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 usefull 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.