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 Windows and UNIX programs, no emulation
+ Windows
and UNIX programs use the same computing and grafic 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
+
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 three 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 ... 30,000 degrees
of
freedom.
Z88I1 and
Z88PAR: This is a
so-called direct sparse matrix
solver with fill-in featuring two modules. Z88I1 computes the pointers
for the
storage scheme of the total stiffness matrix. Z88PAR uses the PARDISO
solver
and computes the stiffness matrices, addes the boundary conditions and
solves
the system of equations. This solver is very fast but uses very much
dynamic
memory. Z88I1/Z88PAR is your choice for medium-sized structures up to
150,000
DOF on ordinary 32 bit PCs. However, we’ve computed structures with ~ 1
million
of DOF very fast using a computer featuring 32 (!) Gbyte of memory, 4
CPUs, 64
bit Windows version of Z88.
Z88I1 and
Z88I2:
This is a so-called sparse matrix 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. This solver needs some considerations but deals
with
structures with more than 100,000 DOF at nearly the same speed as the
solvers
of the large and expensive commercial FEA programs as our tests showed.
In
addition, a minimum of storage is needed. So, this solver is your
choice for large
structures with more than 150,000 … 200,000 DOF. Structures with ~ 5
million
DOF are no problem for Z88I2 if you use a 64 bit operation system
(Windows or
LINUX) along with the 64 bit version of Z88 and about 6 GByte of memory
(with
tricks i.e. compiling Z88 with 8 Byte pointers and 4 Byte integers, 4
GByte
will do). This very stable and proved
solver works always, thus, you may use it as your standard solver.
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 3D
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
or Z88I1 and Z88PAR
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
or Z88I1 and Z88PAR
must have run
before. Z88E stores
the nodal forces in Z88O4.TXT.
The
plot program Z88O
plots deflections and stresses. Operating in 3D mode, you
may use wireframe or hidden line scenes or scenes with lighting. Z88O
replaces
the former plot programs Z88P and Z88O V12. The Windows version works
with the WinAPI and OpenGL, the LINUX
version works with GTK+ and OpenGL.
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 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 Z88O can be started in text mode from
consoles, but naturally also in an X window. As GTK+ programs the
Z88-Commander Z88COM and the plot program Z88O 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, 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 Z88N
+ Z88I1.TXT Input file (general structure data)
for the solvers Z88F,
Z88I2 and Z88PAR
+ Z88I2.TXT
Input file (boundary conditions) for
the solvers Z88F,
Z88I2 and Z88PAR
+ Z88I3.TXT
Input file (control values) for the
stress processor Z88D
+ Z88I4.TXT
Input file (control
values) for the sparse matrix solvers Z88I1/Z88I2 and Z88I1/Z88PAR
+ Z88I5.TXT Input file for surface and
pressure loads
for the solvers Z88F, Z88I2 and Z88PAR
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,
boundary conditions |
Yes |
Yes |
Yes |
|
ASCII |
Input |
stress parameter
header file |
Yes |
Yes |
Yes |
|
ASCII |
Input |
header file for
sparse matrix solvers |
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 Z88O |
No 1) |
Yes |
Yes |
Z88O8.TXT |
ASCII |
Output |
for internal use
of Z88O |
No 1) |
Yes |
Yes |
ASCII |
Input |
Color header
file Z88O MS-Win |
Possible |
Yes |
No |
|
ASCII |
Input |
Fonts, Colors,
Dimens. UNIX for Z88COM and Z88O |
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 |