1 THE FINITE ELEMENT PROGRAM Z88
1.1 GENERAL OVERVIEW FEA PROGRAM Z88
The Z88 philosophy:
+ Fast and compact: Developed for PC, no ported mainframe system
+ Flexible and transparent: Controlled by text files
+ "Small is beautifull" - a modular system vs. monolithic monsters
+ native UNIX and Windows programs, no emulation
+ UNIX and Windows programs use the same computing kernels
+ Full data exchange from and to CAD systems with DXF-Interface
+ mesh import from Pro/ENGINEER
+ Context sensitive online-help under Windows and UNIX
+ No copy protection, no annoying passwords
+ Simplest installation: No subdirectories, no change of system files
+ Under UNIX: Automatic control and cumulative runs
possible
Notes:
Always compare FE calculations with analytical rough calculations,
results of experiments, plausibility considerations and other
tests without exception!
Keep in mind that sign definitions of Z88 (and also other FEM
programs) differ from the usual definitions of the analytical
technical mechanics from time to time .
Z88 is a complex computer program. How Z88 deals with other programs
and utilities etc. is not predictable. We cannot give any advice
and support here! You should switch off at first all other programs
and utilities. Run Z88 "purely" and then start further
programs step-by-step. Z88 uses only documented operating system
calls of Windows and UNIX !
Summary of the Z88 element library:
(You will find the exact description of the element library in
chapter 4.)
Twodimensinal problems: Plane stress, plates,
beams, trusses
Plane Stress Triangle Element No. 3
- Shape functions quadratic
- Quality of displacements very good
- Quality of stresses in the center of gravity good
- Computing effort: average
- Size of element stiffness matrix: 12 * 12
Plane Stress Isoparametric Element No. 7
- Quadratic Isoparametric Serendipity element
- Quality of displacements very good
- Quality of stresses in the Gauss- points very good
- Quality of stresses in the corner nodes good
- Computing effort: High
- Size of element stiffness matrix: 16 * 16
- Linear function
- Quality of displacements exact (Hooke 's law)
- Quality of stresses exact (Hooke ' s law)
- Computing effort: Minimal
- Size of element stiffness matrix: 4 * 4
Plane Stress Isoparametric Element No. 11
- Cubic Isoparametric Serendipity element
- Quality of displacements excellent
- Quality of stresses in the Gauss- points excellent
- Quality of stresses in the corner nodes good
- Computing effort: Very high
- Size of element stiffness matrix: 24 * 24
- Linear function for tensile stress, cubic function for bending stress
- Quality of displacements exact (Hooke 's law)
- Quality of stresses exact (Hooke ' s law)
- Computing effort: Low
- Size of element stiffness matrix: 8 * 8
Plane Stress Isoparametric Element No. 14
- Quadratic Isoparametric Serendipity element
- Quality of displacements very good
- Quality of stresses in the Gauss- points very good
- Quality of stresses in the corner nodes good
- Computing effort: High
- Size of element stiffness matrix: 12 * 12
Isoparametric Plate Element No. 18
- Quadratic Isoparametric Serendipity element following Reissner- Mindlin's theory
- Quality of displacements very good
- Quality of stresses in the Gauss- points good
- Quality of stresses in the corner nodes acceptable
- Computing effort: medium
- Size of element stiffness matrix: 18 * 18
Isoparametric Plate Element No. 19
- Cubic Isoparametric Lagrange element following Reissner- Mindlin's theory
- Quality of displacements very good
- Quality of stresses in the Gauss- points very good
- Quality of stresses in the corner nodes good
- Computing effort: High
- Size of element stiffness matrix: 48 * 48
Isoparametric Plate Element No. 20
- Quadratic Isoparametric Serendipity element following Reissner- Mindlin's theory
- Quality of displacements very good
- Quality of stresses in the Gauss- points good
- Quality of stresses in the corner nodes quite good
- Computing effort: medium
- Size of element stiffness matrix: 24 * 24
Axisymmetric problems:
- Linear function
- Quality of displacements average
- Quality of stresses in the corner nodes inaccurate
- Computing effort: Low
- Size of element stiffness matrix: 6 * 6
- Quadratic Isoparametric Serendipity element
- Quality of displacements very good
- Quality of stresses in the Gauss- points very good
- Quality of stresses in the corner nodes good
