2.5 THE MESH GENERATOR Z88N
The mesh generator Z88N can produce 2-dimensional and 3-dimensional
meshes. Z88N reads the mesh generator input file Z88NI.TXT
and writes the general structure data file Z88I1.TXT.
For the description of Z88NI.TXT
see chapter 3.
A mesh generation is sensible and permitted only for continuum elements:
Super structure | Finite element structure |
Plane stress element No.7 | Plane stress element No.7 |
Torus No.8 | Torus No.8 |
Plane stress element No.11 | Plane stress element No.7 |
Torus No.12 | Torus No.8 |
Hexahedron No.10 | Hexahedron No.10 |
Hexahedron No.10 | Hexahedron No.1 |
Plate No.20 | Plate No.20 |
Plate No.20 | Plate No.19 |
Mixed structures e.g. containing Plane Stress Elements No.7
and Trusses No.9, cannot be processed.
In such a case let the mesh generator process a super structure
containing only Plane Stress Elements No.7 without any Trusses
No.9. Run Z88N. Then convert with the CAD converter Z88X
the file Z88I1.TXT generated by the mesh generator Z88N to the
DXF file Z88X.DXF. Start your CAD programm, import Z88X.DXF and
insert the trusses, in addition you can also define the constraints
on the fly. Export the drawing to Z88X.DXF, run Z88X again and
generate Z88I1.TXT (general structure data) and optionally Z88I2.TXT
(boundary conditions).
Mode of operation of the mesh generator:
The generation of FE meshes proceeds as follows: The continuum
is described by super elements (short SE), which practically corresponds
to a quite rough FE structure. Super elements can be: Hexahedrons No.10,
Plane Stress Element No.7 and Plane Stress Element No.11
as well as Toruses No.8 and Toruses No.12.
and Plates No.20.
The super structure then will be subdivided. This is done super element wise, starting with SE 1, SE 2 up to the last SE. SE 1 produces the finite elements (short FE) 1 to j, SE 2 the FE j+1 to k, SE 3 the FE k+1 to m and so on. Within the SE the direction of the local coordinates determines the nodal numbers and the element numbers of the FE structure. Definition:
> Local x axis runs in direction of local nodes 1 and 2
> Local y axis runs in direction of local nodes 1 and 4
> Local z axis runs in direction of local nodes 1 and 5
Super structures in space are subdivided first in z, then in y and for the end in x direction i. e. the FE element numbers start along the z direction. To plane and axially symmetric structures applies analogously: The numbering starts along the y axis or for axially symmetric elements along the z axis (cylinder coordinates!).
Along the local axises can be subdivided as follows:
> Equidistant
> Increasing geometrically from node 1 to 4 or 5: Mesh becomes
rougher
> Decreasing geometrically from node 1 to 4 or 5: Mesh becomes
finer
It is obvious, that for lines or areas, which two super elements share, the super elements must be subdivided exactly the same! The mesh generator doesn't check this and then generates useless or totally mad FE meshes. Example:
Because the local axises x, y and z are defined by the location
of the local nodes 1, 4 and 5, it is possible to generate almost
arbitrary numberings for nodes and elements of the FE structure
by corresponding construction of the coincidence list in the mesh
generator input file Z88NI.TXT.
Example for the generation of a FE structure with 8 FE Plane Stress Elements No.7 from a super structure with 2 Plane Stress Elements No.7 (looks the same with Toruses No.8):
Specials:
The mesh generator checks which nodes are already known at the
production of new FE nodes. It needs for this check a trap radius
(a computer cannot meet a floating point number exactly). This
trap radius is provided for all 3 axises per default 0.01. Modify
the trap radiuses when processing very small or very large numerical
values.
In addition the mesh generator determines for each super element,
which other super elements meet this super element. For Plane
Stress Elements No.7 and No.11 or Toruses No.8 and No.12 this
can be at the most 8 other SE. This maximum number MAXAN is provided
in Z88.DYN per default 15. Theoretically,
Hexahedrons No.10 can meet 26 other elements (6 areas, 8 corners,
12 edges). Practice has proved, that even complicated space structures
with MAXAN = 15 worked fine. If in doubt increase MAXAN in Z88.DYN.
Attention mesh generator Z88N: The generator can generate
input files with no trouble at all which blast all limits of the
FE processor. Generate therefore at first rougher FE structures,
check with Z88F Test Mode whether
they fit into memory, then refine if necessary. A good starting
point: Produce approx. 5..10 times more finite elements than super
elements.
Note mesh generator Z88N: If coordinate flag KFLAG is set
to 1 in the mesh generator input file Z88NI.TXT
i.e. input values are polar or cylindrical coordinates, then the
generated output file Z88I1.TXT (general structure data) has always
cartesian coordinates and KFLAG is set to 0.