5.2
CRANE TRUSS WITH TRUSSES NO.4
Copy the example file
B2_X.DXF to Z88X.DXF.
B2_X.DXF ---> Z88X.DXF input file for CAD converter Z88X
CAD:
In this example
you should only look at the CAD FE structure without producing it. This
comes
with later examples. Import Z88X.DXF into your CAD program and view it.
Usually
you would draw or model the structure in your CAD system. Do not change
anything and leave your CAD program without saving, converting etc. If
you do not
have any suitable CAD system, then drop this step.
Z88:
Z88X, conversion from Z88X.DXF to
Z88I1.TXT, Z88I2.TXT and Z88I3.TXT.
Windows: In the Z88 commander
launch Z88X, press Button DXF --> Z88I* (default), Run
Button.
LINUX/UNIX:
In
the Z88 commander press button DXF -->
Z88I* under CAD converters.
Z88O, look at finite element structure. Proceed as follows:
Windows: In the Z88
commander launch Z88O, Run Button. Use
the Wireframe Mode. Rotate the
structure with the keys F2~F7, reset
with F8. Pan with the arrow keys and Home
and End, zoom in and out with Prior
and Next. Then press the Autoscale
Button (3rd button from left), to reset all transformations. Switch on Mouse
(4th button from left). Now you may zoom by the left mouse key pressed,
pan by the
middle mouse key pressed and rotate by the right mouse key pressed. You
may
also
LINUX/UNIX: In the Z88
commander launch Z88O, Run Button. Use
the Wireframe Mode. Rotate the
structure with the keys F2~F7, reset
with F8. Pan with the arrow keys and Home
and End, zoom in and out with Prior
and Next. Then press the Autoscale
Button (6th button from top), to reset all transformations. Switch on Mouse
(7th button from top). Now you may zoom by the left mouse key pressed,
pan by the
middle mouse key pressed and rotate by the right mouse key pressed. You
may
also
Z88F, calculates displacements. Proceed as follows:
Windows: In the Z88 commander
press button Z88F, CD Button (is
default), Run Button.
LINUX/UNIX:
In
the Z88 commander press button Z88F -C.
Windows: In the Z88 commander
press button Z88D, Run Button.
LINUX/UNIX:
In
the Z88 commander press button Z88D.
Windows: In the Z88 commander
press button Z88E, Run Button.
LINUX/UNIX:
In
the Z88 commander press button Z88E.
Windows, LINUX/UNIX: look at the deflected finite
element structure. The deflections are
magnified per default by the factor 100 which is correct for this
example. If you’ll
press
the three displacement buttons (X, Y and Z) you’ll notice that the
nodal
displacements are plotted with different colours. Compare this to the
values in
the displacement file Z88O2.TXT. If you enter 0 0 1 in the flag file for stresses Z88I3.TXT and
run Z88D once more, then firing up again Z88O you’ll see the tensile
stresses
as “reduced stresses” by switching to Reduced
stresses mean value per Element (Windows) or Stresses
per Element (UNIX).
The example is simple and
straight. Experiment with the 3Ds possibilities of the OpenGL plot
program Z88O.
A crane truss consists of
54 trusses, 20 nodes and forms a spatial framework. The nodes 1, 2 and
19, 20
are fixed, the nodes 7 and 8 are loaded per -30,000 N. The total length
is 12 m
. The inputs in the sample file are in mm but inputs in meters are just
as
possible if the other entries like Young's modulus and cross-sectional
area
also refer to meters (or yards or inches). The Young's modulus is
200,000 N/mm2,
Poisson's ratio 0.3, the cross-sectional area 500 mm2 each.
This example is taken from
the (very good) book SCHWARZ, H.R.: FORTRAN Programme zur Methode der
Finiten
Elemente. Teubner Verlag, Stuttgart, Germany 1984.
Take into account: The
header file Z88I3.TXT
for the stress processor can have any content for Trusses No.4. For mixed frameworks containing
hexahedrons and trusses, the entries in Z88I3.TXT do only apply for the
hexahedrons.
5.2.1
Input
With
CAD program:
Proceed after the description chapter 2.7.2. Do
not forget to write on the layer Z88EIO
the element descriptions by TEXT function:
FE 1 4 (1st finite
element type 4)
FE 2 4 (2nd finite element type 4)
..........(Information not shown for elements 3 to 53)
FE 54 4 (54th finite element type 4)
Write on the layer Z88GEN
the general information and material information, like
Z88I1.TXT 3 20 54 60 1 0 0 0
0 (3-D,20 nodes,54 ele,60 DOF, 1 mat info, flags 0 )
MAT 1 1 54 200000 0.3 1 500
(1st mat info from element 1 to element 54,Young's modulus,
Poisson's ratio,
INTORD (any), QPARA is cross-section area of the trusses)
Since Trusses No.4 are structure elements (and thus
cannot be subdivided like finite elements), the mesh generator cannot
be used. You
can immediately write the boundary conditions with the TEXT function on
the
layer Z88RBD: The structure should be fixed to the node 1, 2 and 19,
20. A load
of 30,000 N each is applied to the nodes 7 and 8. The load should be
applied
downward, therefore -30,000 N.