- Computing effort: High
- Size of element stiffness matrix: 16 * 16
- Linear function for torsion and tensile stress, cubic function for bending stress
- Quality of displacements exact (Hooke 's law)
- Quality of stresses exact (Hooke ' s law)
- Computing effort: Low
- Size of element stiffness matrix: 12 * 12
- Cubic Isoparametric Serendipity element
- Quality of displacements excellent
- Quality of stresses in the Gauss- points excellent
- Quality of stresses in the corner nodes good
- Computing effort: Very high
- Size of element stiffness matrix: 24 * 24
- Quadratic Isoparametric Serendipity element
- Quality of displacements very good
- Quality of stresses in the Gauss- points very good
- Quality of stresses in the corner nodes good
- Computing effort: High
- Size of element stiffness matrix: 12 * 12
Space problems:
- Linear function
- Quality of displacements exact (Hooke 's law)
- Quality of stresses exact (Hooke ' s law)
- Computing effort: Minimal
- Size of element stiffness matrix: 6 * 6
- Linear function for tensile stress, cubic function for bending stress
- Quality of displacements exact (Hooke 's law)
- Quality of stresses exact (Hooke ' s law)
- Computing effort: Low
- Size of element stiffness matrix: 12 * 12
- Linear shape functions
- Quality of displacements average
- Stresses in the Gauss- points useable
- Stresses in corner nodes inaccurate
- Computing effort: very high
- Size of element stiffness matrix: 24 * 24
- Quadratic Isoparametric Serendipity element
- Quality of displacements very good
- Stresses in the Gauss- points very good
- Stresses in corner nodes good
- Computing effort: extremely high
- Size of element stiffness matrix: 60 * 60
- Linear shape functions
- Quality of displacements bad
- Stresses in the Gauss- points inaccurate
- Stresses in corner nodes very inaccurate
- Computing effort: medium
- Size of element stiffness matrix: 12 * 12
- Quadratic Isoparametric Serendipity element
- Quality of displacements very good
- Stresses in the Gauss- points very good
- Stresses in corner nodes good
- Computing effort: very high
- Size of element stiffness matrix: 30 * 30
The Z88 computing units:
Overview:
Z88 always exclusively works at the tasks required at the moment.
Thus, Z88 is no gigantic, monolithic program, but consists of
several separate running modules according to the UNIX philosophy
"Small Is Beautiful". They are loaded into the main
memory according to your requirements, execute their tasks and
release the main memory again. In this way Z88's achieves its
enormous speed and faultlessness beating many other FE programs!
The Z88 modules communicate by files, cf. Chapter 3.
Short description of the modules:
I. The Solver
The solver is the heart of any FEA system. It reads the
general structure data Z88I1.TXT and the
boundary conditions Z88I2.TXT. Basically,
the Z88 input files can be created by CAD converter Z88X,
by COSMOS converter Z88G, by net (or mesh)
generator Z88N, by editor or word processor
system or by a mixed procedure, e.g. by CAD and editor. The solver
generates prepared structure data Z88O0.TXT and processed boundary
conditions Z88O1.TXT, calculates the element stiffness matrices,
compiles the total stiffness matrix, scales the system of equations,
solves the (huge) system of equations and stores the displacements
in Z88O2.TXT. Therefore, the main task of every FEA system, the
calculation of displacements, is solved. Thereupon, if you wish,
the stresses can be calculated by Z88D
and/or nodal forces by Z88E.
Z88 features two totally different solvers:
Z88F: This is a so-called direct
solver with skyline storing scheme and an in-situ Cholesky solver.
It is the standard solver of Z88, easy to handle and very fast
for small and medium structures. However, like any direct solver
Z88F reacts badly on ill- numbered nodes but you may improve the
situation with the Cuthill- McKee program Z88H. Z88F is your choice
for small and medium structures, up to 20,000 ... 50,000 degrees
of freedom.
Z88I1 and Z88I2: This is
a so-called iteration solver featuring two modules. Z88I1 computes
the pointers for the storage scheme of the total stiffness matrix.
Z88I2 computes the stiffness matrices, addes the boundary conditions
and solves the system of equations by the method of conjugate
gradients featuring SOR- preconditioning or precontitioning by
an incomplete Cholesky decomposition depending on your choice.
