>      SUBROUTINE INFONO(M,IOPT,TYPESD,NIVEAU,TAB2,TAB4,TAB5,NUMREC,
     +                  XREC,YREC,ZREC)
C AIM : OUTPUT INFORMATION REGARDING A MESH DS ( NOPO )
</PRE>
<P>
The preprocessors <b> IMAGXX</b> and <b> INFOXX</b> are used if a conversational call of
 <b> IMNOPO</b> and <b> INFONO</b>, respectively, is desired.
<P>
 </DL>
<P>
The mesh contained in a file can be plotted via preprocessor <b> TRNOXX</b> [<A HREF="node57.html#mod_96">96</A>].
<P>
<P>
<P>
<H3><A NAME=SECTION051143300000000000000> Creation and modification modules for DS NOPO</A></H3>
<P>
<P>
<P>
The reader is referred to  [<A HREF="node57.html#guide3"><A NAME=tex2html164 HREF="../Guide3/welcome.html">MODULEF User Guide - 3</A></A>] for a description of the mesh construction and  modification methods and modules.
<P>
<P>
<P>
<H3><A NAME=SECTION051143400000000000000> Utilities for the manipulation of a DS NOPO</A></H3>
<P>
<P>
<P>
There are numerous utilities available to manipulate the contents of a DS <b> NOPO</b>, amongst which
we find the utilities to facilitate scrutinizing array <b> NOP5</b>.
<P>
<PRE> 
      SUBROUTINE CLNOPO (M,XM,IANOP2,IANOP4,IA,NCGE,NDSDE,NNO,NONO,
     +                   NPO,NOPOI,COORP,NREF)
C AIM : READ ARRAY NOP5 ET EXPLAIN IT (!)
C ---
C IN :
C --
C M,XM    : THE SUPER ARRAY
C IA      : START ADDRESS OF ARRAY NOP5  ( IANOP5 )
C
C OUT :
C ---
C THE SAME MNEMONICS AS IN BROCHURE &lt; DESCRIPTION OF THE DS &gt;
C IA      : UP-DATE ( START OF THE FOLLOWING ELEMENT )
C COORP   : CPOINT COORDINATES
C NREF    : ARRAY OF REFERENCE NUMBERS
C              3-D : POINTS, EDGES, FACES
C              2-D : POINTS, EDGES


      SUBROUTINE CLNOIA(NCOPNP,NOP5,IA,NCGE,IAS,IAR,IAF,NPO,NOPO)
C AIM : CLEAR ARRAY NOP5 (SEE CLNOPO)
C ---
C OUT : IA, IAS, IAR, IAF, NOPO AND NPO
C ---   ADDRESSES OF REFERENCES OR 0, ARRAY OF POINTS, 
C       THE NUMBER OF POINTS


      SUBROUTINE CLNOIN(NCOPNP,NOP5,IA,NCGE,IAS,IAR,IAF,NPO,NNO,NONO)
C AIM : CLEAR ARRAY NOP5 ( SEE CLNOPO )
C --- 
C OUT :  IA, IAS, IAR, IAF, NPO, NNO, NONO  


      SUBROUTINE CLNO5C(NDIM,NCOPNP,NOP5,IA,NCGE,NDSDE,NNO,NONO,
     +                  NPO,NOPOI,COOR4,COORP)
C AIM : READ NOP5 AND COOR4 ( ALIAS NOP4 ) IN ORDER TO 
C       COMPLETE NONO,NOPOI,...
</PRE>
<P>
Utilities <b> NBSOME</b>, <b> NBARET</b> and <b> NBFACE</b> output the number of vertices, edges and faces
of each type of element.
<P>

<P>
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