Z88I2.TXT 10 (10
boundary conditions altogether)
RBD 1 1 2 2 0 (1st BC: Node 1, DOF 2, Displacement 0 (=fixed in Y
direction)
RBD 2 1 3 2 0 (2nd BC: Node 1, DOF 3, Displacement 0 (=fixed in Z
direction)
RBD 3 2 1 2 0 (3rd BC: Node 2, DOF 1, Displacement 0 (=fixed in X
direction)
RBD 4 2 3 2 0 (4th BC: Node 2, DOF 3, Displacement 0 (=fixed in Z
direction)
RBD 5 7 3 1 -30000 (5th BC: Node 7, DOF 3, load -30,000)
RBD 6 8 3 1 -30000
RBD 7 19 1 2 0
RBD 8 19 3 2 0
RBD 9 20 2 2 0
RBD 10 20 3 2 0
... And write on the layer
Z88GEN into any free place of your drawing the stress parameters for
the stress
calculation:
Z88I3.TXT 0 0 0 (any
stress parameters for Trusses No.4)
Export the drawing as DXF
file with the name Z88X.DXF and then launch the CAD converter Z88X with
the
option "from Z88X.DXF to Z88I*.TXT" (DXF -> I*). The CAD converter
will produce the input files Z88I1.TXT, Z88I2.TXT, Z88I3.TXT.
With
an editor:
Enter the structure data into Z88I1.TXT by
editor (cf. section 3.2):
3 20 54 60 1 0 0
0 0 (3-dim,20
nodes,54 elements,60 DOF, 1 mat info line,flags 0)
1 3 0 2000
0 (1st node, 3 DOF, X, Y and Z
coordinate)
2 3 0 0 0
(2nd
node, 3 DOF, X, Y und Z coordinate)
3 3 1000 1000 2000
4 3 2000 2000
0
5 3 2000 0
0
........... (nodes 6 ..18 dropped here)
19 3 12000 2000
0
20 3 12000 0
0
1 4 (1st element, type Truss No.4)
1 2 (coincidence 1st element)
2 4 (2nd element, type Truss No.4)
4 5 (coincidence 2nd element)
3 4
7 8
.......... (elements 4 ..53 dropped here)
54 4
17 19
1 54 200000 0.3
1 500 (mat
info from ele 1 to 54,Young's
modulus,Poisson's ratio, INTORD (any), QPARA is cross-section area of
the
trusses)
The structure should be
fixed to the node 1, 2 and 19, 20. A load of 30,000 N each is applied
to the
nodes 7 and 8. The load should be applied downward, therefore -30,000
N. Ref. to 3.4:
10 (10 boundary
conditions)
1 2 2 0 (1st BC:
Node 1, DOF 2, Displacement 0
(=fixed in Y direction)
1 3 2 0 (2nd BC:
Node 1, DOF 3, Displacement 0
(=fixed in Z direction)
2 1 2 0 (3rd BC:
Node 2, DOF 1, Displacement 0
(=fixed in X direction)
2 3 2 0 (4th BC:
Node 2, DOF 3, Displacement 0
(=fixed in Z direction)
7 3 1
-30000 (5th BC: Node 7, DOF 3, load -30,000)
8 3 1
-30000
19 1 2 0
19 3 2 0
20 2 2 0
20 3 2 0
The parameter file for the
stress processor Z88I3.TXT
can have any content (cf. sections 3.5 and 4.4), because Gauss points,
radial
and tangential stresses as well as calculation of the von Mises
stresses have
no significance for Trusses No.4.
CAD
and editor:
Because now the structure data Z88I1.TXT, the boundary conditions
Z88I2.TXT and
the header file for the stress processor Z88I3.TXT (with any content)
do exist,
you can launch
>Z88F Cholesky
solver for
computing the deflections
>Z88D
stress processor
>Z88E
nodal force processor
5.2.2
Results
The Cholesky solver Z88F
provides the following output files:
Z88O0.TXT stores the processed structure
data. It is meant for documentation purposes mainly. Z88O1.TXT
stores the processed boundary conditions: For documentation
purposes. Z88O2.TXT, the displacements, the main task and
solution of the FEA
problem. The stress processor Z88D internally uses the
calculated displacements
from Z88F and stores Z88O3.TXT, the calculated stresses. The
results in
Z88O3.TXT do not depend on the header parameters in Z88I3.TXT for
Trusses No.4. The nodal force processor Z88E uses internally
the calculated
deflections of Z88F and stores Z88O4.TXT, the computed nodal
forces.
The following picture of
the plot program shows the deflected structure for FUX, FUY and FUZ =
100 each
(magnifications of the deflections):
Reduced stresses are
not provided in the plot program Z88O for Trusses
No.4. But
Z88O does it because tensile stresses of trusses are equivalent to von Mises stresses. Why don’t you try
it? You only have to outwit Z88O by entering
0 0
1
into Z88I3.TXT. Run Z88D. Then launch Z88O and switch to Reduced stresses mean values per element.
You should switch off Mesh over stresses.
Plotting tensile stresses with Z88O. Enter 0 0 1 into Z88I3.TXT, run
Z88D again. Switch off Mesh over
Stresses.