Like any iteration solver Z88I1/Z88I2 deals well with bad node
numbering, a run with the Cuthill- McKee program Z88H may improve
the situation further, however. Z88I1/Z88I2 is your choice for
large structures.
II. The link to CAD programs
The CAD converter Z88X converts
DXF files from CAD systems into Z88 input files ( net generator
input file Z88NI.TXT, general structure
data Z88I1.TXT, boundary conditions Z88I2.TXT
and stress parameters file Z88I3.TXT )
or, and this is the real goodie, also converts Z88 input files
into DXF files. You cannot only produce input data in the CAD
system and then use in Z88, but you can also complete Z88 entry
files which are always simple ASCII files, e.g. by text editor,
by word processing, by EXCEL or e.g. by your own special programs
and then convert the data sets back into the CAD system by CAD
converters Z88X. In the CAD system you can add more informations,
then push the data again to Z88. This flexibility is unique!
The COSMOS converter Z88G reads
FEA input files following the COSMOS format and generates the
Z88 input files Z88I1.TXT, Z88I2.TXT
and Z88I3.TXT automatically. You may produce
COSMOS data files by various CAD programs. However, Z88G is properly
tested with Pro/ENGINEER with the Pro/MESH option by Parametric
Technology, USA. Thus, you may directly use Pro/ENGINEER 3D models
with Z88 !
The Cuthill- McKee program Z88H
was mainly designed for use with Z88G. It allows the re-numbering
of finite elements meshes and may heavily decrease the memory
needs for meshes generated by automeshers i.e. Pro/MESH.
III. The net generator for ordered meshes
The net (or mesh) generator Z88N
reads the super structure data Z88NI.TXT
and computes the general structure data Z88I1.TXT.
In principle, the net generator file Z88NI.TXT has the same construction
as the file of the general structure data Z88I1.TXT. It can also
be generated by CAD converters Z88X, by editor or word processor
system or with a mixed procedure.
IV. The postprocessors
Stresses are calculated by Z88D.
Z88F or Z88I1 and Z88I2
must have run before. Z88D reads a small parameter file Z88I3.TXT
and stores the stresses in Z88O3.TXT.
Nodal forces are calculated by Z88E.
Z88F or Z88I1 and Z88I2
must have run before. Z88E stores the nodal forces in Z88O4.TXT.
The plot program Z88P plots deflections
and stresses on the CTR or on a HP-GL plotter or a printer capable
of HP-GL, e.g. HP LaserJet. Z88P is suitable for a quick inspection
of the undeflected and the deflected structures as well as for
showing the stresses. Of course, you can show undeflected structures
on your CAD program capable of DXF via CAD converter Z88X, too,
but Z88P is much faster.
V. The file checker
The Filechecker Z88V checks the
input files Z88NI.TXT or Z88I1.TXT to Z88I3.TXT for formal correctness.
In addition, it can show the actual memory defined by you in the
file Z88.DYN.
All modules of Z88 request Memory dynamically:
The user can define this in the file Z88.DYN.
Z88 is delivered with default values which you can and also should
change if necessary. This is possible at any time. The Z88 modules
are genuine 32 bit (or 64 bit) programs and request their memory
by operating system calls via calloc. The header file Z88.DYN
provides how much memory shall be requested. You can request all
virtual memory (virtual memory = main memory + swap area), which
is provided by the operating system. Therefore there is no
limit for the size of the Z88 finite element structures !
You can also fix whether Z88 works with English or German language
in Z88.DYN: Keyword ENGLISH or GERMAN .
Multitasking of Z88:
Absolute multitasking is possible under Windows and UNIX, i. e.
several Z88 modules or other genuine Windows programs can run
parallel. Make sure that you do not overlap the windows (put them
side by side), as if the Z88 modules have once started they are
not evaluating WM_PAINT signals for speed reasons. This means,
that, although the Z88 programs are properly working, displays
and window images can be destroyed if you enlarge, reduce, move
or cover Z88 windows by other programs. This does not have any
influence on the computing results and only by this trick the
outstanding speed of Z88 can be gained. Keep in mind that big
space structures, e.g. with 20 nodes hexahedrons, can put very
heavy load on your computer which can slow down the machine totally.
Thus, let Z88 run alone and do not start any memory eaters like
the various office programs.
