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 and, if nessesary, the file for
surface and pressure loads Z88I5.TXT. Basically, the
Z88 input files can be created by CAD converter Z88X, by COSMOS converter Z88G, by 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 (mesh generator input
file Z88NI.TXT, general structure data Z88I1.TXT, boundary conditions Z88I2.TXT, the file for surface and pressure
loads Z88I5.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 or the NASTRAN format and generates
the Z88 input files Z88I1.TXT, Z88I2.TXT , Z88I5.TXT and Z88I3.TXT automatically. You may produce COSMOS
or NASTRAN data files by various CAD programs. However, Z88G is properly tested
with Pro/ENGINEER with the Pro/MECHANICA 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/MECHANICA.
III.
The mesh generator for ordered meshes
The mesh
generator Z88N
reads the super structure data Z88NI.TXT and computes the general structure data Z88I1.TXT. In principle, the mesh 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
and Z88O plot deflections and stresses on the CTR, Z88P also on a HP-GL
plotter or a printer capable of HP-GL, e.g. HP LaserJet. Z88P and Z88O are
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
Z88O and Z88P are 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, Z88O 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 programs Z88O and 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 or NASTRAN 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
+
Z88G.NAS NASTRAN
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 mesh 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
+ Z88I5.TXT Input file for surface and pressure loads
for the solvers Z88F and 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 mesh
generator file Z88NI.TXT, the general structure data file Z88I1.TXT, the
boundary conditions file Z88I2.TXT, the file for surface and pressure loads
Z88I5.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 |
mesh
generator |
creates |
|
|
|
|
|
|
Pro/ENGINEER
Pro/MECHANICA |
Z88G.COS |
Z88G |
Z88I1.TXT, Z88I2.TXT,
Z88I3.TXT, Z88I5.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, Z88I5.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) |
|
|
|
|
|
|
linear |
No |
Yes |
No |
- |
|
quadratic |
No |
Yes |
Yes |
Hexa No.10
& No.1 |
|
quadratic |
Yes |
No |
No |
- |
|
linear |
Yes |
No |
No |
- |
|
|
|
|
|
|
|
quadratic |
No |
Yes |
No |
- |
|
quadratic |
Yes |
Yes |
Yes |
Plane
stress No.7 |
|
cubic |
No |
Yes |
Yes |
||
quadratic |
Yes |
Yes |
No |
- |
|
|
|
|
|
|
|
linear |
No |
Yes |
No |
- |
|
quadratic |
Yes |
Yes |
Yes |
Torus
No.8 |
|
kubisch |
No |
Yes |
Yes |
||
quadratic |
Yes |
Yes |
No |
- |
|
|
|
|
|
|
|
quadratic |
Yes |
Yes |
No |
- |
|
cubic |
No |
Yes |
No |
- |
|
quadratic |
Yes |
Yes |
Yes |
Pla No.19 &
No.20 |
|
|
|
|
|
|
|
exact |
No |
Yes |
No |
- |
|
exact |
No |
Yes |
No |
- |
|
|
|
|
|
|
|
exact |
No |
Yes |
No |
- |
|
exact |
No |
Yes |
No |
- |
|
exact |
No |
Yes |
No |
- |
Z88
files:
Name |
Type |
Direction |
Purpose |
change,
modify |
MS-Win |
UNIX |
|
|
|
|
|
|
|
ASCII |
Input |
Memory
& Language header file |
Yes,
Recom. |
Yes |
Yes |
|
|
|
|
|
|
|
|
ASCII |
Input |
COSMOS to
Z88 |
Yes, 1) |
Yes |
Yes |
|
ASCII |
Input |
NASTRAN
to Z88 |
Yes,1) |
Yes |
Yes |
|
ASCII |
In/Output |
DXF from
and to Z88 |
Yes, 1) |
Yes |
Yes |
|
|
|
|
|
|
|
|
ASCII |
Input |
mesh
generator input file |
Yes |
Yes |
Yes |
|
ASCII |
Input |
general
structure data |
Yes |
Yes |
Yes |
|
ASCII |
Input |
constraints |
Yes |
Yes |
Yes |
|
ASCII |
Input |
stress parameter
header file |
Yes |
Yes |
Yes |
|
ASCII |
Input |
header
file for iteration solver |
Yes |
Yes |
Yes |
|
ASCII |
Input |
Surface
and pressure loads |
Yes |
Yes |
Yes |
|
|
|
|
|
|
|
|
ASCII |
Output |
processed
structure data |
Possible |
Yes |
Yes |
|
ASCII |
Output |
processed
constraints |
Possible |
Yes |
Yes |
|
ASCII |
Output |
computed
displacements |
Possible |
Yes |
Yes |
|
ASCII |
Output |
computed
stresses |
Possible |
Yes |
Yes |
|
ASCII |
Output |
computed
nodal forces |
Possible |
Yes |
Yes |
|
|
|
|
|
|
|
|
Z88O5.TXT |
ASCII |
Output |
for
internal use of Z88P |
No 2) |
Yes |
Yes |
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 |
Z88O8.TXT |
ASCII |
Output |
for
internal use of Z88O |
No 2) |
Yes |
Yes |
ASCII |
Input |
Color
header file Z88P MS-Win |
Possible |
Yes |
No |
|
ASCII |
Input |
Color
header file Z88O MS-Win |
Possible |
Yes |
No |
|
ASCII |
Input |
Fonts, Colors,
Dimens. UNIX for Z88COM, Z88O and Z88P |
Possible |
No |
Yes |
|
|
|
|
|
|
|
|
ASCII |
Input |
configuration
file Z88COM |
No 2) |
Yes |
No |
|
|
|
|
|
|
|
|
Z88O1.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 |