Hints for the start of Z88:
Windows:
All Z88 modules can be started directly via Explorer, from a group
which contains the various Z88 modules or via Start > Run.
It suffices to call the Z88-Commander Z88COM
for launching all other modules.
UNIX:
Launch the modules directly from a UNIX shell, from the Z88-Commander Z88COM,
or, as an extended possibility, e.g. for large-caliber night runs,
from a shell-script (sh, bash, ksh etc.). You have all
unlimited liberties of the UNIX operating system. All modules
except Z88COM and Z88P can be started in text mode from consoles,
but naturally also in an X window. As Motif programs the Z88-Commander
Z88COM and the plot program Z88P are to start from an X-term.
For a convenient use of Z88, fire up your X-Window-manager, open
an X-term and launch Z88COM. Put Z88COM and the X-Term, which
started Z88COM, side-by-side or over-and-under to see both.
The Input and Output of Z88:
The input and output files are generated either by an editor
(e.g. the editor or notepad of Windows, DOS editors
like edit, UNIX tools like vi, emacs, joe), word processor program
(e.g. WinWord etc.), spreadsheet program
(e.g. Excel) or via CAD converter Z88X
directly in a CAD program, which can read and write DXF files
(e.g. AutoCAD) or by converting a COSMOS file with Z88G,
which came from a 3D CAD program e.g. Pro/ENGINEER..
For the user this means maximum flexibility and transparency,
as the input and output files of Z88 are quite simple ASCII text
files. You can fill the files by arbitrary tools or by hand, and
also by self-written programs, of course. Only make sure to meet
the Z88 conventions for the respective file structure cf. Chapter
3.
You can modify output files as you like, enlarge them with your
own comments, reduce them to the essential or use them as input
for other programs.
Dimensions, i. e. measurement units, are not used explicitly.
You can work in optional measurement systems, e.g. in the Metric
or Imperial measurement system. Use inches, Newtons, pounds, tons,
millimeters, meters, yards - whatever you prefer. But make sure
to keep the one chosen measurement units throughout all computations
of this structure. Example: You want to work with mm and N so
Young's modulus must be used in N/mm*mm.
Note:
The Z88 input files read always:
+ Z88G.COS COSMOS Input file coming from a 3D CAD program, for converter Z88G
+ Z88X.DXF Exchange file for CAD programs and for CAD converter Z88X
+ Z88NI.TXT Input file for the net generator of Z88N
+ Z88I1.TXT Input file (general structure data) for the FE processor of Z88F
+ Z88I2.TXT Input file (boundary conditions) for the FE processor of Z88F
+ Z88I3.TXT Input file (control values) for the stress processor of Z88D
+ Z88I4.TXT Input file (control values)
for the iteration solver Z88I1/Z88I2
The Z88 output files read always
+ Z88O0.TXT Prepared structure data for documentation purposes
+ Z88O1.TXT Prepared boundary conditions for documentation purposes
+ Z88O2.TXT Computed displacements
+ Z88O3.TXT Computed stresses
+ Z88O4.TXT Computed nodal forces
These file names are expected from the Z88 modules and they must
reside in the same Directory as the Z88 modules. You cannot allocate
your own names for data sets. Of course, you may rename the Z88*.*
files after all calculations have been done and save them in other
directories.
Making:
You may allways create the net generator file Z88NI.TXT, the general structure data file Z88I1.TXT, the boundary conditions file Z88I2.TXT and the control values file Z88I3.TXT for the stress prozessor by hand using an editor or the like.
Using automatic generation consider the following possibilities:
| CAD system, e.g. | creates | converter | creates | net generator | creates |
| Pro/ENGINEER
(with Pro/MESH) | Z88G.COS | Z88G | Z88I1.TXT,
Z88I2.TXT, Z88I3.TXT | not necessary | files
still exist |
| AutoCAD | Z88X.DXF | Z88X | Z88NI.TXT | Z88N | Z88I1.TXT |
| AutoCAD | Z88X.DXF | Z88X | Z88I1.TXT,
Z88I2.TXT, Z88I3.TXT | not necessary | files
still exist |
Z88 protocol files:
The Z88 modules always store protocol files .LOG, e.g. Z88F.LOG
documents the steps or errors of the calculation of Z88F. Look
at the various .LOG files in case of doubt. They also document
the current memory needs. UNIX: If different users work
in the same Z88 directory, make sure to have the proper permissions
for the .LOG files, too. Use umask.
Printing of Z88 files
Is not supported by the Z88- Commanders. You print them by the
Explorer of Windows or by an editor or word processing program.
Use the printing routines of the UNIX operating system.
Which Z88 finite Element types can be produced automatically ?
| element type | function | COSMOS | DXF | super element | creates FE
(Z88N) |
| Hexahedron No.1 | linear | No | Yes | No | - |
| Hexahedron No.10 | quadratic | No | Yes | Yes | Hexa No.10 & No.1 |
| Tetrahedron No.16 | quadratic | Yes | No | No | - |
| Tetrahedron No.17 | linear | Yes | No | No | - |
| Plane stress No.3 | quadratic | Yes | Yes | No | - |
| Plane stress No.7 | quadratic | Yes | Yes | Yes | Plane stress No.7 |
| Plane stress No.11 | cubic | No | Yes | Yes | Plane stress No.7 |
| Plane stress No.14 | quadratic | Yes | Yes | No | - |
| Torus No.6 | linear | No | Yes | No | - |
| Torus No.8 | quadratic | No | Yes | Yes | Torus No.8 |
| Torus No.12 | kubisch | No | Yes | Yes | Torus No.8 |
| Torus No.15 | quadratic | Yes | Yes | No | - |
| Plate No.18 | quadratic | Yes | Yes | No | - |
| Plate No.19 | cubic | No | Yes | No | - |
| Plate No.20 | quadratic | Yes | Yes | Yes | Pla No.19 & No.20 |
| Truss No.4 | exact | No | Yes | No | - |
| Truss No.9 | exact | No | Yes | No | - |
| Beam No.2 | exact | No | Yes | No | - |
| Cam No.5 | exact | No | Yes | No | - |
| Beam No.13 | exact | No | Yes | No | - |
Z88 files:
| Name | Type | Direction | Purpose | change, modify | MS-Win | UNIX |
| Z88.DYN | ASCII | Input | Memory & Language header file | Yes, Recom. | Yes | Yes |
| Z88X.DXF | ASCII | In/Output | DXF from and to Z88 | Yes, 1) | Yes | Yes |
| Z88NI.TXT | ASCII | Input | net generator input file | Yes | Yes | Yes |
| Z88I1.TXT | ASCII | Input | general structure data | Yes | Yes | Yes |
| Z88I2.TXT | ASCII | Input | constraints | Yes | Yes | Yes |
| Z88I3.TXT | ASCII | Input | stress parameter header file | Yes | Yes | Yes |
| Z88I4.TXT | ASCII | Input | header file for iteration solver | Yes | Yes | Yes |
| Z88O0.TXT | ASCII | Output | processed structure data | Possible | Yes | Yes |
| Z88O1.TXT | ASCII | Output | processed constraints | Possible | Yes | Yes |
| Z88O2.TXT | ASCII | Output | computed displacements | Possible | Yes | Yes |
| Z88O3.TXT | ASCII | Output | computed stresses | Possible | Yes | Yes |
| Z88O4.TXT | ASCII | Output | computed nodal forces | Possible | Yes | Yes |
| Z88O5.TXT | ASCII | Output | for internal use of Z88P | No 2) | Yes | Yes |
| Z88O6.TXT | ASCII | Output | Main HP- GL file from Z88P | Yes 1) | Yes | Yes |
| Z88O7.TXT | ASCII | Output | Aux. HP- GL file from Z88P | Yes 1) | Yes | Yes |
| Z88P.COL | ASCII | Input | Color header file Z88P MS-Win | Possible | Yes | No |
| Z88.FCD | ASCII | Input | Fonts, Colors, Dimens. UNIX | Possible | No | Yes |
| Z88COM.CFG | ASCII | Input | configuration file Z88COM | No 2) | Yes | No |
| Z88O1.BNY | Binary | In/Output | fast communication file | No 3) | Yes | Yes |
| Z88O2.BNY | Binary | In/Output | fast communication file | No 3) | Yes | Yes |
| Z88O3..BNY | Binary | In/Output | fast communication file | No 3) | Yes | Yes |
| Z88O4..BNY | Binary | In/Output | fast communication file | No 3) 4) | Yes | Yes |